teaching mathematics in the new normal research paper

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1 school and university transitions, 2 mathematics support, 3 mapping the effect of changing the medium of provision, 4 closing remarks, special issue editorial: restarting the new normal.

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Jonathan Gillard, Claire Ketnor, Ciarán Mac an Bhaird, Cathy Smith, Special issue editorial: restarting the new normal, Teaching Mathematics and its Applications: An International Journal of the IMA , Volume 40, Issue 4, December 2021, Pages 249–253, https://doi.org/10.1093/teamat/hrab026

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We are delighted to present this special issue of Teaching Mathematics and Its Applications with the title ‘Restarting the New Normal’. The title itself is an oxymoron since, at the time of conception, it was far from clear whether mathematics teaching would be restarting as before after a significant interruption or transforming to a new normal. The brief of this issue was to consider papers on research in one or more of the following areas: approaches to teaching post-16 mathematics to students during COVID-19 restrictions, the needs of mathematics learners in COVID-19-affected cohorts and general distance learning of mathematics.

Three guest editors, supported and led by an existing editor, began work on the special edition in September 2020. Through this edition we aimed to encourage research and reflection that directly informs future practice. We are appreciative of the effort of the authors, particularly because the papers were written at a time when we were all still affected by the impact of COVID-19.

Teaching during 2020 and 2021 involved quick professional development and learning for staff and students, even for the most technically competent among us. Many were suddenly teaching or supporting students in an environment we were not used to or prepared for. Internationally, there were numerous collaborative events, such as Teaching and Learning Mathematics Online ( http://talmo.uk/ ), which allowed for dialogue between innovators and those with existing experience of distance learning provision. Never before has there been a significant shift in such a short period of time within the teaching of post-16 mathematics.

The early stages of COVID-19 caused the closure of school, college and university campuses globally and led to an urgent requirement to instigate alternative ways of learning and teaching. The term ‘emergency remote teaching’ is often used to cover this initial response. Several of the authors in this special edition point to Hodges et al . (2020) who summarize emergency remote teaching as ‘a temporary shift of instructional delivery to an alternative delivery mode due to crisis circumstances’ that contrasts with ‘experiences that are planned from the beginning and designed to be online’. Remarkably, given the circumstances of that period, practitioners quickly started to investigate and evaluate these initial responses.

As it became apparent that online or remote teaching would continue in the latter parts of 2020 and beyond, the benefit of moving quickly to collate relevant research on best practices was clear. As a result, there are three types of paper within this issue: those focussed on the sudden shift that required instant changes to teaching practice, those considering more established approaches (including from the Open University who already taught online) and those that study iterations aiming to improve an initial design.

The first call for this special issue was in May 2020 and submissions were due in February 2021. Within a short window for submissions, there is naturally less time for planning and implementing research. However, the editors and reviewers were satisfied that the researchers have collected and analysed data to evidence the different effects of COVID-19 that they were investigating. In most cases, studies were undertaken at one institution, with the data analysed ranging from surveys and interviews to measures of student engagement and attainment. Covariables such as gender and ethnicity are also studied. A notable feature of the editing process for this special issue has been the collective refinement of claims and arguments. Reviewers and authors proved open to critiquing the relevance and generalizability of the results with reference to developing teaching practices and issues of professional and intellectual significance.

Time is a premium for everyone, especially during the pandemic, with colleagues juggling several commitments and high workloads. We were impressed in having received exceptional papers, in such exceptional times and in the quality of reviews. We enjoyed reading and looking after them during all the stages of the publication process. We hope you acknowledge, as we do, that these papers have captured incredible efforts that were made by teaching staff and students to provide an enriching learning environment. At time of writing, September 2021, it is clear that the papers not only offer the opportunity to look back at a unique and memorable time in history, but also start a process of recording the deliberations that underpin how we will navigate new teaching considerations and circumstances in mathematics.

Despite many difficulties within the COVID-19 pandemic, there may be some positive consequences. Initial research suggests that young people are now more interested in science careers as a result of COVID-19 ( British Science Association, 2020 ), and one may assume that this could translate to additional students of mathematics in the near future. As we identify below, positive aspects can be seen within this special edition, several of which would have possibly remained unknown if it had not been for the pandemic.

Before briefly describing the contents of the special issue, we make the following remarks, which should be kept in mind, since they may add context to the work described within:

Different countries were, and are, operating under different COVID-19 circumstances and restrictions at any given point in time.

Universities do not have the same timings in the academic year, and our colleagues in countries such as Australia were only part way into their academic year when they were first affected by COVID-19.

There is no one-size-fits-all approach to adjusting education in the time of a pandemic. Adjustments made are likely to be influenced by several factors, including staff expertise and the equipment available to them, the rules and regulations bestowed upon staff by their employer and government and the make-up of the student cohort.

The papers within this issue broadly concern topics such as school and university transitions, mathematics support and mapping the effect of changing the medium of provision. These headings are not exhaustive, and indeed it can be argued that several of the included papers fall under more than one of these classifications. The descriptions that follow are not an attempt to summarize the papers but to give an indication of how we classified them into each topic.

The paper by Hodds compares the entry competences of students arriving at a UK university in October 2020 with those who entered in previous years, by use of a common diagnostic test. Despite this paper offering some positive news, its results are in contrast with those of Golding who did note a decrease in mathematical preparedness, a profound impact upon the learning experience of the 16–18-year-old advanced mathematics students and a stark decline in their confidence. While these papers address mathematical preparedness within the curriculum, Lyakhova et al . point out the effect of COVID-19 on mathematics outreach events and report on student engagement with video materials offered to 16–18 year olds in Wales. The two papers focussing on school-age students both warn of disparate experiences, with a few students adapting successfully to a combination of asynchronous resources and interactive support while many struggled to learn mathematics at a distance despite their familiarity with technology in other guises. Papers in this section also raise equations about the purpose and effectiveness of current school-leaving examinations.

The paper by Gilbert et al . talks of the adjustments made to mathematics and statistics support services, describing results of a questionnaire distributed internationally early in the pandemic and follow-up interviews with practitioners 7 months later. They acknowledge some merits of support provision taking place online, but envisage that face-to-face support will return as the dominant mode of provision when circumstances allow. Crowley et al .’s evaluation of online mathematics support argues that such provision will become increasingly important and valuable in the future. Analysis of student interactions with their online mathematics support materials showed high engagement levels, but there could be some confounding variables partially explaining this success. Mullen et al . compare student and tutor perspectives on mathematics support in two institutions, one in Ireland and one in Australia. Responses in interviews mainly revolved around five key common themes. Finally, Mac an Bhaird et al . reflect on undergraduate experiences of online study groups and drop-in mathematics support, describing what they felt to be the positive and negative aspects of the online provision. The study groups were a new initiative as a reaction to low student engagement with drop-in sessions. The findings are used by the authors to suggest modes of future support.

Technology has a key role in underpinning the adjustments made to the delivery of teaching. Hilliam et al . offer their experiences from the Open University, who are well versed in online and distance learning. They summarize and evaluate their attempts before the pandemic to improve consistency of academic and pastoral support for all of their students. This paper discusses some issues and solutions that other practitioners are likely to meet as they develop their online provision.

Several papers focus on the early pedagogic issues and solutions trialled by mathematics lecturers, both in the emergency phase and as practice settled. Ní Fhloinn and Fitzmaurice describe the results of an international survey asking practitioners what hardware and software they have used and what training and support was made available to them. They also tried to understand the rationale of the choices made by those surveyed regarding the live and pre-recorded lectures. Lishchynska et al . compare face-to-face small-group tutorial delivery with a virtual alternative. Key issues were described, and factors to consider when developing future remote delivery are offered. Finally, Kempen and Liebendörfer investigated students’ reported use of a variety of teaching resources in a newly online linear algebra course in Germany. They offered the valuable comment, easily forgotten, that enabling social contact between students is important.

The impact of COVID-19 teaching on students should be considered over different timescales. Focussing on the immediate impact, Hyland and O’Shea research student perspectives on COVID-19 closures at Irish universities. The surveyed students also describe how they would like teaching to be delivered in the future. Büchele et al . examine measures of student participation, predictors of performance and student malpractice, comparing 2020 with two previous years. They identify an emerging gender gap negatively affecting women and comment on the effectiveness of their provision. Shaw and Tranter conduct a statistical analysis of awarding gaps in the student cohort, before and after an early period of lockdown. They provide evidence to suggest that the awarding gap for students with a lower-socioeconomic background had worsened, but the gap for Black and Minority Ethnic students had reduced.

This special issue represents a snapshot of the research conducted into the impact of COVID-19 upon post-16 mathematics education. We anticipate further innovations, continued evaluation and consideration of best practice, particularly as COVID-19 may have to be tolerated indefinitely ( Kissler et al ., 2020 ).

As we exit the pandemic hopefully and learn to live with COVID-19 as an endemic virus, it will be interesting to see which of our new practices remain and which return to as they were. We hope that the papers in this special issue, which have evaluated the relative merits and disadvantages of doing things differently, will help inform this dialogue.

The fact that the global pandemic is still very much on-going weighs heavily on all of us. We are keen to pay tribute to all students and staff working in education for rapidly adapting to the extreme circumstances that we have operated under, balancing the significant challenges of trying to live normally in a world that is currently anything but normal. A silver lining of the COVID-19 pandemic was the start of significant reflections on teaching practice in the discipline on a scale unseen before. It is safe to say that post-16 mathematics education will not be the same again.

Hodges , C. , Moore , S. , Lockee , B. , Trust , T. & Bond , A. ( 2020 ) The difference between emergency remote teaching and online learning . EDUCAUSE Review , 27 , 1 – 12 . https://er.educause.edu/articles/2020/3/the-difference-between-emergency-remote-teaching-and-online-learning   (accessed 30 September 2021) .

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British Science Association ( 2020 ) Young people are more interested in a scientific career as a result of COVID-19 . British Science Association . https://www.britishscienceassociation.org/blog/young-people-are-more-interested-in-a-scientific-career-as-a-result-of-covid-19   (accessed 30 September 2021) .

Kissler , S. M. , Tedijanto , C. , Goldstein , E. , Grad , Y. H. & Lipsitch , M. ( 2020 ) Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period . Science , 368 , 860 – 868 . https://www.science.org/doi/10.1126/science.abb5793   (accessed 30 September 2021) .

Dr Jonathan Gillard , Reader in Statistics, Cardiff University. Jonathan is a Reader in Statistics at the School of Mathematics at Cardiff University. He is an Editorial Board member of MSOR Connections. Jonathan is currently interested in the statistical analysis of the National Student Survey and the Teaching Excellence Framework. In the past he has published on the effective delivery of mathematics support services, diagnostic testing and new methods for giving student feedback.

Dr Claire Ketnor , Principal Lecturer, Sheffield Hallam University. Claire is the Teaching and Learning Portfolio Lead for the Department of Engineering and Mathematics at Sheffield Hallam University. In teaching mathematics, she develops innovative methods with the aim of improving inclusivity. Claire is an active researcher in teaching and learning pedagogy, having also published under her previous surname Cornock. Her current work includes looking into students’ views on making mistakes. https://orcid.org/0000-0002-6918-5918 .

Dr Ciarán Mac an Bhaird , Assistant Professor and MSC Director, Maynooth University. Ciarán was appointed to his roles in the Department of Mathematics and Statistics at Maynooth University in 2007. He has received multiple awards in recognition of his teaching and support of students. He was a founding committee member of the Irish Mathematics Learning Support Network and conducts research in algebraic number theory, mathematics education and the history of mathematics. https://orcid.org/0000-0001-5971-7709 .

Dr Cathy Smith , Senior Lecturer, Open University. Cathy leads the mathematics education team at The Open University, UK. Her current work involves mathematics teacher professional development, supervision of research students and research. She has a long-standing research interest in pedagogies of advanced mathematics education and in studying discourses of participation in mathematics.

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The impact of the COVID-19 pandemic on mathematics learning in higher education during learning from home (LFH): students' views for the new normal

R Y Tyaningsih 1 , Arjudin 1 , S Prayitno 1 , Jatmiko 2 and A D Handayani 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1806 , International Conference on Mathematics and Science Education (ICMScE) 2020 14-15 July 2020, Jawa Barat, Indonesia Citation R Y Tyaningsih et al 2021 J. Phys.: Conf. Ser. 1806 012119 DOI 10.1088/1742-6596/1806/1/012119

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1 Departemen Pendidikan Matematika, Universitas Mataram, Jl. Majapahit No. 62 Mataram, Indonesia

2 Departemen Pendidikan Matematika, Universitas Nusantara PGRI Kediri, Jl. KH. Achmad Dahlan No. 76 Kediri, Indonesia

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Covid-19 Pandemic has an impact on education that is bringing up new policies for learning from home. The purpose of this study was to determine students' views on learning mathematics in higher education while learning from home and its sustainability towards a new normal. This type of research is qualitative with data collection techniques using online surveys and interviews. Respondents in this study were 169 students of Mathematics Education in Higher Education. The results of this study indicate that 100% of lectures are conducted online with a composition of 34.32% in the form of Asynchronous Online Course, 19.53% Synchronous Online Course, and 46.15% using Hybrid Online Course. The effectiveness of online course that has been carried out was obtained 7.1% very effective, 20.1% effective, 53.8% sufficient, 17.8% less effective, and 1.2% ineffective. Open questions are provided in the questionnaire to allow students to convey constraints/difficulties experienced during Learning from Home (LFH), including network constraints, health problems, costs, the environment, course constraints, and time problems. Student responses regarding the application of the Blended Learning method in the new normal period showed 48% agreed, 31% were doubtful, and 21% disagreed.

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Will we ever teach mathematics again in the way we used to before the pandemic?

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After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal . However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give some background to the impact that emergency remote teaching may have had on teaching mathematics. We examine the possible social implications and then focus on the changing mathematics classroom, focusing on the actual mathematics curriculum, learning design and assessment, the role of collaborative activities and social media, educational videos, and the role of family and parents in future. There are indicators from the literature that educators may not return to the traditional way of teaching entirely, especially in secondary and higher education. We conclude with describing some possible new research areas that have developed through emergency remote teaching, including online education for younger learners, local learning ecosystems, the role of family and parents, instructional design, and the mathematics content of curricula.

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You’re never going to be a lion, and that’s all right, as long as you can act like one when you need to. But right now, as a zebra among a group of lions, when the lions see you they start to think about lunch—and you’re not a guest, you’re on the menu. ( Waldroop & Butler, 2000 , p. 77)

1 Introduction

In a survey paper in 2020, Engelbrecht et al. ( 2020b ) addressed the possible transformation of the mathematics classroom, just as the COVID-19 pandemic struck the world. Since then, the global COVID-19 pandemic has forced this transformation of the mathematics classroom on us—we had to change.

Although there is still a strong and growing worldwide debate on whether we are suffering more from the health crisis or from the economic and social crisis that was caused by the worldwide lockdown of economic, social and educational facilities (as discussed by Chan et al., 2021 ), we do not take a position on this issue as we are facing a new reality. Throughout the world, our lifestyle has changed dramatically and suddenly—we went online : we shop online, we meet friends online, and we learn online (Borba, 2021 ). Whether what we are experiencing economically, socially or in education has been an overreaction caused by the global lockdown or whether it was justified by the intensity of the disease, is not the question that we want to address. In fact, it becomes irrelevant—we have to face the reality that we live in.

Schools and universities were closed in many parts of the world and more than 90% of the world’s registered learners (1.5 billion) were left without education (UNESCO, 2020 ). Borba ( 2021 ) warned of the danger of social inequality that is growing in schools, in that the issue of access is a barrier to some schools and promotes even further social inequality. Being forced to embark on new teaching approaches created an opportunity to understand how human society was responding to challenges in a crisis. Chan et al. ( 2021 ) speculated on whether we should document, describe, or explain the crisis or whether we should try to theorise or predict how the crisis is going to play out. We elaborate on the social impact of the pandemic in Sect.  4 .

Mathematics education across the world has been widely affected by the pandemic and unprecedented scenarios that required expeditious responses had to be addressed (Chirinda et al., 2021 ). The agenda of mathematics education was changed. Teachers and students had to make serious changes to the traditional teaching and learning approach, working and learning from home. We rely on digital technology to conduct lessons and other teaching and learning activities and to connect with our students in remote locations off campus. The new reality, in which we live, is now referred to as a ‘new normal’ (Engelbrecht et al., 2020a ).

This reality, however, is changing at a rapid pace and what we say today may no longer be valid tomorrow. In normal times, papers on digital technology become dated because the technology changes so rapidly. In the new normal, it is not only the technology that evolves—the external environment that forces us to adapt, is also changing at a rapid pace. Chan et al. ( 2021 ) discussed whether the growing worldwide interconnectivity (e.g., through social media) “changes the nature of any potential crisis from a chain of events in a relatively contained ecosystem or society to having global reach” (p. 2). This viral pandemic has given us an opportunity to prepare for similar crises that may happen in future. We do not know—we cannot exclude the possibility of further crises that may hit us, perhaps on an even larger scale.

The COVID-19 pandemic is not the first crisis that we have experienced in mathematics education. Disruptions in education have been happening in many countries, during which times educators have implemented various forms of Emergency Remote Teaching (ERT) and learning through different channels (Chirinda et al., 2021 ; Hodges et al., 2020 ). An array of media and technology has been introduced to create hybrid forms of teaching, including e-learning (Ebner et al., 2020 ), mobile learning (Naciri et al., 2020 ) and flipped classrooms (Tang et al., 2020 ). A variety of media platforms have been used to support online teaching and learning, such as learning management systems, instant messaging applications, instant meeting applications, social media and dynamic geometry packages (Engelbrecht & Oates, 2022 ).

Given that there is little research available on the topic of online education in primary schools, the focus of this paper is on higher education and secondary school contexts and the claims made in this paper relate mainly to these two contexts. Although much of the content of this paper is applicable to mathematics teachers at all levels, in most of the sources that were consulted, the researchers focussed on teaching mathematics at secondary or university level.

A secondary objective with this survey paper—in fact one of the aims of this special issue as a whole—is to relate ideas from literature that seem to articulate some aspects of the mathematics education field from the last two years, that is to give some idea of the rapidly growing amount of literature on the mathematics education situation during and after the pandemic, including the papers in this issue, to which we refer briefly in this survey.

The main aim, however, is to start a debate on how the emergency remote teaching (ERT) strategies that we were forced to introduce during the COVID-19 pandemic, will have a more lasting impact on the way we teach mathematics in future.

So the paper is organised according to the following structure: We begin by discussing emergency remote teaching (ERT) experiments that have been implemented during the pandemic, especially in schools and universities (Sect.  2 ). This is followed by a discussion on the impact on teachers and the social implications in mathematics education (Sects. 3 and 4). In Sect.  5 we discuss the impact that ERT may have on mathematics education itself, focussing on some theoretical perspectives, the mathematics curriculum itself, instructional and learning design, collaborative activities and social media, educational videos and the role of parents and family. The paper is concluded with a section on new possible research possibilities.

2 Emergency remote teaching (ERT)

For years, teachers have been wondering about what mathematics education would be like if the internet were in fact to enter the mathematics classroom. With the pandemic, the discussion about a changing classroom has been accelerated dramatically. The internet, homes and parents have become more important in mathematics education during the pandemic. In this paper we summarise findings and concerns regarding the future of mathematics education, in the post-pandemic world. Learning and teaching in the new normal since March 2020, is now commonly referred to as emergency remote teaching (ERT) (Chirinda et al., 2021 ; Hodges et al., 2020 ). Hodges et al. ( 2020 ) described ERT as

a temporary shift of instructional delivery to an alternate delivery mode due to crisis circumstances. It involves the use of fully remote teaching solutions for instruction or education that would otherwise be delivered face-to-face or as blended or hybrid courses and that will return to that format once the crisis or emergency has abated. (p. 6)

At many institutions, ERT offerings included the usage of learning management systems, procurement of devices for students who did not have access to computers, and providing free data for accessing the course material to ensure that online learning did not become prohibitive to students and staff in terms of affordability (Engelbrecht et al., 2020a ).

Worldwide, most teachers had not performed online teaching prior to the pandemic and ERT became quite a challenge as countries began to experiment with ERT to cope with the COVID-19 pandemic. As the expectations have been in the past that we will return to the conventional format, once the crisis or emergency is over (Sulistyani et al., 2021 ), ERT was seen as a non-permanent shift in teaching that is different from the online teaching and learning that has existed for years (Chirinda et al., 2021 ; Hodges et al., 2020 ).

The ERT educational situation is referred to (tongue-in-cheek) as panic-gogy (panic + pedagogy) (Kamanetz, 2020 ). Panic-gogy means addressing the question of how teachers are moving into this environment with their teaching approaches, but it is more than just the didactical approach—it includes understanding students’ practical resources and problems, such as availability of digital devices, internet access, family responsibilities, students sent home who need to find a new place to live, and financial constraints.

We briefly discuss a few examples of studies that have been conducted during the ERT period within the pandemic. We relate teachers’ experiences of ERT at schools and universities, focusing on the ways in which teachers supported mathematics learning, perspectives of students, and choices of resources.

The strategies that South African teachers used to support continued mathematics learning at home during the pandemic, during the phases of moving to ERT and with the gradual reopening of schools later as regulations were relaxed, were explored by Vale and Graven ( 2022 ) (in this issue) using activity theory. Their results showed that teachers’ voices can inform possible ways forward for the purpose of managing mathematical learning gaps and meeting on-going learning needs.

The perspective of students was explored in a few studies as well. Thurm et al. ( 2022 ) (in this issue) examined students’ experiences with ERT in Belgium, Germany and the Netherlands. In detail, they analysed how these experiences related to their teachers’ beliefs and practices, what didactical approaches and formative assessment practices secondary mathematics students experienced, and which beliefs they held concerning digital mathematics education. They found that even though students preferred regular face-to-face (f-2-f) teaching, they appreciated synchronous delivery of ERT as well.

As for higher education, responses of universities to the COVID-19 pandemic have been reported on in many studies (e.g., Bakker & Wagner, 2020 ; Hyland & O’Shea, 2021 ) as most institutions moved to fully online instruction in March 2020. There had been an increase in the use of e-learning in universities over the past decades before the pandemic with a substantial amount of research on online instruction in mathematics courses that has been published (Borba et al., 2016 ; Hyland & O’Shea, 2021 ). It is not clear how much of this previous research was incorporated into initiatives during the pandemic.

In a more systemic study from several countries from Southeast Asia, Atweh et al. ( 2022 ) (in this issue) described teacher experiences as they dealt with changes in their programme delivery, focussing on the ethical constructs of responsiveness and responsibility to guide actions in response to a crisis. They identified challenges for mathematics teacher educators to re-design their curriculum, teaching, assessment, and equitable access towards more relevant, productive, and equitable mathematics teacher education. The perspective of equity was taken up by Maass et al. ( 2022 ) (in this issue), who analysed the contribution of mathematical modelling to citizenship education, taking the context of COVID-19 as an example, as it has affected the quality of human life of students in the western world.

