what is the purpose of formative assessment in education

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What Is the Purpose of Formative Assessment? A Look at the Process of Monitoring Student Growth

The purpose of formative assessment in education is to monitor students’ progress over the course of their learning so that teachers have the feedback they need to adapt instruction in real time.

It's important to note that formative assessment is not a one-and-done test. Formative assessment is a continuous process of checking for understanding and adjusting instruction until the student has mastered the content or skill. This continuous process is what differentiates formative assessment from other forms of testing.

What Is Formative Assessment in Education?

According to the Standards for Educational and Psychological Testing , formative assessment is defined as “an assessment process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning with the goal of improving students’ achievement of intended instructional outcomes.” The key word in this definition is “process,” which highlights the defining feature of formative assessment as an activity, as opposed to a specific test.

Formative assessment takes place during a lesson, and provides information teachers need to adjust their instruction so that every learner in the class can master the content. This process differentiates formative assessment as an assessment for learning, as opposed to summative, which is an assessment of learning.

Formative assessment can determine student understanding relative to learning goals or standards and provide feedback about possible actions to be taken or alternative pathways to a goal. The optimal formative assessment system places the feedback loop at the center of instruction. The loop begins at any point to answer three critical questions about the student:

• Where are you now?
• Where are you going?
• How are you going to get there?

Delve deeper into the three types of assessment and the differences between summative and formative assessments on our blog.

What Is the Primary Purpose of Formative Assessment?

The primary purpose of formative assessment is to inform teachers about whether or not students are actually learning the material taught in day-to-day classroom instruction. Some examples include exit slips , low-stake quizzes, polls, think-pair-share, as well as digital tools for formative assessment . Since formative assessments are given as learning is taking place, teachers (or the technology they're using) can quickly adjust instruction to meet students’ needs in real time.

Note the Characteristics of Formative Assessment

The generally agreed upon characteristics of formative assessments include the focus on process and they are delivered informally, with greater frequency (even daily), and do not lend themselves to formal scoring and grading.

Why Formative Assessment Can Be Challenging

Formative assessment can be challenging in a high-stakes assessment environment that requires regular summative, quantifiable achievement indices. Under these circumstances, there can be pressure to use assessment information as a component of class grades, which could demotivate students. The use of data for a purely instructional purpose can become secondary or non-existent in this climate. Therefore, the challenge is to preserve a balance in the classroom that buffers against the impact of testing and shifts the instructional emphasis toward individual student progress, particularly for those who have been identified as low performing.

The Need for Professional Development

Some teachers will already be well versed in the formative assessment process, while others will need to develop the skills to do it successfully. Black and Wiliam, in their seminal 1998 paper “ Inside the Black Box ,” said formative assessment is "at the heart of effective teaching" and focuses on using classroom evidence to "adapt teaching to meet student needs."

Using formative assessment effectively in the classroom is, in general, a difficult skill for teachers to master. In order to have the greatest impact on formative assessment, professional development should target the intersection between teacher content knowledge and relevant pedagogical strategies for teaching content to students.

Research on teacher effectiveness has shown that content knowledge and pedagogical-content knowledge, which represents teaching practices tailored specifically to the domain, have a significant impact on student achievement. In fact, pedagogical-content knowledge may play a more central role than simple knowledge of the content. Mathematics educator E.G. Begle found that the number of credits a teacher had in mathematics methods courses was a stronger indicator of student performance than the number of credits in mathematics content courses. Education professor D.H. Monk also found that math and science education coursework had a positive effect on student learning and was sometimes more influential than additional subject matter preparation.

This research suggests that it is the intersection of teacher content knowledge and pedagogical-content knowledge that best improves student performance, with pedagogical-content knowledge augmenting or offsetting content knowledge. Bottom line: sometimes additional content knowledge simply is not necessary to teach some courses, but pedagogical knowledge of how to teach the content to students continues to impact student performance.

Putting It Together in the Classroom

To enhance the development of teachers’ formative assessment skills, professional development should focus on a three-step process of Probe-Diagnose-Respond (PDR). Good teaching probes student understanding by creating opportunities for them to demonstrate their thinking; diagnoses student understanding by analyzing what their responses reveal about their thinking; and responds to students’ level of understanding appropriately.

This framework’s three components that support the formative assessment process are described as:

Probe for student understanding . A teacher creates opportunities for individual students and the larger class to demonstrate their thinking, and determines whether an issue is particular to one student or may be an issue for the larger class. These opportunities may present themselves naturally through classroom discourse, or be generated by tools at the appropriate time.

Diagnose student understanding . A teacher must diagnose student understanding. Preliminary diagnoses can lead to further probing, to better assess what is at issue and how best to respond. There are many reasons students may have limited understanding. They may not have sufficient background knowledge to understand the topic, or they may not have understood the question or problem being posed. They may have misconceptions about a topic that hinder their understanding, or they may have a tentative understanding that needs to be developed.

Respond to diagnosis . A teacher’s diagnosis should lead to an appropriate instructional response. Good responses don’t focus on correcting students’ errors, but on leading students to desired understandings and sound thinking that will enable them to correct their own errors. Responsive teachers do this in a way that values students’ efforts, builds their self-confidence, and encourages them to view themselves as contributing members in a community of learners.

Final Thoughts on Formative Assessment

Students in a given classroom often differ in many ways (e.g., cultural background or previous opportunities to learn knowledge and skills). A commitment to the achievement of all learners requires teachers to tailor instructional strategies to the needs of each student. An effective approach for accomplishing this is through periodic formative assessments that vary both in terms of timing as well as mode of delivery. By understanding what needs to be taught, the current state of student understanding, how best to deliver instruction, and how to assess understanding (formative and summative evaluations), teachers can more effectively impart meaningful instruction.

Learn how Waggle , the award-winning personalized learning program, addresses formative assessment for students in Grades K–8.

Get a free guide to choosing the right assessments for your district.

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Teachers' Essential Guide to Formative Assessment

Topics:   Tech & Learning Assessment Classroom Media & Tools

How can I use formative assessment to plan instruction and help students drive their own learning?

What is formative assessment?