The perspective of students studying mathematics at university level in Ireland was analysed in a study by Hyland and O’Shea ( 2021 ), who investigated the impact of the COVID-19 closures. Their results showed that most students dealt with the rapid changes in a resilient and mature manner, particularly when confronted with adversity. The results confirmed the widespread use of learning management systems such as Moodle and Blackboard to provide access to a variety of resources for students. The asynchronous nature of the recorded lectures and lecture notes uploaded to such learning management systems confirms the notion of “domestication of new media” (Engelbrecht et al., 2020b ), a term used to designate the process in which teachers tend just to convert their traditional courses to an online platform.

In a study in South America, Villarreal et al. ( 2022 ) (in this issue) analysed the educational experiences of pre-service mathematics teachers enrolled in mathematics teacher education programmes, as the pandemic was unrolling. Their results suggest the need to rethink teacher education programmes, regarding the integration of technologies in mathematics classes, the opportunities offered by hybrid education, and teacher education for distance teaching.

Furthermore, in their study, Hyland and O’Shea ( 2021 ) pointed out that lectures, tutorials and support services that had been offered in the pre-COVID times, involving different atmospheres and methods of interaction that students engaged with at various levels, migrated online during the pandemic and largely similar modes of delivery were employed. They considered this issue as important and suggested that tutorials and support services may be priorities in future blended educational approaches (Hyland & O’Shea, 2021 ). In teacher education, according to Mulenga and Marbán ( 2020 ), prospective teachers believe that digital learning will enable a mathematics pedagogical shift to a less traditional way of teaching that is more interesting and entertaining than the customary conventional and traditional way.

Hyland and O’Shea ( 2021 ) also examined student perceptions on ERT during the COVID-19 period. They found that students dealt with the rapid changes in a resilient and mature manner, and identified insights from the students’ perspectives that have the potential to improve the teaching and learning of mathematics at university level. Unger and Meiran ( 2020 ) reported anxiety and reduced performance among their students brought about by the transition to online learning. Similarly, Adnan and Anwar ( 2020 ) described dissatisfaction among students, with the vast majority of their students preferring f-2-f contact with teachers.

In a longitudinal study, Liebendörfer et al. ( 2022 ) (in this issue) investigated the issue of how students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online. The results illustrated the strengths and limitations of digital materials provided by the lecturer and the use of complementary media, also revealing the double-edged role of simple, often anonymous exchanges with few binding forces for either side, and the significance of stable learning partnerships for students’ success.

In a case study by McMurtrie ( 2021 ) about a health and humanities programme at the University of Wisconsin at Madison, it was found that 40% of the students did not have internet service that was reliable enough for streaming, and the programme therefore moved to lower-tech, asynchronous learning. Overall, universities realised that it is better to keep it simple—they focus on ‘quick-and-dirty operations’ such as creating discussion boards, posting assignments, or using conference platforms for live or pre-recorded lectures. McMurtrie ( 2021 ) also related an essay titled “Please do a bad job of putting your courses online” by Rebecca Barret-Fox in which she attempted to settle people's nerves and make sure they put students first and stuck to the basics. She proposed doing away with the fancy technology and intensive demands on students, saying that it is not realistic to expect the remote-learning transition to be seamless, let alone pleasant. Since she posted her essay about sticking to the basics, she has heard from many colleagues, thanking her for reassuring them that lowering the technology bar, does not imply that they are bad teachers. Her conclusion is that it is not the technology that will save us, but the pedagogy (McMurtrie, 2021 ).

3 Impact on school and university teachers

The imperative on teachers to change their teaching approach radically, had a severe impact on teachers. As it was, teachers were already struggling to balance teaching, research and other obligations, including the work-life balance (Houlden & Veletsianos, 2020 ; Rapanta et al., 2020 ). Almost overnight, teachers were asked to become designers and implementers of new pedagogies using tools and resources that few had properly mastered before. Teaching staff on all levels had to prepare and deliver their teaching from home, with all the practical and (especially) technical challenges this entails. Many teachers had never taught an online course (Hodges et al., 2020 ).

Furthermore, as empirical studies pointed out, many university teachers did not have the necessary pedagogical content knowledge, including technical and administrative aspects of teaching online and pedagogical foundations and knowledge of principles needed to facilitate meaningful online learning experiences (Ching et al., 2018 ; Rapanta et al., 2020 ). Teachers and professors had to figure out the intricacies of their learning management systems, unfamiliar conferencing technologies, and new protocols for coursework and tests, as they were trying to find out where students were, physically as well as academically, and what they needed.

In their study Rapanta et al. ( 2020 ) focused on the pedagogical preparedness of university teachers with no or little experience in online teaching, as the instructional environment was complex and inexperience brought shortcomings in organisational planning. They pointed out that teachers were inundated with advice, tips and tricks, mostly on tools and resources that they could use, instead of the f-2-f classes. In many instances teachers were lacking the foundational knowledge needed to judge which teaching approach was likely to be successful (Rapanta et al., 2020 ).

The roles that prospective mathematics teachers assign to technologies for teaching in pandemic conditions were explored in a study in Colombia by Villa-Ochoa et al. ( 2022 ) (in this issue). Based on the construct of Humans-with-Media and the Learning by Expanding theory as frameworks, their study investigated the impact of technology on the Activity System and they discussed the opportunities and limitations of students’ conceptions about teaching and technology during a pandemic.

4 Social implications

In this section we briefly discuss social implications of the COVID-19 crisis, which have been explored in several studies. The implications can be grouped into two main categories, social injustice issues that were amplified during the pandemic and personal issues that learners and teachers experienced because of the isolation during the pandemic.

Regarding the issue of equity, Borba ( 2021 ) discussed the connections of humans to the virus, how it laid bare social inequality, in that many children across the world just did not have access to internet, and how it changed the agenda of mathematics education. Chan et al. ( 2021 ) warned about the dangers of possible inequities that may come with ERT, including unequal access to the internet and to computers and other hardware, as well as the unequal availability of space at home for uninterrupted time for learning. These inequities probably magnify the effects of poverty.

Based on the theoretical framework of critical mathematics education, Borba ( 2021 ) highlighted that education is not neutral—it can promote equality or inequality. Indicators from Forbes show that social inequality has been growing during this pandemic (Gavioli, 2020 ). Owners of the big social media and of high tech companies are the winners as people move more and more online: these companies run online social networks and online shopping services, and store digital data in online systems.

Social inequality has been growing in schools during the pandemic, in that as most schools and universities went online and suspended f-2-f classes, the issue of access was becoming a barrier that increased social inequality (Borba, 2021 ), which led to some extreme cases, where universities even opted to move away from online education because of inequitable access. Educational inequality was high even before the pandemic, and currently it is accelerating at an alarming pace. Vegas and Winthrop ( 2020 ) provided alarming statistics on the outcomes of millions of students having been out of school for long periods, and high percentages of children, especially in low-income countries, who failed to master the basic secondary-level skills needed to function in work. It has been the children in the poorest countries who have been left the furthest behind.

On the other hand, for some students in wealthy communities, schooling has been good during the pandemic. Some of them were taught in their homes by a teacher hired by their parents or by their well-educated parents using well advanced internet facilities and modern teaching resources (Vegas & Winthrop, 2020 ).

The differences in access to remote learning opportunities are not only between rich and poor countries but also within countries. UNICEF estimated that 463 million children—at least one-third of the world’s total, the majority of whom are in the developing world—had no access to remote learning via radio, television, or online content (Vegas & Winthrop, 2020 ). Moving to online teaching may have had negative implications such as political consequences, in that it could evoke student protests rather than being experienced as pedagogical innovation (Czerniewicz, 2020 ). On the positive side, some students who had not had access to proper education before, could now be reached, in that good teachers could make their teaching available to a much wider audience.

Engaging a social justice framework to explore the teaching and learning of mathematics during the COVID-19 lockdown in a context of historical disadvantage in South Africa, Chirinda et al. ( 2021 ) targeted secondary school mathematics teachers in finding out how teachers responded to ERT during the pandemic. Their findings showed how mathematics teachers became learners themselves, as they had to adapt to digital teaching, find solutions to unfamiliar problems, and acquire knowledge from a larger mathematics education community around the globe.

Teachers with low salaries were not likely to have the best mobile phones, laptops, or internet access, and differences between the ‘haves’ and the ‘have-nots’ were amplified by COVID-19. Overall, the role of mathematics education for resisting inequality in the world, is a topic that should be researched (Borba, 2021 ).

The second concern about the social impact of the pandemic has more to do with the students’ and teachers’ personal experiences. The increased isolation caused a lack of motivation during the closure, and students were more likely to experience increased anxiety during the pandemic (Huang & Zhao, 2020 ). Hyland and O’Shea ( 2021 ) recommended that educators should be extra vigilant of students’ well-being, given the reduction in access to general support services such as counselling. Unger and Meiran ( 2020 ) called for students’ mental health to be monitored during pandemics.

The issue of priorities was raised by Chan et al. ( 2021 ) as in crisis time we tend to focus rather on more important issues, such as the well-being of our families, our communities and our students. As teachers, we may consider it important to help our students achieve their immediate needs, even if those needs relate to systems that we do not necessarily agree with. Or we may prefer addressing the bigger problems, attempting to change systems.

Packer ( 2022 ) was concerned about how the public-school system in the USA will survive the pandemic. Teachers, whose status had been in decline for a long time, were leaving the field. In 2021 nearly one million people resigned from public education in the USA, 40% more than in the previous year. Students were leaving the public system as well. Since 2020, nearly 1.5 million children were taken from public schools to attend private schools or to be home-schooled (Packer, 2022 ).

Already in 2005, Borba and Villarreal ( 2005 ) synthesised how the notion of humans-with-media could be understood, based on the work of Lave ( 1988 ) and Levy ( 1993 ), contributing to the notion that learning is social, not only in the sense that it involves more than one person, but that it also involves ‘things’, e.g., pieces of software, hardware, and the internet. Consequently Borba ( 2021 ) showed that different media shape humans, but also gave evidence of how humans shape technology. He reported on the interaction between a piece of software and how high school students would interact with the software and with the teacher.

5 The changing classroom—impact on mathematics education

In a review of research on online learning in mathematics, Engelbrecht et al. ( 2020b ) investigated how mathematics classrooms have developed with the growth of the internet and interactive devices. Although some people claimed that f-2-f interaction is fundamental to any learning that occurs in mathematics education, everyone was aware of the fact that classrooms are changing. We could speak of a classroom in movement or a distributed classroom— it moves from the traditional cubic space to a combination of a classroom with a bedroom for one student, an office for another, and some kind of computer centre for others (Borba, 2021 ).

Morin ( 2016 ) described how students exposed to online learning have their own concerns, new motivations and new challenges with respect to education. Hyland and O’Shea ( 2021 ) claimed that massive open online courses, blended learning, flipped classrooms and other technological approaches used before COVID-19, might not be as fully used in current post-COVID-19 teaching as one might have hoped. They considered these approaches to be noticeably different from current instruction in which many teachers just use traditional versions of courses as models for the online versions without taking full advantage of the new opportunities afforded by the technology—in fact, many teachers just published their lectures online.

More generally, Engelbrecht et al. ( 2020b ) posed the question of whether digital technologies would be able to provide alternative ways to support mathematics education. Based on the theoretical construct of humans-with-media, Borba ( 2021 ) connected the pandemic to three different trends in mathematics education, namely, the use of digital technology, philosophy of mathematics education, and critical mathematics education. He discussed the possibilities and drawbacks of having more and more online education using the notion of humans-with-media and its perspective of collective knowledge production involving human and non-human actors.

In a systematic literature review on the use of flipped classrooms, Cevikbas and Kaiser ( 2022 ) (in this issue) focused on opportunities and pitfalls regarding pandemic-related issues. Their results demonstrated that flipped classrooms can be a promising pedagogy that has numerous benefits for mathematics teaching and learning, although it cannot be seen as panacea for pandemic-related issues, as it also has several significant pitfalls. Their review contributed to gaining insight into successful implementations of flipped classroom pedagogy, not only during the pandemic but also beyond the pandemic.

In the following, the impact of the pandemic on changing the mathematics classroom is discussed relating to possible future constructs and theoretical perspectives to analyse the changing classroom, the mathematics curriculum, instruction and learning design and assessment, collaborative activities and social media, and the role of parents and family.

5.1 Possible future constructs and theoretical perspectives

A number of theoretical frameworks exist (Brown, 2017 ) for using digital technologies in mathematics education, e.g., Instrumental Orchestration (Trouche, 2004 ); the Structuring Features of Classroom Practice framework (Ruthven, 2014 ); Pedagogical Technology Knowledge (Thomas & Hong, 2013 ); and Enactivism (Khirwadkar et al., 2020 ). In instrumental orchestration, digital tools are shifted from a tool to an instrument—the focus is on how the teacher supports this process. The framework by Ruthven ( 2014 ) focuses strongly on how this occurs and includes structuring features of classroom practices that influence how digital technology is integrated (Brown, 2017 ; Ruthven, 2014 ). Thomas and Hong ( 2013 ) introduced the construct pedagogical technology knowledge (PTK), which includes the teachers’ perspective on the technology, their familiarity with the technology as a teaching tool, and their understanding of mathematics. It has been assumed that teachers with high levels of PTK would focus on mathematical concepts, appreciate the mathematical benefits of using technology and take a multi-representational approach, whereas teachers with a low level of PTK would focus on operational matters, procedures and technical skills (Brown, 2017 ). Before the pandemic, teachers were using technology either to a limited or to a more sophisticated extent. Those with a low PTK, used it to a lower extent and focussed on operations, procedural and technical aspects of technology use. Others, with a higher PTK, used technology with a stronger multi-representational approach.

Callaghan et al. ( 2022 ) (in this issue) used an enactivist approach, including the inputs of all role players (teachers, learners, policy makers and the community) to address the situation that has evolved. In an enactivist perspective, cognition grows from a network of interactions among agents and their environment. Since existing prescriptions on how to develop a mathematics environment limit the viability, in an enactivist approach the point of departure is that the mathematics community does not simply react to the pandemic as a problem—it is seen as an opportunity for the mathematics community along with all role players to collaborate and to adapt and redesign mathematics education within the constraints related to the pandemic (Khirwadkar et al., 2020 ). Hoyles ( 2018 ) agreed that mathematics teachers must be part of the transformative process as co-designers to transform mathematical practice using digital technologies. As already suggested in this paper, the perspective anchored in the construct humans-with-media is evolving and emphasises the role of non-humans in mathematics education: Besides digital technologies (e.g., Geogebra, internet, online environments), homes, and other types of technologies emerged as having agency in mathematics education.

So, in re-imagining the way we teach mathematics, an enactivist approach could facilitate the involvement of the entire relevant community, interacting with all agents and their environment—to move from the pre-pandemic pedagogy and the panic-gogy phases during ERT, to a post-pandemic pedagogy (Callaghan et al., 2022 ).

5.2 The mathematics curriculum

The COVID-19 pandemic made the public aware of the important role that mathematics plays in our society. The mathematical topics involved in modelling the course of the pandemic mathematically inspired the imagination of a much wider section of the general public, and students were interested in learning more about these topics. The question of curriculum is widely discussed in this special issue of ZDM – Mathematics Education . The mathematics that has been getting publicity during the pandemic was discussed in a number of papers in this issue. These would include, e.g., exponential growth, interpretation of graphs, and other mathematics content used by the media to interpret the pandemic.

A very old, but still crucial question has been becoming particularly popular in this crisis time: What mathematics should be taught when? This question needs on-going thought, discussion and research and there will never be a final answer. The answers change with time. New realities, such as the pandemic, may give new insights concerning what is currently relevant.

Mathematics educators and curriculum developers need to identify mathematics that is needed for modelling and interpreting crises so that this mathematics can inform the public. This could be translated to the following question: What mathematics should every citizen know? Chan et al. ( 2021 ) broke this issue down to asking what mathematics everyone should know to understand the following four current issues of relevance, but they may change and evolve in time:

interconnectivity,

biodiversity,

wealth distribution.

When we develop new curricula in mathematics education, we should include these relevant topics to inform the general public about the mathematics—citizens should be equipped to understand the mathematics they will experience in the world (Chan et al., 2021 ). Recently, a substantial amount of material has been published by mathematics educators on relevant mathematical topics that could be included in school and university curricula to address this need. In their study (in this issue) Meyer and Lima ( 2022 ) emphasised the importance of using mathematical models and mathematical modelling, using difference equations and ordinary differential equations to model scenarios of the pandemic and the general dynamics of infectious diseases, making provision for possible vaccination, supporting Borba’s ( 2021 ) suggestion that exponential functions should be taught from early ages to university, which may enhance understanding of sigmoids and curves related to the pandemic.

There is also quite a strong focus on developing a public understanding of mathematics that is used by the media to explain and predict trends in the pandemic and other global phenomena. In their study Siller et al. ( 2022 ) addressed the way the media present data on the pandemic, referring to growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Since these reports sometimes appeared contradictory or even false to students, they showed that basic mental models about exponential growth are important for understanding media reports of COVID-19. They also highlighted how the COVID-19 pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Lim et al. ( 2022 ) (in this issue) showed how the proliferation of data visualisations about the pandemic, particularly those found within the media, have brought a corresponding growth of new data visualisation forms. Building on current efforts to expand the teaching and learning of data practices in mathematics education, they provided examples of innovative data visualisations and examined their pedagogical affordances and constraints in eliciting students’ emotions and bodies as a generative direction for making sense of COVID-19 within a mathematics or statistics classroom. Cantoral et al. ( 2022 ) (in this issue) investigated the ways in which the press used graphs to provide information about the pandemic, in order to provide theoretical references to teach mathematics that allow students to understand the information provided in these types of graphs. They concluded that there is a need to incorporate in the teaching of mathematics, a conceptualisation of exponential growth that is linked to the use of graphs in the press.

Kwon et al. ( 2021 ) investigated the use of graphs in Korea’s news media during the COVID-19 outbreak, looking at implications for future teaching and learning of graph literacy in mathematics courses. After examining the Israeli public’s understanding of the mathematics that is required for understanding the pandemic and predicting its spread, Heyd-Metzuyanim et al. ( 2021 ) demonstrated that adults' engagement with such information may be limited.

5.3 Instructional and learning design and assessment

RAPANTA et al. ( 2020 ) characterised instructional and learning design as a process that teachers use to plan, implement, and evaluate their instruction. A good design consists of clear learning objectives, carefully structured content, relevant student activities, controlled workloads for teachers and students, integrated external resources, and assessment connected to the learning objectives. Careful design of learning activities, enabling students to reach the learning outcomes, has been considered as the “the essence of an online course” (Carr-Chellman & Duchastel, 2000 , p. 233). The different design elements, synchronous, asynchronous, online, offline, should be carefully balanced, regarding clear communication, an appropriate adequate level of difficulty for students’ capabilities and expectations, being related to contexts to increase students’ engagement, and being accessible to all—taking the available infrastructure into account (Rapanta et al., 2020 ).

It is clear that the transition to the new pedagogy shifted the focus on to students as responsible for their own learning. This is even more current for assessment, which is growing strongly into a continuous activity with the cognitive expectation of self-regulation (Rapanta et al., 2020 ). Hyland and O’Shea ( 2021 ) reported that students prefer a combination of continuous assessment and online examinations. They reported that many students prefer live synchronous (f-2-f or virtual) lectures and tutorials and consider the opportunities for interaction with teaching staff and other students as important. Meehan and Howard ( 2020 ) supported this view in their study and claimed that students feel that the sudden shift online adversely affected interactive activities.

In the post-pandemic era, the opportunities and affordances that we were exposed to during ERT provided by well-designed online learning environments and their capacity to be stimulating, inclusive and flexible, should still be included in student-centred programmes in higher education. Personalisation of learning and flexible pathways can only be provided with a good course design that takes into consideration the full context of the teachers’ and learners’ humans-with media experiences. If teachers invest time in developing learning activities that address learners’ social and cognitive needs, learning outcomes will improve (Rapanta et al., 2020 ).

Online assessment has long been investigated and implemented (Sandene et al., 2005 ; Sangwin, 2012 ), and likewise there have been a growing number of studies that examined peer interactions in the online space (e.g., Goos & Geiger, 2012 ; Larkin & Jamieson-Proctor, 2015 ; Mojica-Casey et al., 2014 ). The need for the development of authentic formative assessment activities that can be used online asynchronously and which facilitate active student learning and peer collaboration, was pointed out by Engelbrecht and Oates ( 2022 ). Responding to the challenges of the COVID-19 pandemic, we need to design new learning activities that combine the three types of an online presence, namely, social, cognitive and facilitatory.

Sandene et al. ( 2005 ) posed some key issues for technology-based online assessment in mathematics focussing on measurement implications, including equity, efficiency compared with paper and pencil, and operational implications. Sangwin ( 2012 ) described the development of STACK, an advanced general computer assessment system for mathematics, with an emphasis on formative assessment, which allowed students to enter mathematical solutions in the form of algebraic expressions, as opposed to the more common use of automatically generated multiple-choice questions.

Cusi et al. ( 2022 ) (in this issue) focussed on developing assessment schemes that maintain the pedagogical continuity that educational institutions typically require, during the lockdowns and even in the post-lockdown emergency period. They investigated teachers’ perspectives on the assessment difficulties with which they had to contend, the techniques adopted to deal with these difficulties, and the ways in which the lockdown experience could affect the future evolution of teachers’ assessment practices.

Domingues and Borba ( 2021 ) discussed mathematics video production by students, as a facet of the transforming classroom. They noticed that students develop further mathematical knowledge when they express this knowledge in a video, which enables a new language with less rigour but with a clearer objective, as it gets students’ attention while emotional and aesthetical concerns are considered. They found that, for teachers and students, producing a mathematics video is more than ‘just turning in a list of mathematics exercises’, and they are convinced that producing videos is a fruitful tool for the teaching and learning of mathematics. They presented a survey of the emergence of videos in mathematics education, showing how the changes in mathematics education during the pandemic involved this form of expressing mathematics and mathematics education.

Although mathematicians had interacted frequently through videos, this newly established trend gained momentum during the pandemic and currently, on occasion, some students use video-classes even more often than books. In countries such as Brazil, students and teachers are also using videos in a different form: teachers are fostering students to produce videos themselves that show what kind of mathematics students have learnt, including videos that contain didactical material. Inspired by the previous work of Canadian authors (see Gadanidis & Scucuglia, 2020 , for a review of part of this work), digital videos in mathematics education seem to have started a new trend.