What makes a good formative assessment, how should i use formative assessment results, how do i know what type of formative assessment to use, what are the benefits of using an edtech tool for formative assessment.

A formative assessment is a teaching practice—a question, an activity, or an assignment—meant to gain information about student learning. It's formative in that it is intentionally done for the purpose of planning or adjusting future instruction and activities. Like we consider our formative years when we draw conclusions about ourselves, a formative assessment is where we begin to draw conclusions about our students' learning.

Formative assessment moves can take many forms and generally target skills or content knowledge that is relatively narrow in scope (as opposed to summative assessments, which assess broader sets of knowledge or skills). Common examples of formative assessments include exit tickets, fist-to-five check-ins, teacher-led question-and-answer sessions or games, completed graphic organizers, and practice quizzes.

In short, formative assessment is an essential part of all teaching and learning because it enables teachers to identify and target misunderstandings as they happen, and to adjust instruction to ensure that all students are keeping pace with the learning goals. As described by the NCTE position paper Formative Assessment That Truly Informs Instruction , formative assessment is a "constantly occurring process, a verb, a series of events in action, not a single tool or a static noun."

As mentioned above, formative assessments can take many forms. The most useful formative assessments share some common traits:

• They assess skills and content that have been derived from the backward planning process . They seek to assess the key learning milestones in the unit or learning sequence.
• They are actionable . They are designed so that student responses either clearly demonstrate mastery of the skills and content, or they show exactly where mastery is lacking or misunderstanding is occurring.
• When possible, they are student-centered . Using an assessment where students measure themselves or their peers, or where they're prompted to reflect on their results, puts students in charge of their own learning. It allows students to consider their own progress and determine positive next steps. Unfortunately, student-centered formative assessments don't always yield the easiest and most actionable information for teachers, so their benefits have to be weighed against other factors.

Formative assessments are generally used for planning future instruction and for helping students drive their own learning. In terms of future instruction, how you use assessment data most depends on what kind of results you get.

• If 80% or more demonstrate mastery , you'll likely want to proceed according to plan with subsequent lessons. For individual students not demonstrating mastery, you'll want to find ways to interject extra support. This might mean a differentiated assignment, a guided lesson during independent work time, or support outside of class.
• If between 50% and 80% demonstrate mastery , you'll need to use class time to have structured differentiation. You'll need to build this into the next lesson(s) if it isn't already planned. This means different activities or guided instruction for different groups of students. Students who've demonstrated mastery could engage in an extension activity or additional practice, or serve as support for other students. Students still attempting mastery could receive additional guided practice or additional instructional materials like multimedia resources or smaller "chunks" of content.
• If fewer than 50% demonstrate mastery , you'll need to do some whole-class reteaching. There are many approaches and concrete strategies for reteaching. Check out this article from Robert Marzano as well this blog post from BetterLesson for ideas.

The above recommendations are general rules of thumb, but your school or district may have specific guidelines to follow around teaching and reteaching. Make sure to consult them first.

Also, it's important to remember that building differentiation into the structure of your class and unit design from the beginning is the best way to make use of formative assessment results. Whether this means a blended or flipped classroom or activity centers, structuring in small-group, student-directed learning activities from the outset will make you more willing—and better prepared—to use formative assessment regularly and effectively in your class.

This is perhaps the most difficult question when it comes to formative assessment. There are so many different methods— just check out this list from Edutopia -- that it's easy to get lost in the sea of options. When it comes to choosing, the most important question is: What type of skill or content are you seeking to measure?

• Content knowledge ("define," "identify," "differentiate") is generally the easiest to assess. For less rigorous objectives like these, a simple fist-to-five survey or exit ticket can work well. An edtech tool can also work well here, as many of them can score and aggregate multiple-choice responses automatically.
• Higher-order thinking skills ("analyze," "synthesize," "elaborate") are generally more difficult and time-consuming to assess. For this, you'll likely use a different question type than multiple choice and need to allow more time for students to work. A good option here is to have students do a peer assessment using a rubric, which has the double benefit of allowing them to reflect on their own learning and cutting down the time you need to spend assessing the work. This can be done through an LMS or another project-based learning app , or through old-school paper and pencil; it just depends on your preference. Because students—and adults, too—often don't know what they don't know, self-assessments may be less accurate and less actionable for these types of skills.
• Process-oriented skills ("script," "outline," "list the steps") also tend to be more difficult to assess. Graphic organizers can work well here, allowing teachers (or peer reviewers) to see how students arrived at their results. STEM apps for higher-order thinking and coding apps can also make this assessment information more accessible.

As mentioned above, one of the big benefits of using a tool for formative assessment is that it allows teachers to more efficiently use their time. Apps like Quizlet and Formative use a quiz format to provide real-time feedback to both students and teachers, and—n their premium versions—provide aggregate qualitative and quantitative assessment data. Other apps, like Kahoot! or Quizizz , provide these features with the added engagement of game-based competition . Apps like Flip (video-based) and Edulastic (tracks against standards) provide assessment data with other additional perks. Check out our list of top tech tools for formative assessment to see a range of options.

Finally, if you're already regularly teaching with technology , using an edtech tool fits seamlessly into the daily activities your students already know how to do. It can be an independent activity that students do as part of a blended classroom, or an outside-of-class activity that's part of a flipped classroom. In this context, both students and teachers will get the most out of the time-saving and student-centered benefits that edtech tools provide.

As an education consultant, Jamie created curriculum and professional development content for teachers. Prior to consulting, Jamie was senior manager of educator professional learning programs at Common Sense and taught middle school English in Oakland, California. For the 2016–2017 school year, Jamie received an Excellence in Teaching award and was one of three finalists for Teacher of the Year in Oakland Unified School District. While teaching, Jamie also successfully implemented a $200,000 school-wide blended-learning program funded by the Rogers Family Foundation and led professional development on a wide range of teaching strategies. Jamie holds a bachelor's degree in philosophy from Eugene Lang College and a master's degree in philosophy and education from Teacher' College at Columbia University. Jamie currently lives in Sao Paulo, Brazil with his 4-year-old son, Malcolm, and his partner, Marijke.

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Eberly Center

Teaching excellence & educational innovation, what is the difference between formative and summative assessment, formative assessment.

The goal of formative assessment is to monitor student learning to provide ongoing feedback that can be used by instructors to improve their teaching and by students to improve their learning. More specifically, formative assessments:

• help students identify their strengths and weaknesses and target areas that need work
• help faculty recognize where students are struggling and address problems immediately

Formative assessments are generally low stakes , which means that they have low or no point value. Examples of formative assessments include asking students to:

• draw a concept map in class to represent their understanding of a topic
• submit one or two sentences identifying the main point of a lecture
• turn in a research proposal for early feedback

Summative assessment

The goal of summative assessment is to evaluate student learning at the end of an instructional unit by comparing it against some standard or benchmark.

Summative assessments are often high stakes , which means that they have a high point value. Examples of summative assessments include:

• a midterm exam
• a final project
• a senior recital

Information from summative assessments can be used formatively when students or faculty use it to guide their efforts and activities in subsequent courses.

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Formative Assessment Types Explained & Simplified: How to Make Them Effective AND Easy

February 21, 2023 by Katelyn Hildebrand

What are the Formative Assessment Types? (Assessment FOR Learning!)

What is formative assessment vs summative, and which formative assessment types are the most effective? How do I progress monitor and track student data? Formative assessment is the number one way to align our instruction with what students need and it is so powerful.

Here are some formative assessment examples and definitions you can use to help tailor your instruction to YOUR students.

This formative assessment types list explains assessment FOR learning and easy ways to make the most of your formative assessments.

Formative assessments are like the secret sauce to teaching. You can have all of the immaculate, detailed lesson plans in the world–- but what really makes the difference is having a teacher that is responsive to the students. That is where the magic happens and instruction is effective because it is tailored to what the student actually needs.

The formative assessment types that will make the biggest difference can still be simple!

Formative Assessment vs. Summative Assessment

There are 2 main types of assessment: formative assessment and summative assessment .

Assessment of Learning vs Assessment for Learning: What’s the Difference?

• determines student achievement levels and helps place students in appropriate groupings and learning settings
• helps the teacher find out what the student needs and how to help them

Formative assessment vs summative assessment: what’s the difference?

Summative Assessment

What is summative assessment?

• Summative Assessment definition: a test given to students at the END of a learning period to assess their level of achievement on a subject; scores are compared to a benchmark goal or set standard.
• Be able to record results
• Be able to report results
• Be completely objective
• End of Unit Tests
• Quarter Benchmark Tests (often district-wide)
• End-of-Year Benchmark Tests
• State Standardized Testing
• For older grades: assignments, homework, tests, and quizzes that accumulate to a student’s final score but do not change instructional strategies

Formative Assessment

What is formative assessment?

• Formative Assessment definition: a test given to students DURING the learning period to guide instruction so that it meets the student’s needs.

Think of assessment as one big category split into 2 groups: formative assessment and summative assessment.

THEN, think of “formative assessment” as split into 3 smaller groups.

These smaller groups are the 3 different formative assessment types.

There are different formative assessment types that you can use to positively impact student success.

Formative Assessment Types

There are 3 types of formative assessment (plus an extra 4th one):

• Screening Assessments
• Diagnostic Assessments
• Progress Monitoring Assessments
• Informal Assessments (which are really a sub-type of progress monitoring)

Which formative assessment type you use depends on what your goal is and who you need to assess.

I pulled the graphic above from my Teacher’s Guide for How to Assess Reading post. It has a lot of information on how to assess each of the Big 5 Areas of Readin g .

1. Screening Assessments:

Goal : Identify any students who are struggling

Who : Assess the entire class

When : At the beginning of a learning period

What to do with data : Find students who are below-level and provide interventions

2. Diagnostic Assessments:

Goal : Figure out WHERE specifically struggling students have gaps and need intervention

Who : Students you identified in the screener assessment

When : After the screener but before interventions are given

What to do with data : Make a personalized student plan to address any gaps you found

3. Progress Monitoring:

Goal : Track student progress on a specific skill

Who : Students who are receiving intervention

When : Regularly and periodically throughout a learning period

What to do with data : Analyze it to see how you need to adjust instruction (I have a post coming soon about analyzing data!)

4. Informal Assessments: (a sub-type of progress monitoring)

Goal : Quickly check student understanding

Who : Whole class or individual students

When : Usually during or right after a lesson

What to do with data : (not always formally recorded)

• use post-lesson data to determine if students understood a lesson
• record anecdotal notes to give a well-rounded picture of student understanding
• use mid-lesson checks to guide lesson pace

For screening and diagnostic assessments, I use this Comprehensive Reading Assessment . For progress monitoring, I use this easy Progress Monitoring flip-card system . I’ll dive into informal assessments below!

Data tracking for formative assessments can give you valuable information when used strategically, like in the tracking sheets that come with these Reading Intervention Binders .

When do I collect data from formative assessments?

Formative assessments are used in different ways.

• Sometimes they are informal and are just used to quickly guide your instruction and get a feel for student understanding.
• Sometimes they will be to identify specific student needs, track progress, and make strategic decisions in your lesson planning and intervention.

Record data for situation #2.

Do not stress about recording data for everything. Because honestly, not all data is equal. And too much data can lead to overwhelm and it’s too hard to glean anything from it then.

In my opinion, if you record every single worksheet/activity/response students do, you will spend all of your time entering numbers and the quality of the data will not always be great anyways.

Instead, collect data several times throughout a learning period using a high-quality, targeted assessment. This will make it easier to ensure the results are reliable and accurate, and lets you zero in on a specific skill. Then analyze THAT data. I’ll have more on how to analyze data soon!

These Reading Intervention Binders make data collection super easy. Each activity in the binder has a matching datasheet you can use to track student progress on reading skills!

These Reading Intervention Binders help you intervene AND track progress at the same time!

These formative assessment strategies will make your note-taking so much easier! Plus here are a couple of FREE editable note-taking tools (you need to have PowerPoint to download them)! 

EASY Formative Note-Taking Strategies:

Note-taking is an important part of making your formative assessments useful, but it’s really hard to complete quickly and keep it organized.

Here are a few easy ways to keep your notes convenient and organized.