As reported by Domingues and Borba ( 2021 ) the generation of videos and its connection to mathematics video festivals contributed to the transformation of the traditional classroom, and were also important during the pandemic. They described an example of a mathematics festival consisting of an online environment ( www.festivalvideomat.com ) and a set of f-2-f annual events. In 2020, these festivals were organised virtually as well. Currently, there are about 600 mathematics videos on the website. The website contains details about news, dates, announcements, guidelines for submitting assignments, and videos that have been submitted. This environment is a locus of research, and a space for exchange and discussion of mathematics ideas between students, teachers and the whole community outside the school.

The combination of research, teaching and outreach work seems to add importance at this time when parents and other role players, such as family members or neighbours, become increasingly important for education, as discussed in the next section of this paper.

5.4 Collaborative activities and social media

Since Vygotsky’s ( 1978 ) work, collaborative learning activities have been employed at an increasing rate all over the world. Today’s employers seem to view the capacity to collaborate in solving problems as similar or even more important for tomorrow’s workers than content knowledge—they are looking for people who can work effectively in teams (Jackson, 2013 ). Teachers are trying to build students’ collaborative skills, but developing these skills has always proved somewhat challenging. In traditional classrooms in school and university where a teacher stands at the front of rows of students sitting at desks, collaboration was often difficult; modern teaching approached have relied on multiple strategies to encourage collaboration, including using technology to promote team projects, linking their students to classrooms across the globe (Jackson, 2013 ).

A growing number of research studies focussing on technology-supported collaborative learning, have appeared. For example, the paradigm of computer-supported collaborative learning as a dynamic, interdisciplinary field of research, already developed nearly two decades ago (Resta & Laferrière, 2007 ), focused on ways in which technology can facilitate the sharing and creation of knowledge and expertise through peer interaction and group learning processes. It included using technology to support synchronous and asynchronous communication between on-campus students as well as students who are geographically distributed.

As in any mathematics course in school and in university, knowledge construction is acquired not only by accessing the information, but also by the interaction that occurs among students and teachers; interactions need to occur collaboratively among participants (Engelbrecht & Oates, 2022 ). Therefore, the focus in education has been changing from a situation of students passively absorbing information from an educator who is teaching by writing on the blackboard— pushing knowledge—to a stronger student driven approach, where students take control of the learning process—a pull process (Bassendowski & Petrucka, 2013 ).

An environment that supports the development of communities and collaborative discussion opportunities can assist students in comprehending and synthesising information, as independent and critical thinkers (Engelbrecht & Oates, 2022 ). Social media have been used as a significant tool in providing such an environment, which supports self-directed and self-determined learning (Blaschke, 2019 ; Schuetz, 2014 ) and foster a sense of belonging, facilitated by collaboration and communication (Balakrishnan et al., 2017 ; Goodyear et al., 2014 ).

In fact, social media, with their key social networking capabilities, seem to be an ideal way of facilitating collaboration, and many studies referenced both the growing use and importance of social media in mathematics education, already before the pandemic (Selwyn & Stirling, 2016 ). For example, Ng and Latif ( 2011 ) described how Facebook and blogs could be used in a blended university mathematics course to complement the f-2-f tutorials in order to foster communication and knowledge exchange among learners, peers and tutors in a more informal manner.

An examination of social media sites on the internet provided some insight into how students use social media. Comment social media streams Footnote 1 (which at times can be surprisingly deep) form an important component in the social interaction leading to learning (Engelbrecht & Oates, 2022 ).

However, while many such studies did indeed support and extol the benefits of social media, others explored the more nuanced impact and issues with respect to academic and cognitive factors, and potential limitations (Staines & Lauchs, 2013 ; van Bommel & Liljekvist, 2015 ). So it is clear that much research is still needed on the role of social media in mathematics education (Mulenga & Marbán, 2020 ; van Bommel & Liljekvist, 2015 ).

The dynamics of social media that capture the imagination of our students and teachers is also changing rapidly, and sometimes differently for students and teachers. Where Facebook was on top previously, most younger people now use Instagram and Whatsapp, and TikTok is becoming increasingly popular.

Engelbrecht and Oates ( 2022 ) addressed three essential questions concerning the role of social media and we do not dwell on these here: these question are still open and need to be researched, especially due to their relevance for changing mathematics education in pandemic times:

Has anything changed? How does the use of contemporary social media differ from previous use?

How might social media best be used and what pitfalls do they entail? How can we combine social media tools with good teaching practices to contribute effectively to student engagement?

How valuable are social media for learning mathematics? What evidence of learning is there in comments in blogs and comment streams on social media platforms?

5.5 Role of parents and family

With many children staying home and working online, the format and boundaries of the traditional classroom were changed and suddenly parents and family members had to engage on tasks that formerly were the responsibility of the teacher. Parents and caregivers had to become full-time educators, trying to balance the competing demands of child rearing, schooling, and their own employment (Biag et al., 2021 ).

Already for decades a strong relationship could be identified between parental involvement in the education of their children, and children’s performance. For example Taylor ( 2020 ) found that an educationally supportive home environment, including intellectually engaging materials in the home, such as books, newspapers and educational toys had a positive impact on learning. Even when less educated parents became involved in their children’s education, children were less likely to experience learning disadvantages (Dearing et al., 2006 ).

During the pandemic many parents were not equipped to assist their children with their studies and many were just too busy with their own programmes to find time to work with their children. Even parents who were able to assist, had to find a balance between supporting their children and applying excessive pressure. There is also the issue of the parents and the teacher presenting the subject matter differently, causing confusion with learners (Hill & Tyson, 2009 ).

A positive relation was found by Taylor ( 2020 ) between learner performance and parental practices such as reading to their children, checking their school bags, keeping track of their reading levels and assuming some degree of responsibility for their children’s reading.

6 New research possibilities

With the forced exposure to ERT during the pandemic, many questions and uncertainties emerged; we clearly need proper research to learn more on what works and what does not. A very real immediate problem is how we communicate our research findings. Since 2020, academic conferences had to be conducted in online or hybrid format. Engelbrecht et al. ( 2022 ) (in this issue) addressed the issue of the nature and format of academic conferences in mathematics education. Surveying active research academics in mathematics education, they investigated the future impact that a change to virtual or hybrid conferences may have on the format and nature of mathematics education conferences. Their findings indicated that although academics are pro-actively thinking about alternative conference formats, the proven value of f-2-f conferences is still very real, showing that it may be too early to have a clear vision of the future format of academic conferences.

It has been noted that there is little research on online education associated with levels below high school. With many educational systems forced to go online because of the pandemic crisis, the argument to use technology is very strong. It is likely that we will have more research associated with this new reality. As this theme develops, mathematics education will have to deal with structural issues, such as the participation of parents or responsible other parties in education as well as the role of homes (Borba, 2021 ).

Educational innovation has been moved suddenly from the margins to the core of the education system, providing opportunities to identify new strategies that can develop young people and prepare them for the changing times, such as the smart use of technology and data that allow for real-time adaptation (Vegas & Winthrop, 2020 ).

The idea of local learning ecosystems was suggested by Vegas and Winthrop ( 2020 ). There is wide evidence that young people engaging in diverse learning opportunities outside of school—from classic extracurricular activities such as music lessons to non-formal education programming—can be quite helpful in boosting the skills and academic competencies of marginalised children. Examples of emerging models include the Educacio360 Footnote 2 initiative in Spain and the Remake Learning Footnote 3 initiative in Pennsylvania, USA, where school districts have engaged to offer general learning opportunities to families and children. Using the experiences registered during COVID-19 will hopefully harness new energies and relations between schools and communities in working together to support children’s learning.

As mentioned before, the pandemic has introduced new actors in the community to support children’s learning. The pandemic has involved community sections that traditionally were not actively involved in education. Relationships and partnerships between teachers and parents developed in ways that we never thought of before. Schools formed new relationships with social welfare organisations, media companies worked with education leaders, technology companies partnered with governments, and local non-profit organisations and businesses contributed to supporting children’s learning in innovative ways (Vegas & Winthrop, 2020 ).

The importance of the actual curriculum is becoming blurred as students increasingly turn to informal educational platforms and social media for their learning interactions. Many students of today and tomorrow want to be involved not only in in how they are taught but also in what they are taught (Dekker, 2021 ; Mkandawire et al., 2018 ). Not unlike an infant learning to speak, they want to decide on what mathematics they learn and how, in a pull approach, rather than a curriculum that is pushed on to them by the educational system (Engelbrecht & Oates, 2022 ). So the role of external resources , such as social media (but some that may be traditional) should be an interesting topic for research in the near future and may become a relevant research topic in mathematics education.

Regarding digital collaboration and social media , Engelbrecht and Oates ( 2022 ) identified a number of issues that seriously need in depth research and investigation.

What technology should students use to support their own mathematical learning as well as collaboratively the learning for other students?

How can social media tools be combined with the best practices in teaching and contribute effectively to student engagement and the development of deeper mathematical understanding?

How can we better understand the critical processes or mediating variables that are needed, such as structuring of tasks, ill-defined problems, student engagement, teacher scaffolding, and the ways they combine to create online written discourse in meaningful mathematical settings (Resta & Laferrière, 2007 )?

How should we design assessment in mathematics education to encourage online collaboration and provide students with formative feedback?

7 Conclusions

One positive result of the pandemic is that there is newly found public recognition of how essential teachers and schools are in society and an opportunity to leverage this support for greater realisation of the importance of education and the role of teachers in society. Currently there is a much greater public appreciation of the importance of the role of teachers. As parents struggled to work with their children at home due to school closures, public recognition of the essential caretaking role schools and teachers play in society has increased significantly (Vegas & Winthrop, 2020 ).

March 2020 will be remembered as the time all the world’s schools closed their doors. As teachers around the world struggled with little forewarning to enter into ERT, parents and families around the world, had to face the shock of life without school. Before the pandemic, the public sector had come to rely on schools as a given—an anchor around which they organised their daily programmes (Vegas & Winthrop, 2020 ).

Suddenly politicians and other prominent people in society urged that education be prioritised. This broad recognition and support for the essential role of education in daily life can be found in media reports across the world. The global education community inspired the UNESCO based broad consortium, with the newly formed Save our Future campaign, bringing together a wide group of role players, to advocate for sustained education funding. Unexpectedly, vast numbers of parents and families around the world share the long-standing concerns of the most vulnerable families: they need a safe and good enough school to send their children to (Vegas & Winthrop, 2020 ). This could be the moment in history when the important role of education in the social and economic stability and prosperity of society becomes more obvious and better understood by the general population. It is an ideal moment in time to deliberate on a vision for how education can emerge stronger from the global pandemic than before and how we can propose a path for capitalising on education’s newfound support in virtually every community across the globe.

For many years, educationists have been pleading to raise the status of teachers in society. “Use the top people of today to teach the next generation” is a quote that has been used often in this regard, without much impact: in many countries becoming a teacher is not the most popular option for high school students, at least in many western countries. The reality, amplified by the pandemic, has brought the issue of education into the living rooms of poor, middle class and elite parents around the world. And, at least for a moment, these parents are getting involved in supporting education. We should exploit this opportunity to make sure that we get the best people of our generation in the teaching profession.

Returning to the question asked in the title of this paper, namely, whether we will ever teach mathematics in the same way we used to, the answer is an easy no never— at least for most people in higher and secondary education. We are fully aware of the fact that institutional systems are slow in changing, but all indications are that the way we teach is changing. We are also aware of some (especially under resourced) primary schools where teaching of mathematics has tended to revert to pre-pandemic f-2-f format, but for the higher education sector and for teachers and students in secondary schools, where basic resources for internet connectivity and usage are available, the answer is an emphatic no .

In being forced to teach differently, we learnt much. Too many of the actions that we were forced to embark on, worked so well that we do not want to stop doing them.

Granted (and as we have mentioned), many of our students are happy that we are now returning to f-2-f lectures in the second half of 2022—they are looking forward to physically seeing and experiencing their fellow students and their teachers. The extent to which we will return, however, does not entail that we will ‘carry on as usual’. Many universities will now move to ‘hybrid’ teaching, where along with the f-2-f lectures there will be strong online activity.

In fact, opinions concerning the extent to which we will return to the conventional approach vary significantly and this issue will have to be ironed out. With this paper we hope to initiate (or at least contribute to) a dialogue on what could be achieved in the medium to long term.

Vegas and Winthrop ( 2020 ) recommended five actions, which need to be focussed on after the pandemic. These actions include (amongst others) a focus on the instructional core, deploying education technology and forging stronger, trusting relationships between parents and teachers.

It is essential that when we return to (an either ‘old’ or ‘new’) normal, we implement what we have learnt during the pandemic. So far we have had little time to reflect on what we were forced to do in a very short time. Many emergent decisions had to be taken at institutional and personal level, and many practices were changed urgently. Little time, however, was devoted to, what Schön ( 1983 ) calls reflection-on-action . We need to now spend time for reflection-on-action (Rapanta et al., 2020 ) and we hope that this paper will contribute to this process.

The outcomes of such a reflection can include greater clarity on course design, the role of the teacher and assessment in online learning. So we would like to see the current pandemic

as a catalyst that highlighted the need for educational change towards more flexible models and practices that best respond to the complexity and unpredictability of today’s fast and interconnected but and still fragile society. (Rapanta et al., 2020 )

We consider that the educational experiences that we had during the pandemic can serve as catalysts for teachers to experiment with new ideas, explore creative alternatives and reflect on their own practices (McKenney et al., 2015 ; Rapanta et al., 2020 ). Studies included reports about mathematics teachers who experienced the pandemic as a prompt to re-examine their teaching (Albano et al., 2021 ; Gosztonyi, 2021 ; Maciejewski, 2021 ). We as academics in mathematics education must be part of the process of reflection and planning, and universities, now more than ever, should invest in professional development of university and school teachers, for the purpose of helping them to be updated on effective pedagogical methods with or without the use of online technologies (Rapanta et al., 2020 ).

Our experiences with the pandemic should inspire our confidence that mathematics and good mathematics teaching can make important contributions towards resolving the problems and issues that came with the pandemic, and we should make sure that we learn from this experience in order to improve our teaching.

Many of our students are Gen Z students (born between 1997 and 2012), as described by Engelbrecht et al. ( 2020b ). To them, interactivity and communication are of great importance. Hyland and O’Shea ( 2021 ) found that students’ ability to collaborate was impacted by problems with peer communication and they reported as follows:

It is interesting to note that although it is likely that many of these students are part of the generation that uses social media the most, they still value the face-to-face nature of communication in lectures, tutorials and support centres. (p. 18)

As raised by Chan et al. ( 2021 ), the central question for both mathematics teaching practices and for research approaches, is, What should be changed and what should be maintained? A possible way to move toward this decision is following an enactive approach consulting with a wide range of stakeholders, including students, teachers, parents, policy makers, and other people from a range of contexts.

In 2020, Engelbrecht et al. ( 2020a ), in an editorial in this same journal, asked the question, Will 2020 be remembered as the year in which education was changed? It is probably too early to tell yet. In fact, education is always evolving, always changing. But at this early stage it certainly seems that the changes in mathematics education that we experienced with the pandemic will be seen as a leap in the growth curve.

Let us conclude and return to the quote at the beginning of this paper. We need to realise that the entire education scene, including (or particularly) mathematics education, is changing rapidly. After COVID-19, we all have understood that there is a need to take stock now, to consider what we have learnt about mathematics education during the crisis, and to realise that all of us have to be part of the solution. Many of our students complained about the absence of f-2-f lectures and meetings and looked forward to f-2-f classes resuming. Other students enjoyed the online environment and did not want to return to a f-2-f environment. We need to decide to what extent we will return to the previous approach—what elements should come back and what elements of ERT should be retained and developed.

As this quote implies: If you are not at the table, you could be on the menu . If we (as zebras) do not act as lions and have our voices heard by those who make decisions, others will decide about the future of mathematics education. If these others (the lions) are our students, we do not really have that much of a problem. As said earlier, we are moving in a direction where students have increasing involvement in how and what they are taught. But if these others are the people outside mathematics and mathematics education, the policy makers and education managers, then we may end up on the menu— teaching mathematics in a way with which we do not agree.

A social media stream is a feed of content that is collected from more than one platform and is most commonly displayed on a website.

Educacio360 is a national education initiative in Spain, with the aim of connecting all learning that takes place in the different teaching and non-teaching times and spaces, and of promoting personalised learning itineraries, inside and outside school. <  https://www-educacio360-cat.translate.goog/?_x_tr_sl=ca&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=sc#crida  > .

Remake Learning is a network in Pennsylvania that ignites engaging, relevant, and equitable learning practices in support of young people navigating rapid social and technological change and involving different role players. <  https://remakelearning.org/about/  > .

Adnan, M., & Anwar, K. (2020). Online learning amid the COVID-19 pandemic: students’ perspectives. Journal of Pedagogical Sociology and Psychology, 2 , 45–51.

Article   Google Scholar  

Albano, G., Antonini, S., Coppola, C., Dello Iacono, U., & Pierri, A. (2021). ‘Tell me about’—A logbook of teachers’ changes from face-to-face to distance mathematics education. Educational Studies in Mathematics, 108 , 15–34.

Atweh, B., Kaur, B., Nivera, G., Abadi, A., & Thinwiangthong, S. (2022). Futures for post-pandemic mathematics teacher education: Responsiveness and responsibility in the face of a crisis. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01394-y

Bakker, A., & Wagner, D. (2020). Pandemic: Lessons for today and tomorrow? Educational Studies in Mathematics, 104 , 1–4.

Balakrishnan, V., Teoh, K. K., Pourshafie, T., & Liew, T. K. (2017). Social media and their use in learning: A comparative analysis between Australia and Malaysia from the learners’ perspectives. Australasian Journal of Educational Technology, 33 (1), 81–97.

Google Scholar  

Bassendowski, S., & Petrucka, P. (2013). The space between: Teaching with push-pull strategies that reflect ubiquitous technology. Journal of Modern Education Review, 3 (1), 1–7.

Biag, M., Gomez, L.M., Imig, D.G., & Vasudeva, A. (2021). Responding to COVID-19 with the aid of mutually beneficial partnerships in education. Frontiers in Education , (5). www.frontiersin.org

Blaschke, L. M. (2019). The pedagogy–andragogy–heutagogy continuum and technology-supported personal learning environments. Open and distance education theory revisited (pp. 75–84). Springer.

Chapter   Google Scholar  

Borba, M. C. (2021). The future of mathematics education since COVID-19: Humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics, 108 , 385–400.

Borba, M. C., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Sánchez Aguilar, M. (2016). Blended learning, e-learning and mobile learning in mathematics education. ZDM – Mathematics Education, 48 (5), 589–610.

Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, experimentation and visualization (Vol. 39). Springer.

Brown, J. P. (2017). Teachers’ perspectives of changes in their practice during a technology in mathematics education research project. Teaching and Teacher Education, 64 , 52–65.

Callaghan, R., Joubert, J., & Engelbrecht, J. (2022). Using enaction to evolve from pre-COVID to post-COVID pedagogy: A case study with South African mathematics teachers. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01416-9

Cantoral, R., Espinoza, L., & Gaete-Peralta, C. (2022). Exponential behavior and variational practices in Chilean newscasts. A socio-epistemological study. ZDM – Mathematics Education.

Carr-Chellman, A., & Duchastel, P. (2000). The ideal online course. British Journal of Educational Technology, 31 (3), 229–241. https://doi.org/10.1111/1467-8535.00154

Cevikbas, M., & Kaiser, G. (2022). Can flipped classroom pedagogy offer promising perspectives for mathematics education on pandemic-related issues? A systematic literature review. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01388-w

Chan, M., Sabena, C., & Wagner, D. (2021). Mathematics education in a time of crisis—A viral pandemic. Educational Studies in Mathematics, 108 (1), 1–13.

Ching, Y.-H., Hsu, Y.-C., & Baldwin, S. (2018). Becoming an online teacher: An analysis of prospective online instructors’ reflections. Journal of Interactive Learning Research, 29 (2), 145–168. https://doi.org/10.24059/olj.v22i2.1212

Chirinda, B., Ndlovu, M., & Spangenberg, E. (2021). Teaching mathematics during the COVID-19 lockdown in a context of historical disadvantage. Education Sciences . https://doi.org/10.3390/educsci11040177

Cusi, A., Schacht, F., Aldon, G., & Swidan, O. (2022). Assessment in mathematics: A study on teachers’ practices in times of pandemic. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01395-x

Czerniewicz, L. (2020). University shutdowns—What we learnt from ‘going online’. https://www.universityworldnews.com/post.php?story=20200325160338881

Dearing, E., Kreider, H., Simpkins, S., & Weiss, H. B. (2006). Family involvement in school and low-income children’s literacy: Longitudinal associations between and within families. Journal of Educational Psychology, 98 (4), 653–664. https://doi.org/10.1037/0022-0663.98.4.653

Dekker, T. J. (2021). The value of curricular choice through student eyes. The Curriculum Journal, 32 (2), 198–214.

Domingues, N. S., & Borba, M. C. (2021). Digital video festivals and mathematics: Changes in the classroom of the 21st century. Journal of Educational Research in Mathematics, 31 (3), 257–275.

Ebner, M., Schön, S., Braun, C., Ebner, M., Grigoriadis, Y., Haas, M., Leitner, P., & Taraghi, B. (2020). COVID-19 epidemic as e-learning boost? Chronological development and effects at an Austrian university against the background of the concept of “e-learning readiness.” Future Internet, 12 , 94. https://doi.org/10.3390/fi12060094

Engelbrecht, J., Borba, M. C., Llinares, S., & Kaiser, G. (2020a). Will 2020a be remembered as the year in which education was changed? ZDM – Mathematics Education, 52 (2), 821–824.

Engelbrecht, J., Kwon, O., Borba, M. C., Yoon, H., Bae, Y., & Lee, K. (2022). The impact of COVID-19 on the format and nature of academic conferences in mathematics education. ZDM Mathematics Education . https://doi.org/10.1007/s11858-022-01421-y

Engelbrecht, J., Llinares, S., & Borba, M. C. (2020b). Transformation of the mathematics classroom with the internet. ZDM – Mathematics Education, 52 (2), 825–841.

Engelbrecht, J., & Oates, G. (2022). Student collaboration in blending digital technology into the learning of mathematics. In M. Borba, J. Engelbrecht, & R. Scucuglia (Eds.), New technologies in mathematics education. Handbook of cognitive mathematics. Springer Nature.

Gadanidis, G., & Scucuglia, R. S. (2020). Making mathematics special through song: What math experiences are worth singing about? The Routledge Companion to Interdisciplinary Studies in Singing, II, II , 462–473.