Taking notes while walking around the classroom:

• Have a paper with a grid of squares on it (see the free download below) . Have each student’s name at the top of a square. Jot notes down in that student’s square as you observe.
• OR, carry around a sticky notepad and write down notes for a student on the top sticky note. Then fold it up and write on a new sticky note for each student. Then after the lesson transfer the notes to a more permanent place like a data binder or spreadsheet.

Taking Notes during the middle of a lesson:

• Have a class roster (see the free download below) printed out and easily accessible WHILE you are teaching. If you notice someone struggling during the middle of instruction, quickly (& discretely) circle/underline/star their name.
• You could also have a notepad easily accessible to write the names of students you want to follow up with when they move on to independent work.

CLICK HERE to download some FREE Editable Note-Taking Tools you can use with these strategies! (note: you will need to have PowerPoint to be able to access and download them)

What do you take notes on?

• Skills the student struggles with
• Consistent mistakes they make
• Specific words or phonics patterns they need more practice on
• Concepts the student is confused on
• Cues you give that you notice work for that student
• Strengths and positive praise you notice about them!! (especially great to share at parent-teacher conferences)

Progress monitoring can be overwhelming, but using a consistent format like these progress monitoring cards can help keep it simple and effective.

Progress Monitoring for Intervention

When Progress monitoring is used to inform intervention, it needs to be more strategic and organized. It’s important to track the student’s response to intervention so you know if your intervention is working. You also need to show evidence of progress by providing data at IEPs and parent-teacher conferences. Organized and specific data is the perfect way to do that!

How do you Progress Monitor?

• Choose one skill the student needs to build (identified from a diagnostic assessment).
• Create a SIMPLE assessment you can give them every 1-3 weeks.
• Keep the assessment the same, just switch out the words/letters/questions.
• Record the scores for each administration and track progress or regression.

FREE Tools for Progress Monitoring:

Here is a simple free progress monitoring form you can use to easily track student progress in any skill, and a motivating free fluency progress tracker that students love to fill out themselves to track their reading fluency!

Formal Progress Monitoring Tips

When you’re trying to balance a bazillion other things on top of regular and consistent progress monitoring, life can get super stressful. The pressure to do it consistently and to measure the right skill is hard. Here are a few tips to make it easier.

Tips for Easier Progress Monitoring:

1. Make it quick!

• It only has to be a few questions , not an entire test. Depending on the skill, it can just be 5 or so quick questions–- I like 5 because it gives easy 20% intervals for scoring.

2. Make it simple.

• For phonics , it can just be reading 5 words.
• For phonemic awareness , it can just be doing the skill for 5 words.
• For fluency, just read a paragraph.
• Comprehension and vocabulary take a little more planning as they need pre-written and thought-out questions, but they can be with quick sentences/sentence sequences instead of entire passages.

3. Make it targeted.

• Just choose ONE skill to assess. For effective progress monitoring, you really need to zero in on just one skill so you can clearly determine if the student has that specific skill mastered.

4. Make it aligned.

• For that one skill you are assessing, make sure your test actually assesses that skill in exactly the way your objective states students will show mastery.

5. Make it consistent.

• Use the same scale/measure for each administration. That way you can see accurate trends quickly at a glance.

6. Make it recorded.

• It can just be a page for each student with several blank 2-row tables on it.
• Write the date across the top and the score underneath.
• When you move onto a new skill, start using a new table.
• Be sure to label each table so you know what skill it goes with and what assessment you used!
• OR, just download this FREE Progress Monitoring Form to record your data!

7. Make it easy.

• I put assessment cards on a binder ring for each topic.
• They range from easy skills to hard skills and there are several cards for each skill (with different words switched in).
• To give the assessment, I just pull out the set I need and flip to the card the student is on.

Informal assessment can have so many variations, and can often be quick and easy.

Informal Assessments (it doesn’t have to be complicated)

Formative assessment does not have to be intimidating and overwhelming. It can be very simple, and you are most likely already doing it. Informal assessments in particular are very natural and easy to weave into your instruction.

To make the most of your informal assessments, let them INFORM your teaching.

• Use them as a gauge to spend more time, move on, or switch gears during a lesson.
• Use them to quickly identify students who are struggling with the lesson.
• Use them as a way to help students be accountable and engaged in their learning.

Your traditional “check for understanding” assessments you give during normal classroom lessons are perfect examples of informal assessments. They are for the teacher to use to guide instruction and monitor the entire class. They don’t have to be turned in to anyone and there is often no standardized way to give them (although some teams and schools might align their informal assessments).

Informal Formative Assessment Strategies

Here are some strategies you can use to quickly assess and gather informal data:

• Observing engagement and participation in practice questions and activities
• Walking around and recording observations as students work
• Talking/listening to students
• Collecting and checking student work

*See the next 2 sections for specific ideas of informal assessments!

Formative assessments can be given at multiple points throughout the day.

WHEN to Give Formative Assessments

Here are some formative assessment examples you might use at different points in learning.

DURING a lesson:

• Students self-check after a practice question and signal if they got it correct
• Students show their responses to practice questions
• Students give a signal for whether they understand or not (thumbs up or down under their chin)
• Students discuss with a partner (the teacher walks around and listens)
• Teacher walks around while students do a practice question and observes student work

AFTER a lesson:

• Worksheets or activities the teacher collects and checks
• Conversations with the teacher
• Walk around while students are working and observe/take notes
• Self-check routines (students grade their own work)

Formal Progress Monitoring:

• Strategic and regular assessments are given to track student progress on a particular skill
• Intentional, regular, and scheduled time is set aside to take these quick assessments

Formative assessment examples can include self-assessment signals, written answers, verbal discussion, or observation.

Formative Assessment Examples: EASY Assessments

Real life is busy and chaotic, and sometimes you just need an easy way to monitor progress! These are all examples of practical and easy informal formative assessments that can help you quickly get a gauge and feel for how the class is doing as a whole, and keep an eye on students who might be struggling in that topic.

Formative Assessment Examples:

• Students show a thumbs up or thumbs down under their chin during a lesson (to answer a yes/no question or to self-assess if they understand or not).
• Students write answers on whiteboards and show the teacher their answer.
• Students just think the answer in their head, then on the teacher’s signal they turn to a neighbor and tell each other what they think the answer is and why.
• Have students whisper the answer into their hand, then “hold it”, and on the count of 3 say it out loud.
• Students can show the answer on their fingers (counting sounds/syllables in words, assigning each answer choice a number, etc.).
• Students have a red, yellow, and green card. They can hold up the color that corresponds with the answer, or use it to self-assess if they understand or not.
• OR, they can have the cards in a pile at their desk and have the top color show how well they are understanding.
• Have students give themselves a self-assessment score (1-3, yes/no, etc.) on a sticky note, write their name on the back, and stick it on the board.
• On a small piece of paper have students answer one question and hand it to the teacher before they walk out the door.
• OR for accurate verbal assessments for reading (like explained in this post on the best assessments for reading ), have them read a few words you point to before they walk out the door (like in the exit tickets pictured in the section above this one).
• Students answer a question on a sticky note , write their name on the back, and stick it in a pile on the teacher’s desk (or have their name on top and the answer on the bottom for more anonymity).

These are all ideas for assessments that will guide your instruction, but not necessarily monitor individual student progress. For that, you will want to use a more formal progress monitoring system like these progress monitoring flip cards .

FREE Reading Intervention Cheat Sheet

With all of this said, formative assessment is only valuable if you are using it ALONGSIDE quality reading intervention . For some quick tips on how to identify student needs and some research-based and targeted reading activities, download this FREE Reading Intervention Cheat Sheet !

You can also check out my Ultimate List of Reading Intervention Activities for tons of hands-on and engaging activities to do with your students.

These reading intervention strategies and ideas will help your struggling readers! Click here to download it for free!

Hopefully, these formative assessment examples helped you understand all of the different types of formative assessment and see the value in using formative assessment vs summative. Progress monitoring and informal assessments help you keep a gauge on student learning and adjust your teaching so you are meeting your students’ needs. And they don’t have to be overwhelming! Real-life formative assessments can be quick and simple while still being powerful.

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Formative, Summative, and More Types of Assessments in Education

All the best ways to evaluate learning before, during, and after it happens.

When you hear the word assessment, do you automatically think “tests”? While it’s true that tests are one kind of assessment, they’re not the only way teachers evaluate student progress. Learn more about the types of assessments used in education, and find out how and when to use them.

Diagnostic Assessments

Formative assessments, summative assessments.

• Criterion-Referenced, Ipsative, and Normative Assessments

What is assessment?

In simplest terms, assessment means gathering data to help understand progress and effectiveness. In education, we gather data about student learning in variety of ways, then use it to assess both their progress and the effectiveness of our teaching programs. This helps educators know what’s working well and where they need to make changes.

There are three broad types of assessments: diagnostic, formative, and summative. These take place throughout the learning process, helping students and teachers gauge learning. Within those three broad categories, you’ll find other types of assessment, such as ipsative, norm-referenced, and criterion-referenced.

What’s the purpose of assessment in education?

In education, we can group assessments under three main purposes:

• Of learning
• For learning
• As learning

Assessment of learning is student-based and one of the most familiar, encompassing tests, reports, essays, and other ways of determining what students have learned. These are usually summative assessments, and they are used to gauge progress for individuals and groups so educators can determine who has mastered the material and who needs more assistance.

When we talk about assessment for learning, we’re referring to the constant evaluations teachers perform as they teach. These quick assessments—such as in-class discussions or quick pop quizzes—give educators the chance to see if their teaching strategies are working. This allows them to make adjustments in action, tailoring their lessons and activities to student needs. Assessment for learning usually includes the formative and diagnostic types.

Assessment can also be a part of the learning process itself. When students use self-evaluations, flash cards, or rubrics, they’re using assessments to help them learn.

Let’s take a closer look at the various types of assessments used in education.

Diagnostic assessments are used before learning to determine what students already do and do not know. This often refers to pre-tests and other activities students attempt at the beginning of a unit.

How To Use Diagnostic Assessments

When giving diagnostic assessments, it’s important to remind students these won’t affect their overall grade. Instead, it’s a way for them to find out what they’ll be learning in an upcoming lesson or unit. It can also help them understand their own strengths and weaknesses, so they can ask for help when they need it.

Teachers can use results to understand what students already know and adapt their lesson plans accordingly. There’s no point in over-teaching a concept students have already mastered. On the other hand, a diagnostic assessment can also help highlight expected pre-knowledge that may be missing.

For instance, a teacher might assume students already know certain vocabulary words that are important for an upcoming lesson. If the diagnostic assessment indicates differently, the teacher knows they’ll need to take a step back and do a little pre-teaching before getting to their actual lesson plans.

Examples of Diagnostic Assessments

• Pre-test: This includes the same questions (or types of questions) that will appear on a final test, and it’s an excellent way to compare results.
• Blind Kahoot: Teachers and kids already love using Kahoot for test review, but it’s also the perfect way to introduce a new topic. Learn how Blind Kahoots work here.
• Survey or questionnaire: Ask students to rate their knowledge on a topic with a series of low-stakes questions.
• Checklist: Create a list of skills and knowledge students will build throughout a unit, and have them start by checking off any they already feel they’ve mastered. Revisit the list frequently as part of formative assessment.

Formative assessments take place during instruction. They’re used throughout the learning process and help teachers make on-the-go adjustments to instruction and activities as needed. These assessments aren’t used in calculating student grades, but they are planned as part of a lesson or activity. Learn much more about formative assessments here.

How To Use Formative Assessments

As you’re building a lesson plan, be sure to include formative assessments at logical points. These types of assessments might be used at the end of a class period, after finishing a hands-on activity, or once you’re through with a unit section or learning objective.

Once you have the results, use that feedback to determine student progress, both overall and as individuals. If the majority of a class is struggling with a specific concept, you might need to find different ways to teach it. Or you might discover that one student is especially falling behind and arrange to offer extra assistance to help them out.

While kids may grumble, standard homework review assignments can actually be a pretty valuable type of formative assessment . They give kids a chance to practice, while teachers can evaluate their progress by checking the answers. Just remember that homework review assignments are only one type of formative assessment, and not all kids have access to a safe and dedicated learning space outside of school.