Gavioli, A. (2020). Bilionários americanos ficaram US$434 bilhões mais ricos desde o início da pandemia, aponta relatório. [American billionaires became US$434 richer since the beginning of the pandemic] https://www.infomoney.com.br/negocios/bilionarios-americanos-ficaram-us-434-bilhoesmais-ricos-desde-o-inicio-da-pandemia-aponta-relatorio/

Goodyear, V. A., Casey, A., & Kirk, D. (2014). Tweet me, message me, like me: Using social media to facilitate pedagogical change within an emerging community of practice. Sport, Education and Society, 19 (7), 927–943.

Goos, M., & Geiger, V. (2012). Connecting social perspectives on mathematics teacher education in online environments. ZDM – The International Journal on Mathematics Education, 44 , 705–715. https://doi.org/10.1007/s11858-012-0441-y

Gosztonyi, K. (2021). How history of mathematics can help to face a crisis situation: The case of the polemic between Bernoulli and d’Alembert about the smallpox epidemic. Educational Studies in Mathematics, 108 , 105–122.

Heyd-Metzuyanim, E., Sharon, A., & Baram-Tsabari, A. (2021). Mathematical media literacy in the COVID-19 pandemic and its relation to school mathematics education. Educational Studies in Mathematics, 108 , 201–225.

Hill, N. E., & Tyson, D. F. (2009). Parental involvement in middle school: A meta-analytic assessment of the strategies that promote achievement. Developmental Psychology, 45 (3), 740–763. https://doi.org/10.1037/a0015362

Hodges, C., Moore, S., Lockee, B., Trust, T., & Bond, A. (2020). The difference between emergency remote teaching and online learning. https://er.educause.edu/articles/2020/3/the-difference-between-emergency-remoteteaching-and-online-learning

Houlden, S., & Veletsianos, G. (2020). Coronavirus pushes universities to switch to online classes—But are they ready? The Conversation , 12 March. https://theconversation.com/coronaviruspushes-universities-toswitch-to-online-classes-but-arethey-ready-132728

Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers through digital technology. Research in Mathematics Education, 20 (6), 1–20.

Huang, Y., & Zhao, N. (2020). Generalized anxiety disorder, depressive symptoms and sleep quality during COVID-19 outbreak in China: A web-based cross-sectional survey. Psychiatry Research, 288 , 112954.

Hyland, D., & O’Shea, A. (2021). The student perspective on teaching and assessment during initial COVID-19 related closures at Irish universities: Implications for the future. Teaching Mathematics and Its Applications: an International Journal of the IMA. 40 (4), 455–477. https://doi.org/10.1093/teamat/hrab017

Jackson, S. (2013). How technology can encourage student collaboration: Find out how technology promotes teamwork and collaboration in the classroom . Common Sense Media.

Kamanetz, A. (2020). ‘Panic-gogy’: Teaching online classes during the coronavirus pandemic. https://www.npr.org/2020/03/19/817885991/panic-gogy-teaching-online-classes-during-the-coronavirus-pandemic

Khirwadkar, A., Khan, S.I. Mgombelo, J., Obradović-Ratković, S., & Forbes, W.A. (2020). Reimagining mathematics education during the COVID-19 pandemic. Brock Education Journal 29(2), 42–46. https://journals.library.brocku.ca/brocked

Kwon, O., Han, C., Lee, C., Lee, K., Kim, K., Jo, G., & Yoon, G. (2021). Graphs in the COVID-19 news: A mathematics audit of newspapers in Korea. Educational Studies in Mathematics, 108 (1–2), 183–200.

Larkin, K., & Jamieson-Proctor, R. (2015). Using transactional distance theory to redesign an online mathematics education course for pre-service primary teachers. Mathematics Teacher Education and Development, 17 (1), 44–61.

Lave, J. (1988). Cognition in practice . Cambridge University Press.

Book   Google Scholar  

Levy, P. (1993). Tecnologias da Inteligência: O futuro do pensamento na era da informática. [Technologies of Intelligence: The future of thinking in the informatics era]. Rio de Janeiro, Brazil: Editora 34.

Liebendörfer, M., Kempen, L., & Schukajlow, S. (2022). First-year university students’ self-regulated learning during the COVID-19 pandemic: A qualitative longitudinal study. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01444-5

Lim, V.Y., Peralta, L.M.M., Rubel, L.H., Jiang, S., Kahn, J.B., & Herbel-Eisenmann, B. (2022). Data visualizations for mathematics education in times of crisis: Engaging the body and emotions through interactivity, multimodality, and narrative. ZDM – Mathematics Education.

Maass, K., Zehetmeier, S., Weihberger, A., & Flösser, K. (2022). Analysing mathematical modelling tasks in light of citizenship education using the COVID-19 pandemic as a case study. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01440-9

Maciejewski, W. (2021). Teaching math in real time. Educational Studies in Mathematics, 108 , 143–159.

McKenney, S., Kali, Y., Markauskaite, L., & Voogt, J. (2015). Teacher design knowledge for technology enhanced learning: An ecological framework for investigating assets and needs. Instructional Science, 43 (2), 181–202. https://doi.org/10.1007/s11251-014-9337-2

McMurtrie, B. (2021). The coronavirus has pushed courses online. Professors are trying hard to keep up. The Chronicle of Higher Education. https://www.chronicle.com/article/the-coronavirus-has-pushed-courses-online-professors-are-trying-hard-to-keep-up/

Meehan, M., & Howard, E. (2020). Undergraduate mathematics students’ perceptions of the affordances and constraints of online learning—Implications for practice. University College Dublin.

Meyer, J.F.C.A., & Lima, M. (2022). Relevant mathematical modelling efforts for understanding COViD-19 dynamics: An educational challenge. ZDM – Mathematics Education.

Mkandawire, M. T., Maulidi, F. K., Sitima, J., & Luo, Z. (2018). Who should be deciding what to be taught in schools? Perspectives from secondary school teacher education in Malawi. Journal of Medical Education and Curricular Development, 5 , 1–10.

Mojica-Casey, M., Dekkers, J., & Thrupp, R. (2014). Research guided practice: Student online experiences during mathematics class in the middle school. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice. Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 469–476). Sydney: MERGA.

Morin, R. (2016). The many faces of digital generation. https://www.curatti.com/digital-generation

Mulenga, E. M., & Marbán, J. M. (2020). Is COVID-19 the gateway for digital learning in mathematics education? Contemporary Educational Technology, 12 (2), ep269.

Naciri, A., Baba, M. A., Achbani, A., & Kharbach, A. (2020). Mobile learning in higher education: Unavoidable alternative during COVID-19. Aquademia, 4 (1), ep20016.

Ng, R. & Latif, L. A. (2011). Social media and the teaching of mathematics in a lifelong learning environment . http://iclll2011.oum.edu.my

Packer, G. (2022). School shouldn’t be a battlefield. The Atlantic , April 2022. https://www.theatlantic.com/magazine/archive/2022/04/pandemic-politics-public-schools/622824/

Rapanta, C., Botturi, L., Goodyear, P., Guàrdia, L., & Koole, M. (2020). Online university teaching during and after the COVID-19 crisis: Refocusing teacher presence and learning activity. Postdigital Science and Education, 2 , 923–945.

Resta, P., & Laferrière, T. (2007). Technology in support of collaborative learning. Educational Psychology Reviews, 19 , 65–83.

Ruthven, K. (2014). Frameworks for analysing the expertise that underpins successful integration of digital technologies into everyday teaching practices. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital age (pp. 373–393). Springer.

Sandene, B., Horkay, N., Bennett, R. E., Allen, N., Braswell, J., Kaplan, B., & Oranje, A. (2005). Online assessment in mathematics and writing: Reports from the NAEP Technology-Based Assessment Project. Research and Development Series . NCES 2005, 457. National Center for Education Statistics.

Sangwin, C. (2012). Computer aided assessment of mathematics using STACK. In Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 695–713). Springer.

Schön, D. (1983). The reflective practitioner: How professionals think in action . Temple Smith.

Schuetz, R. (2014). Self-directed vs. self-determined learning: What's the difference? https://www.rtschuetz.net/2014/12/self-directed-vs-self-determined.html

Selwyn, N., & Stirling, E. (2016). Social media and education … now the dust has settled. Learning, Media and Technology, 41 (1), 1–5.

Siller, H.-S., Elschenbroich, H.-J., Greefrath, G., & Vorhölter, K. (2022). Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01433-8

Staines, Z., & Lauchs, M. (2013). Students’ engagement with Facebook in a university undergraduate policing unit. Australasian Journal of Educational Technology, 29 (6), 792–805.

Sulistyani, N., Utomo1, B., & Kristantol, Y.D. (2021). Emergency remote teaching experiences of mathematics education lectures to address COVID-19 pandemic. Journal of Physics : Conference Series 1806. https://doi.org/10.1088/1742-6596/1806/1/012088

Tang, T., Abuhmaid, A. M., Olaimat, M., Oudat, D. M., Aldhaeebi, M., & Bamanger, E. (2020). Efficiency of flipped classroom with online-based teaching under COVID-19. Interactive Learning Environments . https://doi.org/10.1080/10494820.2020.1817761

Taylor, N. (2020). School lessons from the COVID-19 lockdown. Southern African Review of Education, 26 (1). https://journals.co.za/doi/abs/10.10520/ejc-sare-v26-n1-a10

Thomas, M. O. J., & Hong, Y. Y. (2013). Teacher integration of technology into mathematics learning. International Journal for Technology in Mathematics Education, 20 (2), 69–84.

Thurm, D., Vandervieren, E., Moons, F., Drijvers, P., Barzel, B., Klinger, M., Van der Ree, H., & Doorman, M. (2022). Distance mathematics education in Flanders, Germany, and the Netherlands during COVID-19 lockdown: The student perspective. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01409-8

Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9 (3), 281–307.

UNESCO (2020). COVID-19 education response . https://en.unesco.org/covid19/educationresponse/globalcoalition

Unger, S., & Meiran, W. R. (2020). Student attitudes towards online education during the COVID-19 viral outbreak of 2020: Distance learning in a time of social distance. International Journal of Technology in Educational Science, 4 , 256–266.

Vale, P., & Graven, M. (2022). Strategies implemented by South African teachers to ensure continuing mathematics education during COVID-19. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01408-9

Van Bommel, J., & Liljekvist, Y. (2015). Facebook and mathematics teachers’ professional development: Informing our community. In Proceedings of CERME 9: Ninth Congress of the European Society for Research in Mathematics Education . Charles University in Prague (pp. 2930–2936). Prague, Czech Republic: hal-01289653.

Vegas, E. & Winthrop, R. (2020). Beyond reopening schools: How education can emerge stronger than before COVID-19. Brookings. https://www.brookings.edu/research/beyond-reopening-schools-how-education-can-emerge-stronger-than-before-covid-19/

Villa-Ochoa, J. A., Molina-Toro, F., & Borba, M. C. (2022). Roles of technologies for future teaching in a pandemic. Activity, Agency, and Humans-with-Media. ZDM – Mathematics Education . https://doi.org/10.1007/s11858-022-01429-4

Villarreal, M., Villa-Ochoa, J.A., & Galleguillos, J. (2022). Experiences of preservice mathematics teachers during their education in times of pandemic . ZDM – Mathematics Education.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes . Harvard University Press.

Waldroop, J., & Butler, T. (2000). Maximum success: Changing the 12 behavior patterns that keep you from getting ahead, Chapter 4: Avoiding conflict at any cost . Currency/Doubleday.

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Engelbrecht, J., Borba, M.C. & Kaiser, G. Will we ever teach mathematics again in the way we used to before the pandemic?. ZDM Mathematics Education 55 , 1–16 (2023). https://doi.org/10.1007/s11858-022-01460-5

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Mathematics education in a time of crisis—a viral pandemic

Man ching esther chan.

1 Melbourne Graduate School of Education, The University of Melbourne, Ground floor, 234 Queensberry Street, The University of Melbourne, VIC 3010 Australia

Cristina Sabena

2 Department of Philosophy and Education Sciences, University of Torino, Turin, Italy

David Wagner

3 Faculty of Education, University of New Brunswick, Fredericton, Canada

Crisis and change

“Crisis” is a word that has been used (and possibly abused) a lot in recent years. It may indicate a difficult moment for an individual, a strong feeling of being upset, or a disturbance in a person’s existence. Social crises are different. Across the world, the crisis from the COVID-19 pandemic is inescapable. It strongly upsets us, it disturbs our existence, and unites or divides us in different ways.

In the language of economics, especially in classical economics, “crisis” specifically designates a period of economic depression, namely, the phase of a business cycle that is the consequence of generalised overproduction, the basic characteristics of which are a rapid transition from prosperity to depression, a fall in production, widespread unemployment, falling prices, low wages, and falling profits. A well-known example is the general depression of economic activity that began with the Wall Street crash in 1929, which spread to other countries and lasted until the Second World War. Even in the case of the current pandemic, in all countries the emergence of the pandemic has been accompanied by the emergence of an economic crisis. There is a question that has sparked many political discussions and controversies with inextricable ethical implications: Which is more critical in this pandemic era, the health crisis or the economic crisis?

In this time of global crisis due to the COVID-19 pandemic we, our loved ones, and all people suffered tremendous disruptions, pains, and fears. The physical suffering, the isolation, and the compelling demands to care for others in new ways have been real and deep. While we take time to care for each other, ourselves, and others, as scholars it is also our responsibility in a time of crisis to interpret the changing world and develop appropriate research agendas.

We know that crises are not new. Even pandemics are not new. Nevertheless, we are living in a new era. Crisis theorists explain why our crises are becoming more frequent and larger in scale (Topper & Lagadec, 2013 ). The world is becoming increasingly interconnected due to advanced technologies for the movement of information, people, and goods. This interconnectivity changes the nature of any potential crisis from a chain of events in a relatively contained ecosystem or society to having global reach. This interconnectivity also accelerates the chains of events. These days, crises can ripple through the globe virtually instantaneously. Stock markets respond immediately as they are globally interdependent. Ideas, concepts, and fears spread as quickly through social media. These ripple effects can impact individual behaviour and community action, from local to national communities.

Thus, crisis theorists have been warning us (humanity) for decades about increasingly large and frequent crises. Such a warning had reached the mathematics education community before: the 2017 Mathematics Education and Society conference’s theme was “Mathematics Education and Life at Times of Crisis”. Participants in the conference envisioned social crises and the climate crisis. Now we know that these crises connect with the pandemic—see, for example, Ezeibe et al. ( 2020 ) on social crises and Banerjee ( 2020 ) on the climate crisis in relation to the pandemic. But such warnings extend much further back. We look back to 1973, when Rittel and Webber ( 1973 ) theorised problems that are addressed by natural scientists and social planners and coined the concept of a “wicked problem” to describe the problems they were addressing as inescapable high-stakes human problems that cannot be clearly defined due to their complex interconnectedness, and that have no clear solution nor method for testing solutions. Steffensen ( 2017 ) has pointed to the way climate change presents such problems and identified the importance of such problems to mathematics education. In 1992 , Beck developed the concept of “risk society” to theorise the shift in risks humans face from natural disasters to disasters caused by humans. We know that natural risks are increasingly amplified and even caused by human activity (IPCC Working Group 1, 2021 ).

Topper and Lagadec ( 2013 ) drew on Mandelbrot’s application of fractal geometry to volatile financial markets to underpin their proposal for how to respond to an increasingly unpredictable world. Using this approach in the current crisis, we see that we have to look through the massive changes and upheaval in the pandemic to examine what lies beneath—the structures that have not changed. When people experience crises, we understandably focus on the significant upheavals that dominate our attention, but Mandelbrot’s approach directs us to zoom out and see what we experience as change as representative of something greater and relatively invariant. This approach can help us understand the roots of a crisis. This approach can help us manage the big questions about crises that we face as a field of mathematics education researchers.

Given that we can expect crises more frequently and larger in scale, our research needs to extend beyond this particular crisis to prepare for future crises. That is the goal of this special issue on mathematics education in a time of crisis in this context of a viral pandemic.

To clarify terminology, the virus is called SARS-CoV-2. The disease caused by the virus is called COVID-19. The pandemic is not the virus or the disease alone; it is the social manifestation of the spread of the virus through our interconnected global social systems. The pandemic is both a result of social and environmental realities and a driver of change in these realities. This special issue is focused on the impact of the pandemic on mathematics education in three contexts:

• the teaching and learning of mathematics (in elementary, secondary, and tertiary contexts),
• mathematics education as a research field, and
• mathematics in society.

We distributed the call for papers for this special issue on April 7, 2020. In the call, we said that authors “may wish to position this particular crisis in the context of other interrelated crises that grip our world, such as, climate change, human migration, the rise of xenophobic nationalism, and growing inequalities”. We invited both essays and empirical studies. We received 161 full manuscripts with authors from 36 countries 1 including sixteen countries in Europe, eight in continental Asia, four in South America, three in North America, three in the Pacific Islands (including Australia and New Zealand), and two in Africa.

From the wealth of strong papers we received, it was difficult to choose which papers to move forward in our process. We expected a single special issue but now have a double issue with 20 papers. Many of the papers that we did not move forward for the special issue have been submitted and published elsewhere. We aimed for a set of papers that represented diverse approaches to the crisis and geographic distribution. In relation to geographic distribution, we were interested in both the location of the authors and the contexts of the research. We knew that the crisis was impacting different regions differently, so we wanted to ensure that the special issue would represent a range of perspectives across contexts.

In this introduction to the special issue, we take an opportunity to reflect on crisis in general and the pandemic in particular from the perspective of mathematics education researchers, informed by the extensive reading and interaction we have engaged in as special issue editors. In our “narrative construction of reality” (Bruner, 1991 ), we organise our reflections diachronically, adopting a human dimension of time as “time whose significance is given by the meaning assigned to events within its compass” (p. 6). We therefore first reflect on the moment of crisis, which is our present. Then we will see this crisis as an opportunity to look back and find connections from the past, which may nurture our reflection on the present. Finally, we look forward from this crisis to think about future research and action.

The moment of crisis

At the start of the pandemic at the beginning of 2020, those who followed world news would see similar messages repeat and replicate in different parts of the world. Many countries would first hear about the virus in other countries. Life seemed “normal” until we started to hear about cases emerging in neighbouring regions, countries, and then in our own area. We thought none of this would affect us or our lives until suddenly the government announced that we are in lockdown and people started to make panic purchases that left supermarket shelves empty of daily essentials. Face masks and hand sanitisers became essential items in many countries. We had to navigate and learn the new restriction rules that government officials announced and implemented overnight. Universities and schools made announcements about switching to online teaching or remote learning, and suddenly everyone had to learn to use new online platforms. There was a lot of resistance, frustration, and uncertainty among teachers, students, and parents (Matthews et al., 2021 , in this special issue). Online education resources that had been neglected by many for years became the essential teaching and learning guide (Borba et al., 2010 ; Salmon, 2011 ). Educators had to quickly learn how to teach and engage students in an online environment (Albano et al., 2021 , in this special issue). Activities that were designed to be carried out face-to-face had to be re-designed using breakout rooms, digital whiteboards, or screenshare.

Many researchers had to pause their research projects as schools shut down and the classroom environment drastically changed due to the pandemic. At the same time, some would see this as a unique opportunity to understand how human society was responding to challenges in a crisis, but our research activities were also being challenged because of the crisis. Should our responsibility be to document, describe, or explain this crisis (see, e.g., Little, 1991 )? Or should we try to theorise or predict how this crisis is going to play out and end? How do we balance our ethical responsibility to not put a burden on our participants when they are experiencing high levels of stress and uncertainty but still fulfil our research roles? Many researchers had to navigate and negotiate these questions with ourselves, our colleagues, and our participants when deciding on whether to pursue research during this time.

As time went on, people started to adjust to the “new normal”. Lockdowns became a repeat occurrence in different places. While initially the international community were being physically separated due to travel restrictions, our life appeared to be more closely connected by this pandemic as we realised that we shared many similar experiences in our local context. Online meetings and conferences became commonplace. People started to play around with online backgrounds and filters to decorate our monotonous work-from-home life. In between lockdowns, some started to say that they enjoyed working from home, not having to commute to workplaces.

Questions about this special issue

As we, the special issue editors, started to read queries from scholars interested in contributing to this special issue, we could see that the crisis had made it difficult in different parts of the world to carry out empirical research in schools and with families. Some researchers resorted to investigating their own teaching practice and their own response to the crisis (e.g., Krause et al., 2021 ; Maciejewski, 2021 ; both in this special issue). Others turned to media and textual analysis and showed fascinating and critical demands on statistical literacy and visual representation during this pandemic (e.g., Rubel et al., 2021 ; Sousa Silva et al., 2021 ; both in this special issue). The mathematics curriculum was under scrutiny in terms of preparing citizens to respond to the pandemic (e.g., Zavaleta, 2021 , in this special issue). Government response to the crisis also became a telling lens in revealing how citizens trust or distrust authority in a time of crisis (e.g., Allen & Trinick, 2021 ; in this special issue).

With the vast number of manuscripts submitted to this special issue, the review process was also being challenged. Many potential reviewers found it difficult to commit to reviewing papers. For those who responded, a few raised the question of whether it could be too early to start reflecting on the crisis situation, queried the contribution of papers that focused on documenting the crisis, or raised concerns about prospective non-empirical papers.

Some colleagues raised the concern that those who managed to submit a paper to the special issue were privileged individuals who had time to write at a time of crisis. They noted historic gender inequities in who would take on the sudden demands in home care of children (Flaherty, 2020 ; Vomvoridi-Ivanovic & Ward, 2021 ) and noted the advantages that wealth, and access to research and secure health services confer to the few. We sympathised with these questions and weighed the benefits of research responding to one of the most significant events in education against the worries about the first voices in this research being dominated by voices of privileged demographics. We looked at the authors of the submitted papers by gender and found women barely outnumbered men based on our experiences with gendered names. 2 We considered the regions from which we received papers and found more diverse representation than historical representation as identified by Mesa and Wagner ( 2019 ). In our selection of which papers to invite to move forward in the process, we aimed for representation from diverse regions, considering both the region of the author and the region focused on in the research. Because we received so many strong papers, more than we could accommodate in the special issue, we turned away some papers on the basis of regional representation, and encouraged the authors to submit their work as regular papers in Educational Studies in Mathematics or in other venues. We similarly turned away papers that were not sufficiently focused on the pandemic or did not deal with aspects of it specific to mathematics education.

A related question that emerged in discussing this special issue is this: When is the appropriate time to do research on an emergent phenomenon? We see that there is value in documenting what is going on with the pandemic situation in various contexts. The documentation will certainly allow for more informed reflection on the era in future scholarship. Additionally, the scholarship already prompts reflection. Indeed, all the papers in this special issue have an element of reflection in them. The prompt to share reflections and practices when we are still facing a terrible problem is not only a challenge, but it is also a way to act as a community, to keep us socially close, in a time when we are prevented from meeting physically. Possibly, this also explains the reason why the special issue call received so many papers, even in such a short time. Krause et al. ( 2021 , in this special issue) witnessed a tension between a certain “situatedness” of the current reality and the “generality” (what goes beyond the pandemic situation). The relatively short deadlines we asked for in the call for papers enabled authors to seize fully the situatedness, in a sense contributing to it. On the other hand, we asked for contributions that were able to go beyond the current situation, towards a more general view of crisis. Skovsmose’s ( 2021 , in this special issue) paper took on that challenge directly.