Examples of Formative Assessments

• Exit tickets : At the end of a lesson or class, pose a question for students to answer before they leave. They can answer using a sticky note, online form, or digital tool.
• Kahoot quizzes : Kids enjoy the gamified fun, while teachers appreciate the ability to analyze the data later to see which topics students understand well and which need more time.
• Flip (formerly Flipgrid): We love Flip for helping teachers connect with students who hate speaking up in class. This innovative (and free!) tech tool lets students post selfie videos in response to teacher prompts. Kids can view each other’s videos, commenting and continuing the conversation in a low-key way.
• Self-evaluation: Encourage students to use formative assessments to gauge their own progress too. If they struggle with review questions or example problems, they know they’ll need to spend more time studying. This way, they’re not surprised when they don’t do well on a more formal test.

Find a big list of 25 creative and effective formative assessment options here.

Summative assessments are used at the end of a unit or lesson to determine what students have learned. By comparing diagnostic and summative assessments, teachers and learners can get a clearer picture of how much progress they’ve made. Summative assessments are often tests or exams but also include options like essays, projects, and presentations.

How To Use Summative Assessments

The goal of a summative assessment is to find out what students have learned and if their learning matches the goals for a unit or activity. Ensure you match your test questions or assessment activities with specific learning objectives to make the best use of summative assessments.

When possible, use an array of summative assessment options to give all types of learners a chance to demonstrate their knowledge. For instance, some students suffer from severe test anxiety but may still have mastered the skills and concepts and just need another way to show their achievement. Consider ditching the test paper and having a conversation with the student about the topic instead, covering the same basic objectives but without the high-pressure test environment.

Summative assessments are often used for grades, but they’re really about so much more. Encourage students to revisit their tests and exams, finding the right answers to any they originally missed. Think about allowing retakes for those who show dedication to improving on their learning. Drive home the idea that learning is about more than just a grade on a report card.

Examples of Summative Assessments

• Traditional tests: These might include multiple-choice, matching, and short-answer questions.
• Essays and research papers: This is another traditional form of summative assessment, typically involving drafts (which are really formative assessments in disguise) and edits before a final copy.
• Presentations: From oral book reports to persuasive speeches and beyond, presentations are another time-honored form of summative assessment.

Find 25 of our favorite alternative assessments here.

More Types of Assessments

Now that you know the three basic types of assessments, let’s take a look at some of the more specific and advanced terms you’re likely to hear in professional development books and sessions. These assessments may fit into some or all of the broader categories, depending on how they’re used. Here’s what teachers need to know.

Criterion-Referenced Assessments

In this common type of assessment, a student’s knowledge is compared to a standard learning objective. Most summative assessments are designed to measure student mastery of specific learning objectives. The important thing to remember about this type of assessment is that it only compares a student to the expected learning objectives themselves, not to other students.

Many standardized tests are criterion-referenced assessments. A governing board determines the learning objectives for a specific group of students. Then, all students take a standardized test to see if they’ve achieved those objectives.

Find out more about criterion-referenced assessments here.

Norm-Referenced Assessments

These types of assessments do compare student achievement with that of their peers. Students receive a ranking based on their score and potentially on other factors as well. Norm-referenced assessments usually rank on a bell curve, establishing an “average” as well as high performers and low performers.

These assessments can be used as screening for those at risk for poor performance (such as those with learning disabilities) or to identify high-level learners who would thrive on additional challenges. They may also help rank students for college entrance or scholarships, or determine whether a student is ready for a new experience like preschool.

Learn more about norm-referenced assessments here.

Ipsative Assessments

In education, ipsative assessments compare a learner’s present performance to their own past performance, to chart achievement over time. Many educators consider ipsative assessment to be the most important of all , since it helps students and parents truly understand what they’ve accomplished—and sometimes, what they haven’t. It’s all about measuring personal growth.

Comparing the results of pre-tests with final exams is one type of ipsative assessment. Some schools use curriculum-based measurement to track ipsative performance. Kids take regular quick assessments (often weekly) to show their current skill/knowledge level in reading, writing, math, and other basics. Their results are charted, showing their progress over time.

Learn more about ipsative assessment in education here.

Have more questions about the best types of assessments to use with your students? Come ask for advice in the We Are Teachers HELPLINE group on Facebook.

Plus, check out creative ways to check for understanding ..

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• What is Formative Assessment and What Role Do They Play in Your Classroom? »

What is Formative Assessment and What Role Do They Play in Your Classroom?

Formative assessment stands out as a useful tool that supports teachers’ efforts to enhance their pedagogical approaches and improve students’ goals.

Then why is formative evaluation so crucial in the classroom, and what exactly is it? We’ll define formative assessment, discuss its applications, and discuss how it significantly impacts instruction and learning in this piece. Let’s learn more about this effective teaching method and see how it influences students’ educational experiences globally.

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What is Formative Assessment?

Formative Assessment is an ongoing and continuous evaluation process to gauge the learning progress of students in a classroom. It includes a series of short, quick, informal techniques to check the efficiency of the teaching method in delivering student learning. On one hand, formative assessments help teachers identify the gaps in student understanding of the concepts being taught. On the other hand, they help teachers assess the effectiveness of the lesson plan and make appropriate changes to deliver better learning for students of all capabilities.

Formative assessments, unlike summative assessments, do not review a student’s mastery of the topic. The key objective of formative assessment strategies for teachers is to provide feedback on the learning outcomes and the strengths and weaknesses of individual students. Therefore formative assessments are un-graded, low-stress, informal tools that improve the teaching-learning process .

What Are the Advantages of Formative Assessment?

Having understood what formative assessment is, let us now look at how formative assessment is useful for teachers in delivering better learning experiences for their students.