Responsibilities of mathematics educators in crisis

What are our responsibilities as mathematics educators in such a time of crisis? We recognise that this is a difficult question because of the many competing demands we face. A mathematics educator in a time of big or small crisis would face local, immediate challenges. At the same time, there is also the possibility to step back to ask big questions. Many would find it important to devote time to love the people in their families and communities at a time of crisis. Whether we are mathematics teachers or teacher educators, we would find it important in our teaching roles to help our students achieve their immediate needs, even if those needs relate to problematic systems. For example, students may have a “need” to learn how to prove trigonometric identities in order to pass a course and qualify for a biology programme that sets them up for their career goal. Even if we doubt the value of trigonometric identities in school curriculum (and perhaps especially in a pandemic) or question the focus on these identities for biologists, we may feel obliged to think that it is still important to support the student’s success in the systems that are currently in force. In our research, we may find it important to study the local, immediate needs but also look at the big questions and examine the structure beneath the crisis. What is invariant? And where that structure is unjust, how can it be changed? And it could be equally important to reflect on how all these different levels of action speak to each other: family/community, students, practice-level research, system-level research.

In the papers we received for this special issue, we saw scholars looking for accessible data that would help the field understand the pandemic. This was not easy. The pandemic makes it hard to start new studies involving participants. And we know that studies of social structures really need researchers to listen to the people most impacted by the structures. Over time, we expect that we will see more research that uses data that are harder to access, with deep engagement with the people most impacted by the crises.

We know some mathematics teachers and mathematics teacher educators who have seen the pandemic as a prompt to re-examine their teaching (e.g., Brunetto et al., 2021 , and, in this special issue Albano et al., 2021 ; Gosztonyi, 2021 ; Maciejewski, 2021 ). One may wonder how students would accept a focus on the usual skills and knowledge when they are bombarded daily with media coverage and government releases about the pandemic situation. One should expect that this supposedly powerful mathematics would be used in class to address the most obvious disruption of our era. We would expect a call from students and from society, echoing the decades of injunction from Ubiritan D’Ambrosio ( 1994 , 2007 , 2015 ) and others (e.g., Mendick, 2017 ), to examine the complicity of mathematics in the structures that allowed the virus to thrive, in addition to the possibilities for using mathematics for justice in these times. However, speaking from our own experiences, we see students, teachers, families, and politicians focused on the compelling, immediate, local needs. Many are distracted from asking the deep questions, distracted by our social systems and the immediate needs of disrupted networks.

One thing that is immediately clear in pandemic teaching is the inequities, including:

• unequal access to internet
• unequal access to computers and tablets
• unequal availability of space at home for uninterrupted time
• unequal competing demands for time.

Even while teachers and school systems work very hard at combatting them, these inequities persist. Again, this is another example of something that is invariant in this time of massive change. For example, we have research that shows inequities persisting through the pandemic: rural families in Turkey have greater challenges than others (Yılmaz et al., 2021 , in this special issue), the needs of Indigenous students are ignored (Allen & Trinick, 2021 , in this special issue), students of colour are marginalised (Matthews et al., 2021 , in this special issue), and students who have recently migrated are ignored. The effects of poverty are magnified.

Crisis as an opportunity to look back

For many of us, the pandemic situation appeared as a totally new phenomenon, in front of which we felt completely unprepared. But looking at human history, we may indeed recognise that this phenomenon is not new, rather a sort of periodic feature. We have to recognise also that the memory of previous pandemics is not felt in the same way in the world: it is indeed stronger, and still felt as a trauma, for many Indigenous marginalised groups around the world—for example, that of Māori in New Zealand as documented by Allen and Trinick ( 2021 , in this special issue).

On the other hand, referring to past epidemics may be a way to gain tools for reflection on the present, without feeling the psychological pressure that such a critical situation may place on us. This is the choice made by Gosztonyi ( 2021 , in this special issue) in her experience with a group of secondary teachers deepening the scientific debate arisen in the XVIII century between Bernoulli and d’Alembert about the smallpox epidemic and the risks and advantages of inoculation (a primitive antecedent of vaccination). In her perspective, historical texts are proposed as transitional objects in the interaction with teachers, indirectly stimulating discussions about the problems with which they are concerned.

The past may emerge in our reflection also in sharp contrast with the present. In one of the outcomes of the pandemic crisis, schools closed and teachers had to face a sudden, unexpected change from face-to-face to distance teaching: Albano et al. ( 2021 , in this special issue) report the subjective point of view of Italian teachers by means of logbooks and show that two temporal periods may be identified, namely, the period of bewilderment and the period for reflection and elaboration. Such a reflection/elaboration is prompted by the current situation through a contrast with the past situation. This contrast reveals key elements of the teaching–learning system in which teachers were embedded before the disturbance. Imagining and advocating totally or partially different educational/school settings—possible worlds in Bruner’s words (1986), as Albano et al. pointed out—realises an implied critique of the existing/past world. But the pandemic experience has taught us that the past world rapidly evolved into the existing world, which is, in turn, rapidly evolving into a past world. This evolution leaves us with a minimal sense of what is indeed the actual world and with unstable visions for the future.

A historicized approach is also helpful to understand the present. Ziols and Kirchgasler ( 2021 , in this special issue) explored how distinctions of health and pathology have been dynamically interwoven with mathematics education for two centuries. In this way, they open a dialogue about implications of these historical traces for issues of injustice today. This kind of vision aligns with Mandelbrot’s approach to addressing crisis: to look through or past the shocking disruptions to identify what is invariant (Topper & Lagadec, 2013 ).

Adopting a Bourdieusian approach, Allen and Trinick ( 2021 , in this special issue) framed the difference between Māori and English-language schools’ capacity to maintain continuity of mathematics instruction while schools were closed due to the COVID-19 pandemic, as linked to the limited bank of digital mathematics resources in the Māori language. They interpreted this disparity as the outcome of socially determined differences in cultural capital, which are heritages of the pre-pandemic past.

Borba ( 2021 ) saw the pandemic as a prompt to reflect on mathematics education as a research field, particularly in the growing awareness of the way humans and their media depend on each other for mathematics learning and teaching. Others in the special issue suggested a new research agenda in their discussions. We identify an important opportunity and need to reflect on the field in the ways identified above, to understand the past and present manifestations of research in the field.

We note that the tremendous response to this special issue demonstrates the resiliency of the field and showcased many well-developed research methodologies and collaboration networks. We find the results of the survey done by Bakker et al. ( 2021 ) to be of interest. Just before the pandemic struck, they surveyed mathematics educators around the world to ask what themes research in mathematics education should focus on in the coming decade. They asked respondents a year later (in November 2020) if the pandemic changed their views on the themes. Nine of their respondents identified no changes in their views, eight identified clearly different views, and 45 saw the importance of their initial themes reinforced. One way to see these results is as evidence that the field already understood the important issues that the pandemic revealed. However, we should be careful about this conclusion because we know for ourselves that we use the tools we already know to interpret new phenomena. While we see authors in this special issue using theories and methodologies that fit their previous research approaches, we also see changes. Many researchers are becoming increasingly interested in and aware of the work in our field on online teaching media: for this special issue we received many manuscripts from authors studying the move to online teaching who, as far as we know, have not addressed this teaching medium before. Nevertheless, the fact that the field has people specialised in online teaching research (e.g., Borba et al., 2010 ), for example, for the past thirty years with relatively few people needing to refer to until now, shows that something is working in, shall we say, the ecology of the educational research field that allows us to be responsive to a diverse range of situations.

Crisis as an opportunity to look forward

Crises also prompt us to look forward to projected and potential futures. The Secretary General of the United Nations, in his July 2020 lecture (the Nelson Mandela Lecture), noted that “The pandemic has demonstrated the fragility of our world. It has laid bare risks we have ignored for decades: inadequate health systems; gaps in social protection; structural inequalities; environmental degradation; the climate crisis” (Guterres, 2020 ). He added that “The virus poses the greatest risk to the most vulnerable: those living in poverty, older people, and people with disabilities and pre-existing conditions.” He concluded that “COVID-19 is a human tragedy. But it has also created a generational opportunity. An opportunity to build back a more equal and sustainable world.” Others have made similar observations. For example, novelist Arundahti Roy ( 2020 ) has documented the pandemic in India and concluded:

Historically, pandemics have forced humans to break with the past and imagine their world anew. This one is no different. It is a portal, a gateway between one world and the next. We can choose to walk through it, dragging the carcasses of our prejudice and hatred, our avarice, our data banks and dead ideas, our dead rivers and smoky skies behind us. Or we can walk through lightly, with little luggage, ready to imagine another world. And ready to fight for it.

People who experienced the world before the pandemic as treacherous and broken may wish for a transformed world. As researchers, many of us may have had relatively satisfying experiences before the pandemic, and thus may not wish for world transformation. We should take a moment of crisis as a time to carefully imagine the future.

We should ask, what warrants change and what should be maintained? These questions should be applied both to mathematics teaching practices and to research approaches. And we should inform our considerations with careful attention to the perspectives of a wide range of stakeholders in mathematics education—students, teachers, and others, all from a wide cross section of contexts. The question boils down to a moral question: whose needs should be foregrounded? This question and other related questions were addressed by Adler and Lerman ( 2003 ). We suggest that the pandemic compels new consideration of the ethics of research in mathematics education.

New visions for mathematics teaching

When we look forward as researchers, we should question both curriculum and pedagogies. The question of curriculum is widely discussed in this special issue (Kollosche & Meyerhöfer, 2021 ; Rotem & Ayalon, 2021 ; Sánchez Aguilar and Castañeda, 2021 ; Sousa Silva, et al., 2021 ; Zavaleta, 2021 , all in this special issue). It is indeed helpful to look at the mathematics that has appeared publicly in the pandemic to inform the mathematics that should be taught because citizens should be equipped to understand the mathematics they will experience in the world. Kwon et al., ( 2021 , in this special issue) investigated the use of graphs in Korea’s news media during the COVID-19 outbreak, providing implications for future teaching and learning of graph literacy in school mathematics courses. Heyd-Metzuyanim et al. ( 2021 , in this special issue), after examining the Israeli public’s understanding of mathematical notions that are required for understanding the pandemic and predicting its spread, demonstrate that mathematical identity may significantly hinder adults’ engagement with such information. Kollosche and Meyerhöfer ( 2021 , in this special issue) took a more critical stance and referred to different discussions in German mass media on the pandemic policy in the SARS-CoV-2 crisis in 2020 to argue that the critical evaluation of experts’ use of mathematics by laypersons is not possible in all relevant cases, and discuss possible implications of this result.

We note that when people develop media to inform the public, they make their decisions about what mathematics to use and how to represent it based on the mathematics they expect the public to understand. Thus, we see a circularity: curriculum would be designed on the basis of the mathematics that people are applying in their lives, and such mathematics is influenced by the mathematics learned at school, hence influenced or even determined by the curriculum itself. A time of crisis may help disturb such circularity, identifying the mathematics that are needed in curriculum.

With this new vision, mathematics educators and mathematicians will need to identify mathematics that would be needed for interpreting crises so that this mathematics could inform the public. In addition to the widely circulated mathematics, there is important mathematics being done to address significant needs during the pandemic. Some of this mathematics may be part of the answer to the above question: what mathematics should be taught? Maciejewski ( 2021 , in this special issue) contributed an account of his struggle with this question and reported on his approaches to developing prospective mathematics teachers’ understanding of exponential growth, and connectivity. Also, this question has been discussed less formally, for example, in the closing plenary panel of the International Congress on Mathematical Education in 2021, panellists answered this question. The question of how to address this mathematics requires much more thought. And more research, we suggest. Even so, the question of what mathematics should be taught surely needs attention given the new realities exposed by the pandemic. The basic question underlying any evaluation of mathematics curriculum is this: What should every citizen know? Surely the answer is different than it was thirty years ago, considering the massive changes in interconnectivity in our world and the related growth of planet-wide crises. To answer this question, we need to identify the human and social problems of our time. Here we identify some questions that ask about the root factors in this pandemic; we know there are other questions like these:

• What mathematics is necessary to understand interconnectivity?
• What mathematics is needed to understand climate?
• What mathematics is needed to understand biodiversity?
• What mathematics is needed to understand wealth distribution?

It is not enough to identify pressing problems. They need to be prioritised. The pandemic pushes us to change priorities because we see how fragile societies are. Nevertheless, priority-setting remains an important function. Underneath the question of priority-setting, we will find assumptions about whose interests are most important. There are others who can help us answer these moral questions, but as researchers we have to make these determinations ourselves as we make decisions about where to devote our own resources in research. We can do our own evaluations of priorities, or we can make decisions about whose guidance we follow in such priority-setting.

Again, as it becomes clear in Maciejewski’s ( 2021 , in this special issue) account of teaching mathematics relevant to the pandemic, we see the importance of questions about how it should be taught. Questions of how to teach mathematics are also now impacted with the field’s new understanding of different media for teaching mathematics. Some of the studies in this special issue address the sudden disruptions in teaching media (Albano et al., 2021 ; Borba, 2021 ; both in this special issue), but the studies also identify mathematics teachers’ learning about their teaching and how to use new media. Drijvers et al., ( 2021 , in this special issue) found that teachers in Flanders, Germany, and the Netherlands reported a remarkable increase in their confidence in using digital technologies during the lockdown. We expect that this learning will be applied to emergent practices post-pandemic. Some early results concerning the online education tool of the “micro-classes” in China are given by Xie et al. ( 2021 , in this special issue).

As we reflect on the responsibilities of mathematics educators within the pandemic, we see that the same questions apply to future research. We are reminded that crisis is not new, and thus, we can look to pre-pandemic scholarship for some guidance on future research agenda in relation to crisis. In particular we point to Vithal and Valero’s ( 2003 ) consideration of mathematics education research in social and political crisis and to a symposium convened by Parra et al. ( 2017 ) which prompted conversation about whose perspectives should be foregrounded in research in crisis contexts.

Reflection on the role of mathematics

Finally, we see that the role of mathematics is itself part of the crisis. Mathematics has underpinned technologies that have pushed species into new patterns of behaviour and that have made the world more connected. Thus, mathematics is underneath the emergence of the coronavirus that drove this pandemic and underneath the social systems that paved the way for its rapid spread. Ubiritan D’Ambrosio implored mathematics educators for decades to examine the role of mathematics in shaping the world (e.g., D’Ambrosio, 1994 ) and to advocate for such examination in school mathematics (e.g., D’Ambrosio, 2007 , 2015 ). Meanwhile, the way mathematics has been taught has influenced how people have understood the crisis and thus affected their actions within the crisis, again contributing to the particular rates of spread. For example, mathematics education practices have impacted the ability and willingness of citizens to read and trust statistics and modelling, which impacts both their decisions in the pandemic and the rise of certain political voices. As our field grapples with the new world, we are compelled to consider our complicity in the problems we see before us. Nevertheless, this critical reflection should not undermine our confidence that mathematics and good mathematics teaching can make important contributions to society. Rather, we need to be sure to include self-examination in our visions for the future.

A final word

Etymologically, the term crisis comes from the Greek krisis , which refers to choice, decisions, and decisive phases of an illness. It relates to the word krino , which means to distinguish. If we look at the etymology, it is always a time of crisis, because we are always being called upon to choose among different alternatives; even doing nothing to change a situation is an alternative and a choice. Taking different perspectives and addressing the most dynamic sense of the crisis, the authors of this special issue proactively seized the chance to write in the momentum of the pandemic crisis to offer alternatives to the mathematics education field. In such a perspective, it is our wish that the papers in this special issue will constitute a little light for future generations.

1 We recognise that any count of countries and regions is problematic because there are disputed boundaries.

2 We were aware that this measure may have resulted in misclassification because some names were unfamiliar to us.

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• Adler J, Lerman S. Getting the description right and making it count: Ethical practice in mathematics education research. In: Bishop A, Clements M, Keitel-Kreidt C, Kilpatrick J, Leung F, editors. Second international handbook of mathematics education. Springer; 2003. pp. 441–470. [ Google Scholar ]
• Albano, G., Antonini, S., Coppola, C., Dello Iacono, U., & Pierri, A. (2021). ‘Tell me about’: A logbook of teachers’ changes from face-to-face to distance mathematics education. Educational Studies in Mathematics.  10.1007/s10649-021-10108-2 [ PMC free article ] [ PubMed ]
• Allen, P., & Trinick, T. (2021). Agency-structure dynamics in an indigenous mathematics education community in times of an existential crisis in education, health, and the economy. Educational Studies in Mathematics . 10.1007/s10649-021-10098-1 [ PMC free article ] [ PubMed ]
• Bakker A, Cai J, Zenger L. Future themes of mathematics education research: An international survey before and during the pandemic. Educational Studies in Mathematics. 2021; 107 (1):1–24. doi: 10.1007/s10649-021-10049-w. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Banerjee, N. (2020). COVID-19, public health, and climate change: Q&A with Aaron Bernstein. Global Observatory , March 20, 2020. https://theglobalobservatory.org/2020/03/covid-19-public-health-climate-change-qa-with-aaron-bernstein/ . Accessed 28 Sep 2021.
• Beck U. Risk society: Towards a new modernity. Sage Publications; 1992. [ Google Scholar ]
• Borba, M. (2021). The future of mathematics education since COVID-19: Humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics . 10.1007/s10649-021-10043-2 [ PMC free article ] [ PubMed ]
• Borba, M. C., Malheiros, A. P. d. S., & Zulatto, R. B. A. (Eds.). (2010). Online distance education . Sense Publishers.
• Bruner J. The narrative construction of reality. Critical Inquiry. 1991; 18 (1):1–21. doi: 10.1086/448619. [ CrossRef ] [ Google Scholar ]
• Brunetto, D., Bernardi, G., Andrà, C., & Liljedahl, P. (2021). Teaching as a system: COVID-19 as a lens into teacher change. Educational Studies in Mathematics.   10.1007/s10649-021-10107-3 [ PMC free article ] [ PubMed ]
• D’Ambrosio U. Cultural framing of mathematics teaching and learning. In: Biehler R, Scholz R, Sträßer R, Winkelman B, editors. Didactics of mathematics as a scientific discipline. Kluwer; 1994. pp. 443–455. [ Google Scholar ]
• D’Ambrosio U. The role of mathematics in educational systems. ZDM – Mathematics Education. 2007; 39 (1–2):173–181. doi: 10.1007/s11858-006-0012-1. [ CrossRef ] [ Google Scholar ]
• D’Ambrosio, U. (2015). From mathematics education and society to mathematics education and a sustainable civilization. Proceedings of the eighth international mathematics education and society conference (vol. 1, pp. 19–30). Portland, Oregon, USA.
• Drijvers, P., Thurm, D., Vandervieren, E., Klinger, M., Moons, F., van der Ree, H., Mol, A., Barzel, B., & Doorman, M. (2021). Distance mathematics teaching in Flanders, Germany, and the Netherlands during COVID-19 lockdown. Educational Studies in Mathematics.  10.1007/s10649-021-10094-5 [ PMC free article ] [ PubMed ]
• Ezeibe C, Ilo C, Ezeibe E, Oguonu C, Nwankwo N, Ajaero C, Osadebe N. Political distrust and the spread of COVID-19 in Nigeria. Global Public Health. 2020; 15 (12):1753–1766. doi: 10.1080/17441692.2020.1828987. [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Flaherty, C. (2020, April 21). No room of one’s own: Early journal submission data suggest COVID-19 is tanking women’s research productivity.  Inside Higher Ed . https://www.insidehighered.com/news/2020/04/21/early-journal-submission-data-suggest-covid-19-tanking-womens-research-productivity . Accessed 8 Sep 2021.
• Gosztonyi, K. (2021). How history of mathematics can help to face a crisis situation: The case of the polemic between Bernoulli and d’Alembert about the smallpox epidemic. Educational Studies in Mathematics . 10.1007/s10649-021-10077-6 [ PMC free article ] [ PubMed ]
• Guterres, A. (2020). Secretary-General’s Nelson Mandela lecture: “Tackling the inequality pandemic: A new social contract for a new era”. https://www.un.org/sg/en/content/sg/statement/2020-07-18/secretary-generals-nelson-mandela-lecture-%E2%80%9Ctackling-the-inequality-pandemic-new-social-contract-for-new-era%E2%80%9D-delivered . Accessed 8 Sep 2021.
• Heyd-Metzuyanim, E., Sharon, A., & Baram-Tsabari, A. (2021). Mathematical media literacy in the COVID-19 pandemic and its relation to school mathematics education. Educational Studies in Mathematics . 10.1007/s10649-021-10075-8 [ PMC free article ] [ PubMed ]
• IPCC Working Group 1. (2021). Climate change 2021: The physical science basis [Assessment Rep No. 6]. https://www.ipcc.ch/report/ar6/wg1/ . Accessed 8 Sep 2021.
• Kollosche, D., & Meyerhöfer, W. (2021). COVID-19, mathematics education, and the evaluation of expert knowledge. Educational Studies in Mathematics . 10.1007/s10649-021-10097-2 [ PMC free article ] [ PubMed ]
• Krause, C., Di Martino, P., & Moschkovich, J. (2021). Tales from three countries: Reflections during COVID-19 for mathematical education in the future. Educational Studies in Mathematics . 10.1007/s10649-021-10066-9 [ PMC free article ] [ PubMed ]
• Kwon, O., Han, C. Lee, C., Lee, K., Kim, K., Jo, G., & Yoon, G. (2021). Graphs in the COVID-19 news: A mathematics audit of newspapers in Korea. Educational Studies in Mathematics . 10.1007/s10649-021-10029-0 [ PMC free article ] [ PubMed ]
• Little D. Varieties of social explanation: An introduction to the philosophy of social science. Westview; 1991. [ Google Scholar ]
• Maciejewski, W. (2021). Teaching math in real time. Educational Studies in Mathematics . 10.1007/s10649-021-10090-9 [ PMC free article ] [ PubMed ]
• Matthews, L., Jessup, N., & Sears, R. (2021). Pandemic shifts: Power and reimagined possibilities in mathematics learning for Black communities. Educational Studies in Mathematics. 10.1007/s10649-021-10106-4 [ PMC free article ] [ PubMed ]
• Mendick, H. (2017). Mathematical futures: Discourses of mathematics in fictions of the post-2008 financial crisis. Proceedings of the ninth international mathematics education and society conference , (vol. 1, pp. 74–89), Volos, Greece.
• Mesa V, Wagner D. Behind the door: A critical look at the process of publication in Educational Studies in Mathematics . Educational Studies in Mathematics. 2019; 101 (3):301–324. doi: 10.1007/s10649-019-09900-y. [ CrossRef ] [ Google Scholar ]
• Parra, A., Bose, A., Alshwaikh, J., González, M., Marcone, R., & D’Souza, R. (2017). “Crisis” and interface with mathematics education research and practice: An everyday issue. In A. Chronaki (Ed.), Proceedings of the Ninth International Mathematics Education and Society Conference , Volos, Greece (Vol. 1, pp. 174–178).
• Rittel H, Webber M. Dilemmas in a general theory of planning. Policy Sciences. 1973; 4 (2):155–169. doi: 10.1007/BF01405730. [ CrossRef ] [ Google Scholar ]
• Rotem, S., & Ayalon, M. (2021). Exploring Israeli high school graduates’ explanations for the spread of the coronavirus. Educational Studies in Mathematics. 10.1007/s10649-021-10042-3 [ PMC free article ] [ PubMed ]
• Roy, A. (2020). The pandemic is a portal. Financial Times , April 3, 2020. https://www.ft.com/content/10d8f5e8-74eb-11ea-95fe-fcd274e920ca . Accessed 8 Sep 2021.
• Rubel, L., Nicol, C., & Chronaki, A. (2021). Critical mathematics reading of data visualizations: Reimagining through reformatting, reframing, and renarrating. Educational Studies in Mathematics.  10.1007/s10649-021-10087-4 [ PMC free article ] [ PubMed ]
• Salmon, G. (2011). E-moderating: The key to teaching and learning online (3rd ed.). Routledge.
• Sánchez Aguilar, M., & Castañeda, A. (2021). What mathematical competencies does a citizen need to interpret Mexico’s official information about the COVID-19 pandemic? Educational Studies in Mathematics.  10.1007/s10649-021-10082-9 [ PMC free article ] [ PubMed ]
• Sousa Silva, A., Serrano Barbosa, M., de Souza Velasque, L., da Silveira Barroso Alves, D., & Nascimento Magalhães, M. (2021). The COVID-19 epidemic in Brazil: How statistical education may contribute to unravel the reality behind the charts. Educational Studies in Mathematics.  10.1007/s10649-021-10112-6 [ PMC free article ] [ PubMed ]
• Skovsmose, O. (2021). Mathematics and crises. Educational Studies in Mathematics. 10.1007/s10649-021-10037-0 [ PMC free article ] [ PubMed ]
• Steffensen, L. (2017). Critical mathematics education and post-normal science: A literature overview. Philosophy of Mathematics Education Journal , 32 . https://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome32/index.html . Accessed 8 Sep 2021.
• Topper B, Lagadec P. Fractal crises–A new path for crisis theory and management. Journal of Contingencies and Crisis Management. 2013; 21 (1):4–16. doi: 10.1111/1468-5973.12008. [ CrossRef ] [ Google Scholar ]
• Vithal R, Valero P. Researching mathematics education in situations of social and political conflict. In: Bishop A, Clements M, Keitel-Kreidt C, Kilpatrick J, Leung F, editors. The second international handbook of mathematics education. Springer; 2003. pp. 545–591. [ Google Scholar ]
• Vomvoridi-Ivanovic E, Ward J. Academic motherhood in mathematics teacher education during COVID-19: Breaking the silence and shifting the discourse. REDIMAT-Journal of Research in Mathematics Education. 2021; 10 (1):41–61. doi: 10.17583/redimat.2021.6436. [ CrossRef ] [ Google Scholar ]
• Xie, Z., Xiao, L., Hou, M., Liu, X., & Liu, J. (2021). Micro classes as a primary school-level mathematics education response to COVID-19 pandemic in China: Students’ approval degree and perceived equity. Educational Studies in Mathematics.  10.1007/s10649-021-10111-7 [ PMC free article ] [ PubMed ]
• Yılmaz, A., Gülbağcı Dede, H., Sears, R., & Yıldız Nielsen, S. (2021). Are we all in this together? Mathematics teachers’ perspectives on equity in remote instruction during a pandemic. Educational Studies in Mathematics. 10.1007/s10649-021-10060-1 [ PMC free article ] [ PubMed ]
• Zavaleta, L. (2021). Emergent curriculum in basic education for the new normality in Perú: Orientations proposed from mathematics education. Educational Studies in Mathematics. 10.1007/s10649-021-10100-w [ PMC free article ] [ PubMed ]
• Ziols, R., & Kirchgasler, K. (2021). Health and pathology: A brief history of the biopolitics of US mathematics education. Educational Studies in Mathematics.  10.1007/s10649-021-10110-8 [ PMC free article ] [ PubMed ]