• Provides Clear Learning Goals – By explaining the goal of the lesson, and what the teachers hope for students to take away from the class, formative assessment sets the ground for both students and teachers to gain clarity of the teaching-learning objective. This also equips students to actively participate in the learning process and seek guidance for areas they might find difficult.
• Identifies Learning Gaps Early – Formative assessment techniques help educators catch any deficit in student grasp of a given topic before moving on to the next one. Using formative assessment tools teachers can ascertain the gaps in student learning and address them in real-time to improve student learning and lesson effectiveness.
• Increases Student Engagement – Study after study has proven that formative assessment techniques enhance student engagement through interactive activities and assessments that not only help students and teachers identify learning gaps but also increase student engagement in the topics being taught.
• Enhances Student Motivation – By providing regular and actionable feedback, formative assessments help students work on their eventual understanding and performance. A clear knowledge of the goals and guidance to move towards these goals helps in keeping students motivated and invested in their progress.
• Helps Students Develop Self-Assessment Skills – The informal, regular and low-stress attributes of formative assessments help the students understand their learning gaps easily, informing them of the work required. They also help students identify methods that they learn best through and seek guidance to improve their overall learning and performance.

What Are the Examples of Formative Assessment?

Formative assessment strategies for teachers provide feedback on student learning in the classroom and the effectiveness of the lesson for students with different learning styles and capabilities. Additionally, they give teachers a starting point for the next lesson. While there are many formative assessment strategies, below is a list of some of the most relevant ones. Most of the listed tools can be interactive and online, providing data for easy analysis and immediate action. Digital formative assessments provide teachers with quick data to understand areas that require information reinforcement and topics that need more time and input for better student learning.

• Exit Tickets : Short, end-of-lesson reflections that take only a few minutes for the students to complete to check their understanding. These can be structured and specific or open and explorative. For more ideas and information on different kinds of Exit Tickets, check Exit Ticket Ideas for Teachers
• Thumbs Up/Down : Through a show of Thumbs Up or Down to strategic questions posed on the topic at the end of the lesson, a teacher can get a quick visual check to see if students understood the concept or need more help in grasping the material.
• Mini Quizzes & Polls : Quizzes, questionnaires and polls serve the purpose of a quick assessment of student learning and help teachers prepare for the next lesson. These are usually short, unannounced, and specific and can be prompt-based, MCQs, fill-in-the-blanks etc.
• Classroom Observation of Student Work : A one-on-one assessment method, classroom observation and feedback help teachers understand individual student learning styles, strengths, weaknesses, skills and knowledge, to identify areas that need more support.
• Observation of Group Interactions : This method helps teachers gather inputs on how students process and think about new information, how they work in groups, problem-solve and collaborate. It also highlights the values and skills they are good at and the ones they need help with such as teamwork, communication and concept application.
• Peer Review : Fostering active participation in their learning process and the ability to communicate concepts in their language, this method has students evaluate each other’s learning and work. They learn from each other, leverage their strengths and work on their weak points while building a strong sense of belonging.
• Self-Reflection Prompts or Journals : This assessment technique encourages students to take time to reflect on their learnings, the areas where they see improvement and areas they feel need more work. These could be specific and prompt-based or explorative and open-ended journals that have the students reflect on their learning application, style and growth.
• Higher-order Thinking Questions : Questions such as ‘How’ or ‘Why’ serve as open-ended prompts and those which go beyond concept recall, analysis, information synthesis, and concept evaluation. They help students delve deeper into the importance of the topics they are learning and their real-life applications.
• Class Discussions : Either in pairs or in small groups, students discuss their responses to teacher-prompted questions. These facilitated discussions help students communicate their ideas and thinking, learn from each other and expand topics through discussion.
• Graphic Organisers : Using graphic and visual aids for references, activities, games and puzzles helps students categorise the information inputs easily and understandably through association and concept maps. This also helps revise concepts before moving on to the next step of learning.

How to Give Formative Feedback for Growth and Improvement?

For formative assessments to be useful, the findings need to inform the progress and design of the lesson and be shared as constructive and actionable feedback with the students. Formative feedback highlights the knowledge gaps, appropriate support resources and learning strategies to ensure growth and at-par development amongst students of different capabilities and learning preferences. Below are the key features of valuable and beneficial formative feedback.

• Focus on Specific Behaviours : Identify behaviours and traits you want to encourage in the class such as asking for help, teamwork, creative thinking etc. Use formative assessments to assess and provide specific feedback on the utilisation of those behaviours in action.
• Offer Positive Reinforcement : Always start with sharing feedback on what went well before arriving at areas that need more work. This helps build student confidence and keeps the classroom environment positive.
• Actionable Steps : Always provide suggestions that are useable and clear, serving the purpose of student learning in line with the lesson goals.
• Use Open-Ended Questions : Instead of spoon-feeding students to help them learn better, encourage them to think for themselves through open-ended questions that promote critical thinking and self-reflection.
• Focus on Effort and Progress : Reward and recognise student efforts to process the feedback and the resultant progress by highlighting all improvements – big or small.
• Maintain a Positive Tone : By concentrating on progress and growth, keeping an eye on weak areas and bringing more focus to areas of work you can maintain a positive tone and environment in the classroom. This helps release the stress on both the students and the educators.
• Provide Opportunities for Revision : Set aside some time at the beginning of the class to quickly revisit the previous lesson as a starting point for further learning. Similarly allow students some time to revise and summarise the learning of the current lesson to improve their learning outcome.

What are the Differences Between Formative and Summative Assessment?

Though both, Formative and Summative Assessments serve as evaluation tools, they differ in their objective as well as the outcome.

• The objective of formative assessments in the form of un-graded, informal reviews is to gauge the additional support the student needs for their learning, while summative assessments in the form of graded, formal reviews, test the student’s knowledge and application of the concepts learnt.
• Formative assessment techniques are essentially an ongoing aid to the learning process, while summative assessments are methods of assessing student learning, skills and knowledge at the end of the teaching process.
• Formative assessments support the teaching design, while summative assessments are an evaluation of the learning that takes place as a result of the teaching design.
• Due to their informal, un-graded nature, formative assessments can take place repeatedly as per the educator’s perceived need and preference, while summative assessments are pre-scheduled, structured and definitive.

Formative Assessments Powered by Extramarks

Formative assessments via effective and varied Exit Ticket options created by the Extramarks Assessment Center add the power of appropriate and apt formative assessments to your classroom. Extramarks leverages smart educational technology to assist educators by providing practical, quick, and economical new-age unconventional learning tools that enhance the teaching-learning experience for both the teachers and the students.