Mathematics Resiliency in the New Normal: A Theory Development

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This paper aimed to generate a theory that answers the question, “How do students cope with the challenges in learning mathematics in the normal? This study made used of the deductive axiomatic approach in theory generation following the steps prescribed by Padua (2012). Four axioms were formulated: (1) Students employ time management in studying math; (2) Students uses compensation strategies in overcoming challenges; (3) Students’ resourcefulness leads them to learn mathematics; and (4) Students asked help from teachers and peers in understanding mathematical concepts. Two propositions were derived from these axioms: students’ cope with the challenges in learning mathematics by (1) direct coping strategies support students’ resiliency in learning mathematics and (2) Indirect coping strategies indirectly provide support for coping strategies through planning, socializing with others and increasing empathy. From these propositions, the Students’ Mathematics Resiliency Based Theory is formulated: The Students’ Mathematics Resiliency Theory states that resiliency in learning mathematics is affected by both direct and indirect coping strategies. Direct coping strategies include compensation strategies, while indirect strategies include social, time management, and resourcefulness.

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Agum, A. N. C., Naidas, M. S., Dorado, L. B., Bhattrai, J. L. T., Lagajino, E. L. V., & Mergal, V. C. (2021). Filipino College Students’ Perspectives on the Challenges, Coping Strategies, and Benefits of Self-Directed Language Learning in the New Normal. Human Behavior, Development and Society, 22(2), 72-83.

Avcı, N., & Kaya, G. (2021). The relationship of learned resourcefulness with self-leadership skills: A study with nurse and midwife students. Nurse Education Today, 107, 105125. https://doi.org/10.1016/j.nedt.2021.105125

Ayed, N., Toner, S., & Priebe, S. (2019). Conceptualizing resilience in adult mental health literature: A systematic review and narrative synthesis. Psychology and Psychotherapy: Theory, Research and Practice, 92(3), 299-341. https://doi.org/10.1111/papt.12185

Bettinger, E., Ludvigsen, S., Rege, M., Solli, I. F., & Yeager, D. (2018). Increasing perseverance in math: Evidence from a field experiment in Norway. Journal of Economic Behavior & Organization, 146, 1-15. https://doi.org/10.1016/j.jebo.2017.11.032

Borsboom, D., van der Maas, H. L., Dalege, J., Kievit, R. A., & Haig, B. D. (2021). Theory construction methodology: A practical framework for building theories in psychology. Perspectives on Psychological Science, 16(4), 756-766. https://doi.org/10.1177/1745691620969647 .

Castroverde, F., & Acala, M. (2021). Modular distance learning modality: Challenges of teachers in teaching amid the Covid-19 pandemic. International Journal of Research Studies in Education, 10(8), 7-15. https://doi.org/10.5861/ijrse.2021.602

Chen, C. (2016). The role of resilience and coping styles in subjective well-being among Chinese university students. The Asia-Pacific Education Researcher, 25, 377-387. https://doi.org/10.1007/s40299-016-0274-5

Chen, C., Song, X., Wei, W., Zhong, H., Dai, J., Lan, Z., ... & Jia, H. (2017). The microbiota continuum along the female reproductive tract and its relation to uterine-related diseases. Nature communications, 8(1), 875. https://doi.org/10.1038/s41467-017-00901-0

Chen, H. Y., Das, A., & Ivanov, D. (2019). Building resilience and managing post-disruption supply chain recovery: Lessons from the information and communication technology industry. International Journal of Information Management, 49, 330-342. https://doi.org/10.1016/j.ijinfomgt.2019.06.002

Dilla, S. C., Hidayat, W., & Rohaeti, E. E. (2018). Gender and Resilience Factors in Achieving High School Mathematical Creative Thinking Ability. Journal of Maldives, 2(1), 129-139.

Dray, J., Bowman, J., Campbell, E., Freund, M., Wolfenden, L., Hodder, R. K., ... & Wiggers, J. (2017). Systematic review of universal resilience-focused interventions targeting child and adolescent mental health in the school setting. Journal of the American Academy of Child & Adolescent Psychiatry, 56(10), 813-824. https://doi.org/10.1016/j.jaac.2017.07.780

Ferrari, R. (2015). Writing narrative style literature reviews. Medical writing, 24(4), 230-235. https://doi.org/10.1179/2047480615Z.000000000329

Grageda, C. N., Diokno, R. P., & Abadiano, M. N. (2023). Teaching Experiences of Early Childhood Educators in the New Normal: The Multi-Faceted Endeavor Theory. Russian Law Journal, 11(9s), 184-196. https://doi.org/10.52783/rlj.v11i9s.1578

Grey, I. M., Al Saihati, B., & McClean, B. (2013). Teaching behaviour change skills to undergraduate medical students. Journal of Contemporary Medical Education, 1(4), 231-237. https://doi.org/10.5455/jcme.20131105073307

Gueta, M. and Janer, S. (2021). Distance learning challenges on the use of self-learning module. United International Journal for Research & Technology, 2(7), 58-71.

Henningsen, D. D., & Henningsen, M. L. M. (2018). Does brainstorming promote cohesiveness? How the rules of brainstorming mirror symbolic convergence. Communication Reports, 31(2), 103-114. https://doi.org/10.1080/08934215.2017.1394476

Hernandez‐Martinez, P., & Williams, J. (2013). Against the odds: resilience in mathematics students in transition. British Educational Research Journal, 39(1), 45-59. https://doi.org/10.1080/01411926.2011.623153

Kiel, Y., & Callaman, R. (2021). Assessing students’ mathematics resiliency: basis for an intervention program. Unpublished Institutional Research of USeP.

Kooken, J., Welsh, M. E., McCoach, D. B., Johnston-Wilder, S., & Lee, C. (2016). Development and validation of the mathematical resilience scale. Measurement and Evaluation in Counseling and Development, 49(3), 217-242. https://doi.org/10.1177/0748175615596782

Lehmann, J., & Joseph, S. (2015). Biochar for Environmental Management: Science, Technology and Implementation (2nd ed.). Routledge. https://doi.org/10.4324/9780203762264 .

Mamman, A. (2013). Time management in teaching of technical education in Nigeria: the case of Kaduna Polytechnic. International Journal of Development and Sustainability, 2(2), 1357-1364.

Masten, A. S. (2014). Global perspectives on resilience in children and youth. Child development, 85(1), 6-20. https://doi.org/10.1111/cdev.12205

Mickenberg, I. (2017). Brainstorming: Developing the Facts to Build Theory of Defense. National Defender Training Project. Retrieved from https://www.opd.ohio.gov/static/Law+Library/Training/OPD+Training+Materials/2017+Trial+Advocacy+Program/Brainstorming_--_Mickenberg.pdf

Nisbet, R., Miner, G., & Yale, K. (2018). The Data Mining and Predictive Analytic Process. Handbook of Statistical Analysis and Data Mining Applications. Academic press.

Novikov, P. S. (2011). Axiomatic method. Encyclopedia of Mathematics. https://www.encyclopediaofmath.org/index.php/Axiomatic_method

Oxford, R. (1990). The Role of Styles and Strategies in Second Language Learning. ERIC Clearinghouse and Linguistic Washington DC.

Padua, R. (2012). Teaching Theory Development. Training presentation from Cebu Normal University, Philippines.

Pai, N., & Vella, S. L. (2018). Can one spring back from psychosis? The role of resilience in serious mental illness. The Australian and New Zealand Journal of Psychiatry, 52(11), 1093-1094. https://doi.org/10.1177/0004867418802900

Russo, J., Minas, M., Hewish, T., & McCosh, J. (2020). Using prompts to empower learners: Exploring primary students' attitudes towards enabling prompts when learning mathematics through problem solving. Mathematics Teacher Education and Development, 22(1), 48-67.

Seeber, I., De Vreede, G. J., Maier, R., & Weber, B. (2017). Beyond brainstorming: Exploring convergence in teams. Journal of Management Information Systems, 34(4), 939-969. https://doi.org/10.1080/07421222.2017.1393303

Selden, R., Widdowson, P., & Brooker, P. (2016). A reader's guide to contemporary literary theory. Taylor & Francis.

Shieh, C. J., & Yu, L. (2016). A study on information technology integrated guided discovery instruction towards students’ learning achievement and learning retention. EURASIA Journal of Mathematics, Science and Technology Education, 12(4), 833-842. https://doi.org/10.12973/eurasia.2015.1554a .

Simbulas, L. S. (2018). Aptitude, Resilience, and Teacher Attributes of Learners: A Structural Model on Mathematics Achievement [Unpublished Doctoral dissertation]. Bukidnon State University.

Smith, K. J., Haight, T. D., Emerson, D. J., Mauldin, S., & Wood, B. G. (2020). Resilience as a coping strategy for reducing departure intentions of accounting students. Accounting Education, 29(1), 77-108. https://doi.org/10.1080/09639284.2019.1700140

Stainton, A., Chisholm, K., Kaiser, N., Rosen, M., Upthegrove, R., Ruhrmann, S., & Wood, S. J. (2019). Resilience as a multimodal dynamic process. Early intervention in psychiatry, 13(4), 725-732. https://doi.org/10.1111/eip.12726

Stergiou, D., & Airey, D. (2018). Understandings of Tourism Theory. Tourism Review, 73(2), 156-168. https://doi.org/10.1108/tr-07-2017-0120

Trueman, M., & Hartley, J. (1996). A comparison between the time-management skills and academic performance of mature and traditional-entry university students. Higher education, 32(2), 199-215. https://doi.org/10.1007/BF00138396

Van de Ven, A. H. (2016). Grounding the research phenomenon. Journal of Change Management, 16(4), 265-270. https://doi.org/10.1080/14697017.2016.1230336

Williams, J. M., & Bryan, J. (2013). Overcoming adversity: High‐achieving African American youth's perspectives on educational resilience. Journal of Counseling & development, 91(3), 291-300. https://doi.org/10.1002/j.1556-6676.2013.00097.x

Wu, Y., Yu, W., Wu, X., Wan, H., Wang, Y., & Lu, G. (2020). Psychological resilience and positive coping styles among Chinese undergraduate students: a cross-sectional study. BMC psychology, 8(1), 1-11. https://doi.org/10.1186/s40359-020-00444-y

Xu, J. (2013). Why do students have difficulties completing homework? The need for homework management. Journal of Education and Training Studies, 1(1), 98-105. https://doi.org/10.11114/jets.v1i1.78

Yerizon, Y., Putra, A. A., & Subhan, M. (2018). Mathematics learning instructional development based on discovery learning for students with intrapersonal and interpersonal intelligence (preliminary research stage). International Electronic Journal of Mathematics Education, 13(3), 97-101. https://doi.org/10.12973/iejme/2701

Zalaghi, H., & Khazaei, M. (2016). The role of deductive and inductive reasoning in accounting research and standard setting. Asian Journal of Finance & Accounting, 8(1), 23-37. https://doi.org/10.5296/ajfa.v8i1.8148

Zamirinejad, S., Hojjat, S. K., Golzari, M., Borjali, A., & Akaberi, A. (2014). Effectiveness of resilience training versus cognitive therapy on reduction of depression in female Iranian college students. Issues in mental health nursing, 35(6), 480-488. https://doi.org/10.3109/01612840.2013.879628

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Glimpses of Teaching in the New Normal: Changes, Challenges, and Chances

The current context on virtual education has provided a plethora of studies investigating educational institutions’ response strategies to remote and online learning formats. However, to provide a much-grounded description of the realities in the field, this study explored the role of teachers in the virtual learning environment through their narratives reflective of their experiences. Furthermore, it employed a qualitative narrative and descriptive research method anchored on the tenets of Husserlian descriptive phenomenology. Six higher education professors from different colleges and universities in Central Visayas, Philippines served as the participants of the study. Data were collected from in-depth interviews done virtually via Zoom. Based on participant narratives, the following emerged as themes: changes, challenges, and chances, respectively, in all the teaching-learning phases, from preparation and implementation to assessment. These changes , challenges , and chances shared by the participants have shed light on teaching being a multifaceted profession, putting emphasis on teachers as innovators of change. Thus, it is recommended that colleges and universities should establish an institutional based framework for emergency remote teaching. The framework should highlight policies on virtual education, upscale and upskill teachers, address learning losses, and promote strategies to build resilience in students and teachers.  

https://doi.org/10.26803/ijlter.21.4.16

Amir, L. R., Tanti, I., Maharani, D. A., Wimardhani, Y. S., Sulijaya, B., & Puspitawati, R. (2020). Student perspective of classroom and distance learning during COVID-19 pandemic in the undergraduate dental study program Universitas Indonesia. BMC Medical Education, 20, 392. https://doi.org/10.1186/s12909-020-02312-0

Archambault, L. M. (2011). The practitioner’s perspective on teacher education: Preparing for the online classroom. Journal of Technology and Teacher Education, 19(1), 73-91. https://www.learntechlib.org/primary/p/31410/

Bacus, R. C., & Alda, R. C. (2022). Senior high school teaching: A phenomenological inquiry. Malaysian Journal of Learning & Instruction, 19(1), 242-276. https://doi.org/10.32890/mjli2022.19.1.9

Colaizzi, P. F. (1978). Psychological research as the phenomenologist views it. In R. S. Valle, & K. Mark (Eds.), Existential phenomenological alternatives for psychology (pp. 48-71). Oxford University Press.

Dhawan, S. (2020). Online learning: A panacea in the time of COVID-19 crisis. Sage Journal, 49(1), 5-22. https://doi.org/10.1177/0047239520934018

Griffin, J. (2020). Teacher observation, feedback, and support in the time of COVID-19: Guidance for virtual learning. Center on Great Teachers and Leaders at the American Institutes for Research. https://files.eric.ed.gov/fulltext/ED610628.pdf

Guangul, F. M., Suhail, A. H., Khalit, M. I., & Khidhir, B. (2020). Challenges of remote assessment in higher education in the context of COVID-19: A case study of Middle East College. Educational Assessment, Evaluation and Accountability, 32, 519 535. https://doi.org/10.1007/s11092-020-09340-w

Hattie, J. (1999). Influences on student learning. University of Auckland. https://cdn.auckland.ac.nz/assets/education/about/research/documents/influences-on-student-learning.pdf

Izhar, N. A., Na, Y. M. A., & Na, K. S. (2021). Teaching in the time of COVID-19: The challenges faced by teachers in initiating online class sessions. International Journal of Academic Research in Business and Social Sciences, 11(2), 1294-1306. https://hrmars.com/papers_submitted/9205/teaching-in-the-time-of-covid-19-the-challenges-faced-by-teachers-in-initiating-online-class-sessions.pdf

Joaquin, J., Biana, H., & Dacela, M. (2020). The Philippine higher education sector in the time of COVID-19. Frontiers in Education. https://doi.org/10.3389/feduc.2020.576371

Koehler, M., Mishra, P., Kereluik, K., Shin, T., & Graham, C. (2004). The technological pedagogical content knowledge framework. In J. M. Spector et al. (Eds.), Handbook of research on educational communications and technology (pp. 101-111). http://www.matt koehler.com/publications/Koehler_et_al_2014.pdf

Lambert, V. A., & Lambert, C. E. (2012). Qualitative descriptive research: An acceptable design. Pacific Rim International Journal of Nursing Research, 16(4), 255-256. https://he02.tci-thaijo.org/index.php/PRIJNR/article/view/5805

Lewis, C., & Abdul-Hamid, H. (2006). Implementing effective online teaching practices: Voices of exemplary faculty. Innovative Higher Education, 31(2). 83-98. https://doi.org/10.1007/s10755-006- 9010-z

Mahyoob, M. (2020). Challenges of e-learning during the COVID-19 pandemic experienced by EFL learners. Arab World English Journal, 11(4), 351-362. https://dx.doi.org/10.24093/awej/vol11no4.23

Mananay, J. (2018). The lived experience of college teachers on the use of social media in teaching. International Journal of Research Science & Management, 5(8), 106-114. https://doi.org/10.5281/zenodo.1401358

Merriam-Webster. (n.d.). Change. Merriam-Webster.com dictionary. Retrieved October 15, 2021, from https://www.merriam- webster.com/dictionary/change

Miyagawa, S., & Perdue, M. (2020). A renewed focus on the practice of teaching. Inside Higher Education. https://www.insidehighered.com/advice/2020/11/11/switching-online-teaching-during-pandemic-may-fundamentally-change-how-faculty

Navarosa, D., & Fernando, C. (2020). Education in the new normal: A closer look at the Philippines’ learning solutions amidst the pandemic. UNDERSCORE Online. https://medium.com/underscore-online/education-in-the-new-normal-a-closer-look-at-philippines-learning-solutions-amidst-the-pandemic-ba0adc339d8f

Nicol, D. (2010). From monologue to dialogue: Improving written feedback processes in mass higher education. Assessment and Evaluation in Higher Education, 35(5), 501 517. https://doi.org/10.1080/02602931003786559

Republic of the Philippines. Commission on Higher Education (CHED). (2020). CHED memorandum order no. 4, series of 2020: Guidelines on the implementation of flexible learning. https://ched.gov.ph/wp-content/uploads/CMO-No.-4-s.-2020-Guidelines-on-the-Implementation-of-Flexible-Learning.pdf

Rotas, E. E., & Cahapay, M. B. (2020). Difficulties in remote learning: Voices of Philippine university students in the wake of COVID-19 crisis. Asian Journal of Distance Education, 15(2), 147-158. https://doi.org/10.5281/zenodo.4299835

Saxena, A. (2020). The changing role of the educator in the new normal. Education Digest. https://www.highereducationdigest.com/the-changing-role-of-the-educator-in-the-new-normal/

Singh, V., & Thurman, A. (2019). How many ways can we define online learning? A systematic literature review of definitions of online learning (1988–2018). American Journal of Distance Education, 33(4), 289-306. https://doi.org/10.1080/08923647.2019.1663082

West, E., Jones, P., & Semon, S. (2012). Promoting community for online learners in special education. Journal of Digital Learning in Teacher Education, 28(3), 108-116. https://doi.org/10.1080/21532974.2012.10784688

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Lived Experiences of Teachers in Teaching Contextualized Mathematics During the New Normal Education

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Blended learning: the new normal and emerging technologies

• Charles Dziuban 1 ,
• Charles R. Graham 2 ,
• Patsy D. Moskal   ORCID: orcid.org/0000-0001-6376-839X 1 ,
• Anders Norberg 3 &
• Nicole Sicilia 1  

International Journal of Educational Technology in Higher Education volume  15 , Article number:  3 ( 2018 ) Cite this article

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This study addressed several outcomes, implications, and possible future directions for blended learning (BL) in higher education in a world where information communication technologies (ICTs) increasingly communicate with each other. In considering effectiveness, the authors contend that BL coalesces around access, success, and students’ perception of their learning environments. Success and withdrawal rates for face-to-face and online courses are compared to those for BL as they interact with minority status. Investigation of student perception about course excellence revealed the existence of robust if-then decision rules for determining how students evaluate their educational experiences. Those rules were independent of course modality, perceived content relevance, and expected grade. The authors conclude that although blended learning preceded modern instructional technologies, its evolution will be inextricably bound to contemporary information communication technologies that are approximating some aspects of human thought processes.

Introduction

Blended learning and research issues.

Blended learning (BL), or the integration of face-to-face and online instruction (Graham 2013 ), is widely adopted across higher education with some scholars referring to it as the “new traditional model” (Ross and Gage 2006 , p. 167) or the “new normal” in course delivery (Norberg et al. 2011 , p. 207). However, tracking the accurate extent of its growth has been challenging because of definitional ambiguity (Oliver and Trigwell 2005 ), combined with institutions’ inability to track an innovative practice, that in many instances has emerged organically. One early nationwide study sponsored by the Sloan Consortium (now the Online Learning Consortium) found that 65.2% of participating institutions of higher education (IHEs) offered blended (also termed hybrid ) courses (Allen and Seaman 2003 ). A 2008 study, commissioned by the U.S. Department of Education to explore distance education in the U.S., defined BL as “a combination of online and in-class instruction with reduced in-class seat time for students ” (Lewis and Parsad 2008 , p. 1, emphasis added). Using this definition, the study found that 35% of higher education institutions offered blended courses, and that 12% of the 12.2 million documented distance education enrollments were in blended courses.

The 2017 New Media Consortium Horizon Report found that blended learning designs were one of the short term forces driving technology adoption in higher education in the next 1–2 years (Adams Becker et al. 2017 ). Also, blended learning is one of the key issues in teaching and learning in the EDUCAUSE Learning Initiative’s 2017 annual survey of higher education (EDUCAUSE 2017 ). As institutions begin to examine BL instruction, there is a growing research interest in exploring the implications for both faculty and students. This modality is creating a community of practice built on a singular and pervasive research question, “How is blended learning impacting the teaching and learning environment?” That question continues to gain traction as investigators study the complexities of how BL interacts with cognitive, affective, and behavioral components of student behavior, and examine its transformation potential for the academy. Those issues are so compelling that several volumes have been dedicated to assembling the research on how blended learning can be better understood (Dziuban et al. 2016 ; Picciano et al. 2014 ; Picciano and Dziuban 2007 ; Bonk and Graham 2007 ; Kitchenham 2011 ; Jean-François 2013 ; Garrison and Vaughan 2013 ) and at least one organization, the Online Learning Consortium, sponsored an annual conference solely dedicated to blended learning at all levels of education and training (2004–2015). These initiatives address blended learning in a wide variety of situations. For instance, the contexts range over K-12 education, industrial and military training, conceptual frameworks, transformational potential, authentic assessment, and new research models. Further, many of these resources address students’ access, success, withdrawal, and perception of the degree to which blended learning provides an effective learning environment.

Currently the United States faces a widening educational gap between our underserved student population and those communities with greater financial and technological resources (Williams 2016 ). Equal access to education is a critical need, one that is particularly important for those in our underserved communities. Can blended learning help increase access thereby alleviating some of the issues faced by our lower income students while resulting in improved educational equality? Although most indicators suggest “yes” (Dziuban et al. 2004 ), it seems that, at the moment, the answer is still “to be determined.” Quality education presents a challenge, evidenced by many definitions of what constitutes its fundamental components (Pirsig 1974 ; Arum et al. 2016 ). Although progress has been made by initiatives, such as, Quality Matters ( 2016 ), the OLC OSCQR Course Design Review Scorecard developed by Open SUNY (Open SUNY n.d. ), the Quality Scorecard for Blended Learning Programs (Online Learning Consortium n.d. ), and SERVQUAL (Alhabeeb 2015 ), the issue is by no means resolved. Generally, we still make quality education a perceptual phenomenon where we ascribe that attribute to a course, educational program, or idea, but struggle with precisely why we reached that decision. Searle ( 2015 ), summarizes the problem concisely arguing that quality does not exist independently, but is entirely observer dependent. Pirsig ( 1974 ) in his iconic volume on the nature of quality frames the context this way,

“There is such thing as Quality, but that as soon as you try to define it, something goes haywire. You can’t do it” (p. 91).

Therefore, attempting to formulate a semantic definition of quality education with syntax-based metrics results in what O’Neil (O'Neil 2017 ) terms surrogate models that are rough approximations and oversimplified. Further, the derived metrics tend to morph into goals or benchmarks, losing their original measurement properties (Goodhart 1975 ).

Information communication technologies in society and education

Blended learning forces us to consider the characteristics of digital technology, in general, and information communication technologies (ICTs), more specifically. Floridi ( 2014 ) suggests an answer proffered by Alan Turing: that digital ICTs can process information on their own, in some sense just as humans and other biological life. ICTs can also communicate information to each other, without human intervention, but as linked processes designed by humans. We have evolved to the point where humans are not always “in the loop” of technology, but should be “on the loop” (Floridi 2014 , p. 30), designing and adapting the process. We perceive our world more and more in informational terms, and not primarily as physical entities (Floridi 2008 ). Increasingly, the educational world is dominated by information and our economies rest primarily on that asset. So our world is also blended, and it is blended so much that we hardly see the individual components of the blend any longer. Floridi ( 2014 ) argues that the world has become an “infosphere” (like biosphere) where we live as “inforgs.” What is real for us is shifting from the physical and unchangeable to those things with which we can interact.

Floridi also helps us to identify the next blend in education, involving ICTs, or specialized artificial intelligence (Floridi 2014 , 25; Norberg 2017 , 65). Learning analytics, adaptive learning, calibrated peer review, and automated essay scoring (Balfour 2013 ) are advanced processes that, provided they are good interfaces, can work well with the teacher— allowing him or her to concentrate on human attributes such as being caring, creative, and engaging in problem-solving. This can, of course, as with all technical advancements, be used to save resources and augment the role of the teacher. For instance, if artificial intelligence can be used to work along with teachers, allowing them more time for personal feedback and mentoring with students, then, we will have made a transformational breakthrough. The Edinburg University manifesto for teaching online says bravely, “Automation need not impoverish education – we welcome our robot colleagues” (Bayne et al. 2016 ). If used wisely, they will teach us more about ourselves, and about what is truly human in education. This emerging blend will also affect curricular and policy questions, such as the what? and what for? The new normal for education will be in perpetual flux. Floridi’s ( 2014 ) philosophy offers us tools to understand and be in control and not just sit by and watch what happens. In many respects, he has addressed the new normal for blended learning.

Literature of blended learning

A number of investigators have assembled a comprehensive agenda of transformative and innovative research issues for blended learning that have the potential to enhance effectiveness (Garrison and Kanuka 2004 ; Picciano 2009 ). Generally, research has found that BL results in improvement in student success and satisfaction, (Dziuban and Moskal 2011 ; Dziuban et al. 2011 ; Means et al. 2013 ) as well as an improvement in students’ sense of community (Rovai and Jordan 2004 ) when compared with face-to-face courses. Those who have been most successful at blended learning initiatives stress the importance of institutional support for course redesign and planning (Moskal et al. 2013 ; Dringus and Seagull 2015 ; Picciano 2009 ; Tynan et al. 2015 ). The evolving research questions found in the literature are long and demanding, with varied definitions of what constitutes “blended learning,” facilitating the need for continued and in-depth research on instructional models and support needed to maximize achievement and success (Dringus and Seagull 2015 ; Bloemer and Swan 2015 ).

Educational access

The lack of access to educational technologies and innovations (sometimes termed the digital divide) continues to be a challenge with novel educational technologies (Fairlie 2004 ; Jones et al. 2009 ). One of the promises of online technologies is that they can increase access to nontraditional and underserved students by bringing a host of educational resources and experiences to those who may have limited access to on-campus-only higher education. A 2010 U.S. report shows that students with low socioeconomic status are less likely to obtain higher levels of postsecondary education (Aud et al. 2010 ). However, the increasing availability of distance education has provided educational opportunities to millions (Lewis and Parsad 2008 ; Allen et al. 2016 ). Additionally, an emphasis on open educational resources (OER) in recent years has resulted in significant cost reductions without diminishing student performance outcomes (Robinson et al. 2014 ; Fischer et al. 2015 ; Hilton et al. 2016 ).

Unfortunately, the benefits of access may not be experienced evenly across demographic groups. A 2015 study found that Hispanic and Black STEM majors were significantly less likely to take online courses even when controlling for academic preparation, socioeconomic status (SES), citizenship, and English as a second language (ESL) status (Wladis et al. 2015 ). Also, questions have been raised about whether the additional access afforded by online technologies has actually resulted in improved outcomes for underserved populations. A distance education report in California found that all ethnic minorities (except Asian/Pacific Islanders) completed distance education courses at a lower rate than the ethnic majority (California Community Colleges Chancellor’s Office 2013 ). Shea and Bidjerano ( 2014 , 2016 ) found that African American community college students who took distance education courses completed degrees at significantly lower rates than those who did not take distance education courses. On the other hand, a study of success factors in K-12 online learning found that for ethnic minorities, only 1 out of 15 courses had significant gaps in student test scores (Liu and Cavanaugh 2011 ). More research needs to be conducted, examining access and success rates for different populations, when it comes to learning in different modalities, including fully online and blended learning environments.

Framing a treatment effect

Over the last decade, there have been at least five meta-analyses that have addressed the impact of blended learning environments and its relationship to learning effectiveness (Zhao et al. 2005 ; Sitzmann et al. 2006 ; Bernard et al. 2009 ; Means et al. 2010 , 2013 ; Bernard et al. 2014 ). Each of these studies has found small to moderate positive effect sizes in favor of blended learning when compared to fully online or traditional face-to-face environments. However, there are several considerations inherent in these studies that impact our understanding the generalizability of outcomes.

Dziuban and colleagues (Dziuban et al. 2015 ) analyzed the meta-analyses conducted by Means and her colleagues (Means et al. 2013 ; Means et al. 2010 ), concluding that their methods were impressive as evidenced by exhaustive study inclusion criteria and the use of scale-free effect size indices. The conclusion, in both papers, was that there was a modest difference in multiple outcome measures for courses featuring online modalities—in particular, blended courses. However, with blended learning especially, there are some concerns with these kinds of studies. First, the effect sizes are based on the linear hypothesis testing model with the underlying assumption that the treatment and the error terms are uncorrelated, indicating that there is nothing else going on in the blending that might confound the results. Although the blended learning articles (Means et al. 2010 ) were carefully vetted, the assumption of independence is tenuous at best so that these meta-analysis studies must be interpreted with extreme caution.

There is an additional concern with blended learning as well. Blends are not equivalent because of the manner on which they are configured. For instance, a careful reading of the sources used in the Means, et al. papers will identify, at minimum, the following blending techniques: laboratory assessments, online instruction, e-mail, class web sites, computer laboratories, mapping and scaffolding tools, computer clusters, interactive presentations and e-mail, handwriting capture, evidence-based practice, electronic portfolios, learning management systems, and virtual apparatuses. These are not equivalent ways in which to configure courses, and such nonequivalence constitutes the confounding we describe. We argue here that, in actuality, blended learning is a general construct in the form of a boundary object (Star and Griesemer 1989 ) rather than a treatment effect in the statistical sense. That is, an idea or concept that can support a community of practice, but is weakly defined fostering disagreement in the general group. Conversely, it is stronger in individual constituencies. For instance, content disciplines (i.e. education, rhetoric, optics, mathematics, and philosophy) formulate a more precise definition because of commonly embraced teaching and learning principles. Quite simply, the situation is more complicated than that, as Leonard Smith ( 2007 ) says after Tolstoy,

“All linear models resemble each other, each non nonlinear system is unique in its own way” (p. 33).

This by no means invalidates these studies, but effect size associated with blended learning should be interpreted with caution where the impact is evaluated within a particular learning context.

Study objectives

This study addressed student access by examining success and withdrawal rates in the blended learning courses by comparing them to face-to-face and online modalities over an extended time period at the University of Central Florida. Further, the investigators sought to assess the differences in those success and withdrawal rates with the minority status of students. Secondly, the investigators examined the student end-of-course ratings of blended learning and other modalities by attempting to develop robust if-then decision rules about what characteristics of classes and instructors lead students to assign an “excellent” value to their educational experience. Because of the high stakes nature of these student ratings toward faculty promotion, awards, and tenure, they act as a surrogate measure for instructional quality. Next, the investigators determined the conditional probabilities for students conforming to the identified rule cross-referenced by expected grade, the degree to which they desired to take the course, and course modality.

Student grades by course modality were recoded into a binary variable with C or higher assigned a value of 1, and remaining values a 0. This was a declassification process that sacrificed some specificity but compensated for confirmation bias associated with disparate departmental policies regarding grade assignment. At the measurement level this was an “on track to graduation index” for students. Withdrawal was similarly coded by the presence or absence of its occurrence. In each case, the percentage of students succeeding or withdrawing from blended, online or face-to-face courses was calculated by minority and non-minority status for the fall 2014 through fall 2015 semesters.

Next, a classification and regression tree (CART) analysis (Brieman et al. 1984 ) was performed on the student end-of-course evaluation protocol ( Appendix 1 ). The dependent measure was a binary variable indicating whether or not a student assigned an overall rating of excellent to his or her course experience. The independent measures in the study were: the remaining eight rating items on the protocol, college membership, and course level (lower undergraduate, upper undergraduate, and graduate). Decision trees are efficient procedures for achieving effective solutions in studies such as this because with missing values imputation may be avoided with procedures such as floating methods and the surrogate formation (Brieman et al. 1984 , Olshen et al. 1995 ). For example, a logistic regression method cannot efficiently handle all variables under consideration. There are 10 independent variables involved here; one variable has three levels, another has nine, and eight have five levels each. This means the logistic regression model must incorporate more than 50 dummy variables and an excessively large number of two-way interactions. However, the decision-tree method can perform this analysis very efficiently, permitting the investigator to consider higher order interactions. Even more importantly, decision trees represent appropriate methods in this situation because many of the variables are ordinally scaled. Although numerical values can be assigned to each category, those values are not unique. However, decision trees incorporate the ordinal component of the variables to obtain a solution. The rules derived from decision trees have an if-then structure that is readily understandable. The accuracy of these rules can be assessed with percentages of correct classification or odds-ratios that are easily understood. The procedure produces tree-like rule structures that predict outcomes.

The model-building procedure for predicting overall instructor rating

For this study, the investigators used the CART method (Brieman et al. 1984 ) executed with SPSS 23 (IBM Corp 2015 ). Because of its strong variance-sharing tendencies with the other variables, the dependent measure for the analysis was the rating on the item Overall Rating of the Instructor , with the previously mentioned indicator variables (college, course level, and the remaining 8 questions) on the instrument. Tree methods are recursive, and bisect data into subgroups called nodes or leaves. CART analysis bases itself on: data splitting, pruning, and homogeneous assessment.

Splitting the data into two (binary) subsets comprises the first stage of the process. CART continues to split the data until the frequencies in each subset are either very small or all observations in a subset belong to one category (e.g., all observations in a subset have the same rating). Usually the growing stage results in too many terminate nodes for the model to be useful. CART solves this problem using pruning methods that reduce the dimensionality of the system.

The final stage of the analysis involves assessing homogeneousness in growing and pruning the tree. One way to accomplish this is to compute the misclassification rates. For example, a rule that produces a .95 probability that an instructor will receive an excellent rating has an associated error of 5.0%.

Implications for using decision trees

Although decision-tree techniques are effective for analyzing datasets such as this, the reader should be aware of certain limitations. For example, since trees use ranks to analyze both ordinal and interval variables, information can be lost. However, the most serious weakness of decision tree analysis is that the results can be unstable because small initial variations can lead to substantially different solutions.

For this study model, these problems were addressed with the k-fold cross-validation process. Initially the dataset was partitioned randomly into 10 subsets with an approximately equal number of records in each subset. Each cohort is used as a test partition, and the remaining subsets are combined to complete the function. This produces 10 models that are all trained on different subsets of the original dataset and where each has been used as the test partition one time only.

Although computationally dense, CART was selected as the analysis model for a number of reasons— primarily because it provides easily interpretable rules that readers will be able evaluate in their particular contexts. Unlike many other multivariate procedures that are even more sensitive to initial estimates and require a good deal of statistical sophistication for interpretation, CART has an intuitive resonance with researcher consumers. The overriding objective of our choice of analysis methods was to facilitate readers’ concentration on our outcomes rather than having to rely on our interpretation of the results.

Institution-level evaluation: Success and withdrawal

The University of Central Florida (UCF) began a longitudinal impact study of their online and blended courses at the start of the distributed learning initiative in 1996. The collection of similar data across multiple semesters and academic years has allowed UCF to monitor trends, assess any issues that may arise, and provide continual support for both faculty and students across varying demographics. Table  1 illustrates the overall success rates in blended, online and face-to-face courses, while also reporting their variability across minority and non-minority demographics.

While success (A, B, or C grade) is not a direct reflection of learning outcomes, this overview does provide an institutional level indication of progress and possible issues of concern. BL has a slight advantage when looking at overall success and withdrawal rates. This varies by discipline and course, but generally UCF’s blended modality has evolved to be the best of both worlds, providing an opportunity for optimizing face-to-face instruction through the effective use of online components. These gains hold true across minority status. Reducing on-ground time also addresses issues that impact both students and faculty such as parking and time to reach class. In addition, UCF requires faculty to go through faculty development tailored to teaching in either blended or online modalities. This 8-week faculty development course is designed to model blended learning, encouraging faculty to redesign their course and not merely consider blended learning as a means to move face-to-face instructional modules online (Cobb et al. 2012 ; Lowe 2013 ).

Withdrawal (Table  2 ) from classes impedes students’ success and retention and can result in delayed time to degree, incurred excess credit hour fees, or lost scholarships and financial aid. Although grades are only a surrogate measure for learning, they are a strong predictor of college completion. Therefore, the impact of any new innovation on students’ grades should be a component of any evaluation. Once again, the blended modality is competitive and in some cases results in lower overall withdrawal rates than either fully online or face-to-face courses.

The students’ perceptions of their learning environments

Other potentially high-stakes indicators can be measured to determine the impact of an innovation such as blended learning on the academy. For instance, student satisfaction and attitudes can be measured through data collection protocols, including common student ratings, or student perception of instruction instruments. Given that those ratings often impact faculty evaluation, any negative reflection can derail the successful implementation and scaling of an innovation by disenfranchised instructors. In fact, early online and blended courses created a request by the UCF faculty senate to investigate their impact on faculty ratings as compared to face-to-face sections. The UCF Student Perception of Instruction form is released automatically online through the campus web portal near the end of each semester. Students receive a splash page with a link to each course’s form. Faculty receive a scripted email that they can send to students indicating the time period that the ratings form will be available. The forms close at the beginning of finals week. Faculty receive a summary of their results following the semester end.

The instrument used for this study was developed over a ten year period by the faculty senate of the University of Central Florida, recognizing the evolution of multiple course modalities including blended learning. The process involved input from several constituencies on campus (students, faculty, administrators, instructional designers, and others), in attempt to provide useful formative and summative instructional information to the university community. The final instrument was approved by resolution of the senate and, currently, is used across the university. Students’ rating of their classes and instructors comes with considerable controversy and disagreement with researchers aligning themselves on both sides of the issue. Recently, there have been a number of studies criticizing the process (Uttl et al. 2016 ; Boring et al. 2016 ; & Stark and Freishtat 2014 ). In spite of this discussion, a viable alternative has yet to emerge in higher education. So in the foreseeable future, the process is likely to continue. Therefore, with an implied faculty senate mandate this study was initiated by this team of researchers.

Prior to any analysis of the item responses collected in this campus-wide student sample, the psychometric quality (domain sampling) of the information yielded by the instrument was assessed. Initially, the reliability (internal consistency) was derived using coefficient alpha (Cronbach 1951 ). In addition, Guttman ( 1953 ) developed a theorem about item properties that leads to evidence about the quality of one’s data, demonstrating that as the domain sampling properties of items improve, the inverse of the correlation matrix among items will approach a diagonal. Subsequently, Kaiser and Rice ( 1974 ) developed the measure of sampling adequacy (MSA) that is a function of the Guttman Theorem. The index has an upper bound of one with Kaiser offering some decision rules for interpreting the value of MSA. If the value of the index is in the .80 to .99 range, the investigator has evidence of an excellent domain sample. Values in the .70s signal an acceptable result, and those in the .60s indicate data that are unacceptable. Customarily, the MSA has been used for data assessment prior to the application of any dimensionality assessments. Computation of the MSA value gave the investigators a benchmark for the construct validity of the items in this study. This procedure has been recommended by Dziuban and Shirkey ( 1974 ) prior to any latent dimension analysis and was used with the data obtained for this study. The MSA for the current instrument was .98 suggesting excellent domain sampling properties with an associated alpha reliability coefficient of .97 suggesting superior internal consistency. The psychometric properties of the instrument were excellent with both measures.

The online student ratings form presents an electronic data set each semester. These can be merged across time to create a larger data set of completed ratings for every course across each semester. In addition, captured data includes course identification variables including prefix, number, section and semester, department, college, faculty, and class size. The overall rating of effectiveness is used most heavily by departments and faculty in comparing across courses and modalities (Table  3 ).

The finally derived tree (decision rules) included only three variables—survey items that asked students to rate the instructor’s effectiveness at:

Helping students achieve course objectives,

Creating an environment that helps students learn, and

Communicating ideas and information.

None of the demographic variables associated with the courses contributed to the final model. The final rule specifies that if a student assigns an excellent rating to those three items, irrespective of their status on any other condition, the probability is .99 that an instructor will receive an overall rating of excellent. The converse is true as well. A poor rating on all three of those items will lead to a 99% chance of an instructor receiving an overall rating of poor.

Tables  4 , 5 and 6 present a demonstration of the robustness of the CART rule for variables on which it was not developed: expected course grade, desire to take the course and modality.

In each case, irrespective of the marginal probabilities, those students conforming to the rule have a virtually 100% chance of seeing the course as excellent. For instance, 27% of all students expecting to fail assigned an excellent rating to their courses, but when they conformed to the rule the percentage rose to 97%. The same finding is true when students were asked about their desire to take the course with those who strongly disagreed assigning excellent ratings to their courses 26% of the time. However, for those conforming to the rule, that category rose to 92%. When course modality is considered in the marginal sense, blended learning is rated as the preferred choice. However, from Table  6 we can observe that the rule equates student assessment of their learning experiences. If they conform to the rule, they will see excellence.

This study addressed increasingly important issues of student success, withdrawal and perception of the learning environment across multiple course modalities. Arguably these components form the crux of how we will make more effective decisions about how blended learning configures itself in the new normal. The results reported here indicate that blending maintains or increases access for most student cohorts and produces improved success rates for minority and non-minority students alike. In addition, when students express their beliefs about the effectiveness of their learning environments, blended learning enjoys the number one rank. However, upon more thorough analysis of key elements students view as important in their learning, external and demographic variables have minimal impact on those decisions. For example college (i.e. discipline) membership, course level or modality, expected grade or desire to take a particular course have little to do with their course ratings. The characteristics they view as important relate to clear establishment and progress toward course objectives, creating an effective learning environment and the instructors’ effective communication. If in their view those three elements of a course are satisfied they are virtually guaranteed to evaluate their educational experience as excellent irrespective of most other considerations. While end of course rating protocols are summative the three components have clear formative characteristics in that each one is directly related to effective pedagogy and is responsive to faculty development through units such as the faculty center for teaching and learning. We view these results as encouraging because they offer potential for improving the teaching and learning process in an educational environment that increases the pressure to become more responsive to contemporary student lifestyles.

Clearly, in this study we are dealing with complex adaptive systems that feature the emergent property. That is, their primary agents and their interactions comprise an environment that is more than the linear combination of their individual elements. Blending learning, by interacting with almost every aspect of higher education, provides opportunities and challenges that we are not able to fully anticipate.

This pedagogy alters many assumptions about the most effective way to support the educational environment. For instance, blending, like its counterpart active learning, is a personal and individual phenomenon experienced by students. Therefore, it should not be surprising that much of what we have called blended learning is, in reality, blended teaching that reflects pedagogical arrangements. Actually, the best we can do for assessing impact is to use surrogate measures such as success, grades, results of assessment protocols, and student testimony about their learning experiences. Whether or not such devices are valid indicators remains to be determined. We may be well served, however, by changing our mode of inquiry to blended teaching.

Additionally, as Norberg ( 2017 ) points out, blended learning is not new. The modality dates back, at least, to the medieval period when the technology of textbooks was introduced into the classroom where, traditionally, the professor read to the students from the only existing manuscript. Certainly, like modern technologies, books were disruptive because they altered the teaching and learning paradigm. Blended learning might be considered what Johnson describes as a slow hunch (2010). That is, an idea that evolved over a long period of time, achieving what Kaufmann ( 2000 ) describes as the adjacent possible – a realistic next step occurring in many iterations.

The search for a definition for blended learning has been productive, challenging, and, at times, daunting. The definitional continuum is constrained by Oliver and Trigwell ( 2005 ) castigation of the concept for its imprecise vagueness to Sharpe et al.’s ( 2006 ) notion that its definitional latitude enhances contextual relevance. Both extremes alter boundaries such as time, place, presence, learning hierarchies, and space. The disagreement leads us to conclude that Lakoff’s ( 2012 ) idealized cognitive models i.e. arbitrarily derived concepts (of which blended learning might be one) are necessary if we are to function effectively. However, the strong possibility exists that blended learning, like quality, is observer dependent and may not exist outside of our perceptions of the concept. This, of course, circles back to the problem of assuming that blending is a treatment effect for point hypothesis testing and meta-analysis.

Ultimately, in this article, we have tried to consider theoretical concepts and empirical findings about blended learning and their relationship to the new normal as it evolves. Unfortunately, like unresolved chaotic solutions, we cannot be sure that there is an attractor or that it will be the new normal. That being said, it seems clear that blended learning is the harbinger of substantial change in higher education and will become equally impactful in K-12 schooling and industrial training. Blended learning, because of its flexibility, allows us to maximize many positive education functions. If Floridi ( 2014 ) is correct and we are about to live in an environment where we are on the communication loop rather than in it, our educational future is about to change. However, if our results are correct and not over fit to the University of Central Florida and our theoretical speculations have some validity, the future of blended learning should encourage us about the coming changes.

Adams Becker, S., Cummins, M., Davis, A., Freeman, A., Hall Giesinger, C., & Ananthanarayanan, V. (2017). NMC horizon report: 2017 higher Education Edition . Austin: The New Media Consortium.

Google Scholar  

Alhabeeb, A. M. (2015). The quality assessment of the services offered to the students of the College of Education at King Saud University using (SERVQUAL) method. Journal of Education and Practice , 6 (30), 82–93.

Allen, I. E., & Seaman, J. (2003). Sizing the opportunity: The quality and extent of online education in the United States, 2002 and 2003. Retrieved from http://files.eric.ed.gov/fulltext/ED530060.pdf

Allen, I. E., Seaman, J., Poulin, R., & Straut, T. T. (2016). Online report card: Tracking online education in the United States, 1–4. Retrieved from http://onlinelearningsurvey.com/reports/onlinereportcard.pdf

Arum, R., Roksa, J., & Cook, A. (2016). Improving quality in American higher education: Learning outcomes and assessments for the 21st century . San Francisco: Jossey-Bass.

Aud, S., Hussar, W., Planty, M., Snyder, T., Bianco, K., Fox, M. A., & Drake, L. (2010). The condition of education - 2010. Education, 4–29. https://doi.org/10.1037/e492172006-019

Balfour, S. P. (2013). Assessing writing in MOOCs: Automated essay scoring and calibrated peer review. Research and Practice in Assessment , 2013 (8), 40–48.

Bayne, S., Evans, P., Ewins, R.,Knox, J., Lamb, J., McLeod, H., O’Shea, C., Ross, J., Sheail, P. & Sinclair, C, (2016) Manifesto for teaching online. Digital Education at Edinburg University. Retrieved from https://onlineteachingmanifesto.wordpress.com/the-text/

Bernard, R. M., Abrami, P. C., Borokhovski, E., Wade, C. A., Tamim, R. M., Surkes, M. A., & Bethel, E. C. (2009). A meta-analysis of three types of interaction treatments in distance education. Review of Educational Research , 79 (3), 1243–1289. https://doi.org/10.3102/0034654309333844 .

Article   Google Scholar  

Bernard, R. M., Borokhovski, E., Schmid, R. F., Tamim, R. M., & Abrami, P. C. (2014). A meta-analysis of blended learning and technology use in higher education: From the general to the applied. Journal of Computing in Higher Education , 26 (1), 87–122.

Bloemer, W., & Swan, K. (2015). Investigating informal blending at the University of Illinois Springfield. In A. G. Picciano, C. D. Dziuban, & C. R. Graham (Eds.), Blended learning: Research perspectives , (vol. 2, pp. 52–69). New York: Routledge.

Bonk, C. J., & Graham, C. R. (2007). The handbook of blended learning: Global perspectives, local designs . San Francisco: Pfeiffer.

Boring, A., Ottoboni, K., & Stark, P.B. (2016). Student evaluations of teaching (mostly) do not measure teaching effectiveness. EGERA.

Brieman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and regression trees . New York: Chapman & Hall.

California Community Colleges Chancellor’s Office. (2013). Distance education report.

Cobb, C., deNoyelles, A., & Lowe, D. (2012). Influence of reduced seat time on satisfaction and perception of course development goals: A case study in faculty development. The Journal of Asynchronous Learning , 16 (2), 85–98.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika , 16 (3), 297–334 Retrieved from http://psych.colorado.edu/~carey/courses/psyc5112/readings/alpha_cronbach.pdf .

Article   MATH   Google Scholar  

Dringus, L. P., and A. B. Seagull. 2015. A five-year study of sustaining blended learning initiatives to enhance academic engagement in computer and information sciences campus courses. In Blended learning: Research perspectives. Vol. 2. Edited by A. G. Picciano, C. D. Dziuban, and C. R. Graham, 122-140. New York: Routledge.

Dziuban, C. D., & Shirkey, E. C. (1974). When is a correlation matrix appropriate for factor analysis? Some decision rules. Psychological Bulletin , 81(6), 358. https://doi.org/10.1037/h0036316 .

Dziuban, C., Hartman, J., Cavanagh, T., & Moskal, P. (2011). Blended courses as drivers of institutional transformation. In A. Kitchenham (Ed.), Blended learning across disciplines: Models for implementation , (pp. 17–37). Hershey: IGI Global.

Chapter   Google Scholar  

Dziuban, C., & Moskal, P. (2011). A course is a course is a course: Factor invariance in student evaluation of online, blended and face-to-face learning environments. The Internet and Higher Education , 14 (4), 236–241.

Dziuban, C., Moskal, P., Hermsdorfer, A., DeCantis, G., Norberg, A., & Bradford, G., (2015) A deconstruction of blended learning. Presented at the 11 th annual Sloan-C blended learning conference and workshop

Dziuban, C., Picciano, A. G., Graham, C. R., & Moskal, P. D. (2016). Conducting research in online and blended learning environments: New pedagogical frontiers . New York: Routledge, Taylor & Francis Group.

Dziuban, C. D., Hartman, J. L., & Moskal, P. D. (2004). Blended learning. EDUCAUSE Research Bulletin , 7 , 1–12.

EDUCAUSE. (2017) 2017 key issues in teaching & learning. Retrieved from https://www.EDUCAUSE.edu/eli/initiatives/key-issues-in-teaching-and-learning

Fairlie, R. (2004). Race and the digital divide. The B.E. Journal of Economic Analysis & Policy , 3 (1). https://doi.org/10.2202/1538-0645.1263 .

Fischer, L., Hilton, J., Robinson, T. J., & Wiley, D. (2015). A Multi-institutional Study of the Impact of Open Textbook Adoption on the Learning Outcomes of Post-secondary Students . Journal of Computing in Higher Education. https://doi.org/10.1007/s12528-015-9101-x .

Floridi, L. (2008). A defence of informational structural realism. Synthese , 161 (2), 219–253.

Article   MathSciNet   Google Scholar  

Floridi, L. (2014). The 4th revolution: How the infosphere is reshaping human reality . Oxford: Oxford University Press.

Garrison, D. R., & Vaughan, N. D. (2013). Blended learning in higher education , (1st ed., ). San Francisco: Jossey-Bass Print.

Garrison, D. R., & Kanuka, H. (2004). Blended learning: Uncovering its transformative potential in higher education. The Internet and Higher Education , 7 , 95–105.

Goodhart, C.A.E. (1975). “Problems of monetary management: The U.K. experience.” Papers in Monetary Economics. Reserve Bank of Australia. I.

Graham, C. R. (2013). Emerging practice and research in blended learning. In M. G. Moore (Ed.), Handbook of distance education , (3rd ed., pp. 333–350). New York: Routledge.

Guttman, L. (1953). Image theory for the structure of quantitative variates. Psychometrika , 18 , 277–296.

Article   MathSciNet   MATH   Google Scholar  

Hilton, J., Fischer, L., Wiley, D., & Williams, L. (2016). Maintaining momentum toward graduation: OER and the course throughput rate. International Review of Research in Open and Distance Learning , 17 (6) https://doi.org/10.19173/irrodl.v17i6.2686 .

IBM Corp. Released (2015). IBM SPSS statistics for windows, version 23.0 . Armonk: IBM Corp.

Jean-François, E. (2013). Transcultural blended learning and teaching in postsecondary education . Hershey: Information Science Reference.

Book   Google Scholar  

Jones, S., Johnson-Yale, C., Millermaier, S., & Pérez, F. S. (2009). U.S. college students’ internet use: Race, gender and digital divides. Journal of Computer-Mediated Communication , 14 (2), 244–264 https://doi.org/10.1111/j.1083-6101.2009.01439.x .

Kaiser, H. F., & Rice, J. (1974). Little Jiffy, Mark IV. Journal of Educational and Psychological Measurement , 34(1), 111–117.

Kaufmann, S. (2000). Investigations . New York: Oxford University Press.

Kitchenham, A. (2011). Blended learning across disciplines: Models for implementation . Hershey: Information Science Reference.

Lakoff, G. (2012). Women, fire, and dangerous things: What categories reveal about the mind . Chicago: The University of Chicago Press.

Lewis, L., & Parsad, B. (2008). Distance education at degree-granting postsecondary institutions : 2006–07 (NCES 2009–044) . Washington: Retrieved from http://nces.ed.gov/pubs2009/2009044.pdf .

Liu, F., & Cavanaugh, C. (2011). High enrollment course success factors in virtual school: Factors influencing student academic achievement. International Journal on E-Learning , 10 (4), 393–418.

Lowe, D. (2013). Roadmap of a blended learning model for online faculty development. Invited feature article in Distance Education Report , 17 (6), 1–7.

Means, B., Toyama, Y., Murphy, R., & Baki, M. (2013). The effectiveness of online and blended learning: A meta-analysis of the empirical literature. Teachers College Record , 115 (3), 1–47.

Means, B., Toyama, Y., Murphy, R., Kaia, M., & Jones, K. (2010). Evaluation of evidence-based practices in online learning . Washington: US Department of Education.

Moskal, P., Dziuban, C., & Hartman, J. (2013). Blended learning: A dangerous idea? The Internet and Higher Education , 18 , 15–23.

Norberg, A. (2017). From blended learning to learning onlife: ICTs, time and access in higher education (Doctoral dissertation, Umeå University).

Norberg, A., Dziuban, C. D., & Moskal, P. D. (2011). A time-based blended learning model. On the Horizon , 19 (3), 207–216. https://doi.org/10.1108/10748121111163913 .

Oliver, M., & Trigwell, K. (2005). Can ‘blended learning’ be redeemed? e-Learning , 2 (1), 17–25.

Olshen, Stone , Steinberg , and Colla (1995). CART classification and regression trees. Tree-structured nonparametric data analysis. Statistical algorithms. Salford systems interface and documentation. Salford Systems .

O'Neil, C. (2017). Weapons of math destruction: How big data increases inequality and threatens democracy . Broadway Books.

Online Learning Consortium. The OLC quality scorecard for blended learning programs. Retrieved from https://onlinelearningconsortium.org/consult/olc-quality-scorecard-blended-learning-programs/

Open SUNY. The OSCQR course design review scorecard. Retrieved from https://onlinelearningconsortium.org/consult/oscqr-course-design-review/

Picciano, A. G. (2009). Blending with purpose: The multimodal model. Journal of Asynchronous Learning Networks , 13 (1), 7–18.

Picciano, A. G., Dziuban, C., & Graham, C. R. (2014). Blended learning: Research perspectives , (vol. 2). New York: Routledge.

Picciano, A. G., & Dziuban, C. D. (2007). Blended learning: Research perspectives . Needham: The Sloan Consortium.

Pirsig, R. M. (1974). Zen and the art of motorcycle maintenance: An inquiry into values . New York: Morrow.

Quality Matters. (2016). About Quality Matters. Retrieved from https://www.qualitymatters.org/research

Robinson, T. J., Fischer, L., Wiley, D. A., & Hilton, J. (2014). The Impact of Open Textbooks on Secondary Science Learning Outcomes . Educational Researcher. https://doi.org/10.3102/0013189X14550275 .

Ross, B., & Gage, K. (2006). Global perspectives on blended learning: Insight from WebCT and our customers in higher education. In C. J. Bonk, & C. R. Graham (Eds.), Handbook of blended learning: Global perspectives, local designs , (pp. 155–168). San Francisco: Pfeiffer.

Rovai, A. P., & Jordan, H. M. (2004). Blended learning and sense of community: A comparative analysis with traditional and fully online graduate courses. International Review of Research in Open and Distance Learning , 5 (2), 1–13.

Searle, J. R. (2015). Seeing things as they are: A theory of perception . Chicago: Oxford University Press.

Sharpe, R., Benfield, G., Roberts, G., & Francis, R. (2006). The undergraduate experience of blended learning: A review of UK literature and research. The Higher Education Academy, (October 2006).

Shea, P., & Bidjerano, T. (2014). Does online learning impede degree completion? A national study of community college students. Computers and Education , 75 , 103–111 https://doi.org/10.1016/j.compedu.2014.02.009 .

Shea, P., & Bidjerano, T. (2016). A National Study of differences between distance and non-distance community college students in time to first associate degree attainment, transfer, and dropout. Online Learning , 20 (3), 14–15.

Sitzmann, T., Kraiger, K., Stewart, D., & Wisher, R. (2006). The comparative effectiveness of web-based and classroom instruction: A meta-analysis. Personnel Psychology , 59 (3), 623–664.

Smith, L. A. (2007). Chaos: a very short introduction . Oxford: Oxford University Press.

Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, translations and boundary objects: Amatuers and professionals in Berkely’s Museum of Vertebrate Zoology, 1907-39. Social Studies of Science , 19 (3), 387–420.

Stark, P. & Freishtat, R. (2014). An evaluation of course evaluations. ScienceOpen. Retrieved from https://www.stat.berkeley.edu/~stark/Preprints/evaluations14.pdf .

Tynan, B., Ryan, Y., & Lamont-Mills, A. (2015). Examining workload models in online and blended teaching. British Journal of Educational Technology , 46 (1), 5–15.

Uttl, B., White, C. A., & Gonzalez, D. W. (2016). Meta-analysis of faculty’s teaching effectiveness: Student evaluation of teaching ratings and student learning are not related. Studies in Educational Evaluation , 54 , 22–42.

Williams, J. (2016). College and the new class divide. Inside Higher Ed July 11, 2016.

Wladis, C., Hachey, A. C., & Conway, K. (2015). Which STEM majors enroll in online courses, and why should we care? The impact of ethnicity, gender, and non-traditional student characteristics. Computers and Education , 87 , 285–308 https://doi.org/10.1016/j.compedu.2015.06.010 .

Zhao, Y., Lei, J., Yan, B., Lai, C., & Tan, H. S. (2005). What makes the difference? A practical analysis of research on the effectiveness of distance education. Teachers College Record , 107 (8), 1836–1884. https://doi.org/10.1111/j.1467-9620.2005.00544.x .

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The authors acknowledge the contributions of several investigators and course developers from the Center for Distributed Learning at the University of Central Florida, the McKay School of Education at Brigham Young University, and Scholars at Umea University, Sweden. These professionals contributed theoretical and practical ideas to this research project and carefully reviewed earlier versions of this manuscript. The Authors gratefully acknowledge their support and assistance.

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Dziuban, C., Graham, C.R., Moskal, P.D. et al. Blended learning: the new normal and emerging technologies. Int J Educ Technol High Educ 15 , 3 (2018). https://doi.org/10.1186/s41239-017-0087-5

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Editorial article, editorial: eye tracking for stem education research: new perspectives.

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Editorial on the Research Topic Eye tracking for STEM education research: new perspectives

The integration of eye-tracking (ET) technology into STEM education research marks a pivotal shift toward a more nuanced educational methodologies' comprehension and improvement. The Research Topic titled “Eye-Tracking for STEM Education Research: New Perspectives,” introduced a series of pioneering studies that employ ET technology to dissect and understand the complex nature of learning in the realms of science, technology, engineering, and mathematics.

The issue commences with an insightful exploration of how the combination of ET and artificial intelligence is transforming the landscape of competency assessment within engineering education. The paper “Eye-Tracking and Artificial Intelligence for Competency Assessment in Engineering Education: A Review” ( Ndiaye et al. ) serves as a cornerstone for this edition, highlighting the interdisciplinary fusion that characterizes the subsequent contributions. This contribution also introduces a new dimension to the forefront of research in the field. Since the launch of this Research Topic, there has been a significant advancement in technology. Artificial Intelligence (AI) is undoubtedly an aspect that the global community must integrate, a notion that holds particularly true for STEM education and its research endeavors.

Further, the issue delves into the application of ET in specific STEM disciplines. In the domain of physics education, ET's role as a pivotal feedback mechanism in teacher training is explored, alongside its utility in analyzing the cognitive processes involved in understanding vector fields ( Hahn and Klein ). These investigations pave the way for similar explorations within chemistry education, where studies examine the relationship between pupil dilation and cognitive load during instructional video sessions ( Rodemer et al. ), therefore expanding the possibilities educators will soon have at their disposal to facilitate their students' problem-solving process in real time. This line of inquiry in this Research Topic was also elaborated in chemistry, showcasing ET's critical role in dissecting the problem-solving process from another perspective ( Tóthová and Rusek ). Additionally, the assessment of collaborative knowledge construction ( Lämsä et al. ) revealed various methods by which students form conceptions of scientific phenomena in their minds.

A standout contribution within mathematics education revolves around the use of ET in statistics, specifically in how students engage with data. This research sheds light on the nuanced ways students navigate statistical information, offering a fresh perspective on data interpretation and processing ( Schreiter and Vogel ) which is associated with students' graph interpretation processes ( Thomaneck et al. ) or the way they are able to link information from multiple representation ( Susac et al. ) – a discipline every student faces. This study also brought further confirmation into the sometimes debated ( Schindler and Lilienthal, 2019 ) eye-mind hypothesis ( Just and Carpenter, 1980 ).

The issue rounds off by emphasizing the significance of visual representation in STEM learning, particularly through a study on organic chemistry ( Braun et al. ). This research examined how students employ ET technology to navigate the drawing of complex molecular structures, underscoring the technology's value in understanding and enhancing visual learning strategies.

This Research Topic not only highlighted the multifaceted applications of eye tracking in STEM education research but also reinforces its potential to significantly enrich our comprehension of learning dynamics and instructional methods across diverse scientific disciplines. The authors provide multiple implications for further research which promises more interesting findings in the near future.

Author contributions

MR: Writing – original draft, Writing – review & editing. PK: Writing – review & editing. MS: Writing – review & editing.

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Just, M. A., and Carpenter, P. A. (1980). A theory of reading: from eye fixations to comprehension. Psychol. Rev. 87, 329.

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Schindler, M., and Lilienthal, A. J. (2019). Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry. Educ. Stu. Mathematics 101, 123–139. doi: 10.1007/s10649-019-9878-z

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Keywords: eye-tracking (ET), STEM - science technology engineering mathematics, education research, Research Topic, innovations in research methodology

Citation: Rusek M, Klein P and Schindler M (2024) Editorial: Eye tracking for STEM education research: new perspectives. Front. Educ. 9:1389962. doi: 10.3389/feduc.2024.1389962

Received: 22 February 2024; Accepted: 18 March 2024; Published: 26 March 2024.

Edited and reviewed by: Lianghuo Fan , East China Normal University, China

Copyright © 2024 Rusek, Klein and Schindler. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Martin Rusek, martin.rusek@pedf.cuni.cz

This article is part of the Research Topic

Eye Tracking for STEM Education Research: New Perspectives