Formative Assessments Created by the Extramarks Assessment Centre

It can collect, compile and analyse the responses of all your students to develop an effective exit ticketing process.

Last Updated on June 14, 2024

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Formative Assessment

Formative assessment is a process that involves the ongoing use of information about students’ knowledge, understanding and skills to target teaching and address student learning needs. Formative assessment provides teachers and students with opportunities for feedback throughout teaching and learning and provides evidence about progress to inform the next steps in learning.

All assessment can be used in a formative way by teachers and/or students. Assessment becomes formative when information about student learning is used to adapt teaching to meet student learning needs and when students are provided with timely feedback and opportunities to improve.

Teachers can use formative assessment to identify what students know and can do before new content is taught. Through formative assessment, progress can be monitored over time and students can become active participants in the learning process. Formative assessment can help both teachers and students to develop a greater awareness of learning through goal setting, monitoring the learning progress and adapting goals for future learning.

The purpose of formative assessment is to:

• inform teaching and learning to meet student learning needs
• identify misunderstandings and skills not yet mastered to guide teacher action
• focus on learning processes to inform next steps for teacher and student
• provide students with opportunities to improve
• reflect on the learning process and set learning goals.

Formative assessment includes:

• identifying where student learning is going and what success looks like​​
• finding evidence of student learning in a variety of ways
• providing feedback that supports the student to progress in their learning
• providing opportunities for students to give feedback to one another on learning
• self-evaluating or making judgements in relation to goals and/or criteria.

Image long description: A diagram showing the Formative assessment process. Five circles are connected by arrows, showing that the process is circular and continuous. The top circle contains the text ‘Identifying where the learning is going and what success looks like’, with an arrow pointing to the next circle, which contains the text ‘Finding evidence of learning in a variety of ways’. An arrow points to a third circle which is surrounded by 3 double-sided arrows, with the text ‘Using feedback’. Around this circle there is text reading ‘Interpreting information’, ‘Providing and actioning feedback’ and ‘Evaluating feedback’. An arrow points to the next circle with the text ‘Determining next steps’. An arrow points to the next circle with the text ‘Adapting goals’. An arrow from the fifth circle points to the first circle.

This model emphasises the importance of feedback in decisions that teachers and students make about progress, and the next steps in teaching and learning. The process involves:

• identifying where the learning is going, what is being learnt, why and how it will be learnt, and providing clear expectations for success
• finding evidence of learning in a variety of ways to understand where student learning is at that point in time
• determining how information about learning will be interpreted, what feedback will be provided and when, how the feedback will be actioned, and the process for evaluation
• deciding how the information will be used to move the learning forward and determining next steps in teaching and learning
• adapting teacher and student goals by reflecting on the learning process.

Formative assessment approaches

Teachers and students may use a range of approaches to engage in the process of formative assessment. The following examples outline some of these approaches.

Teacher observations

Teacher observations can provide information about student progress and achievement in relation to the syllabus. Observations can occur informally during teaching and learning, or formally, where specific learning requires teacher observation of student knowledge and/or skill.

Assessment experiences may include:

• student participation in practical activities
• student application of skills to demonstrate understanding of key concepts
• student application of learning in familiar and unfamiliar contexts
• teacher questioning to observe individual level of understanding
• teacher–student discussions or conferences.

Teacher observation can be used to interpret information about student progress in relation to:

• knowledge of key concepts
• application of knowledge and understanding to new contexts and situations
• development and application of skills
• communication, collaboration and critical and creative thinking.

Peer assessment and self-assessment

Peer assessment and self-assessment can provide students and teachers with information to inform goal setting and reflect on learning. For peer assessment and self-assessment to be effective and meaningful, students need to be explicitly shown how to assess their own work and the work of others. Formally, students may use criteria to make decisions about their own progress and to provide feedback on the progress of others. Informally, students may use prompts to ask questions about the quality of their own work and the work of others. Using peer assessment and self-assessment enables students to take a more active role in their learning. It encourages them to reflect on where they are in their learning, identify the next steps needed to make progress and monitor their progress over time.

Peer assessment

Peer assessment involves students assessing each other's work in relation to specific goals or criteria. Students provide feedback to one another and respond to this feedback to improve their learning. Teachers should model how to assess learning and use appropriate language to clarify expectations for assessment that incorporates peer feedback. Feedback may take a variety of forms and should provide opportunities for students to develop their social, collaborative and reflective skills.

Students may provide feedback to their peers about:

• what has been completed
• strengths and/or aspects that have been completed well
• suggestions for how to improve with reference to specific learning goals and/or criteria
• alternative strategies to refine learning.

Self-assessment

Self-assessment involves students assessing their own learning in relation to personal learning goals to identify what they know, the direction they need to take and how they are going to get there. This can provide both teachers and students with information to support future teaching and learning.

Self-assessment questions may include:

• What do I already know about this learning area?
• What will help me achieve this learning goal and why is it important?
• How will I know when I achieve my learning goals?
• How can I use criteria to improve?
• What do I notice when I compare my work to exemplars and/or the work of others?
• How can I use feedback to improve?
• What strategies can I use when I find myself being challenged?
• How has my learning improved through collaborating with others?

Prompts for students may include:

• Things I have learnt are …
• I need to work on …
• I collaborated by …
• Next time I will ...
• I will use my new skills to ...
• I will use my knowledge to ...
• My strength today was …
• My biggest improvement is …
• I would like to learn more about …

Self-assessment experiences may include:

• reflections on learning processes
• creating portfolios of work
• self-assessment of progress in relation to the syllabus
• evaluating own contributions to a group task
• reassessing learning goals based on feedback.

Collaboration

Collaborative activities enable teachers to assess learning that occurs as a result of interaction between students. Students interact through common or related activities, often using modelled, guided and independent approaches to learning. Collaboration can occur using a variety of tools and in face-to-face and digital modes. For effective collaboration, the group should have a clear understanding of the purpose and goals.

Collaborative assessment experiences may include:

• group discussions to evaluate and challenge views
• team-based investigations, including the allocation of specific roles and responsibilities
• group-prepared presentations
• group-based problem-solving in authentic contexts.

When collaborative activities are used for assessment purposes, evidence can be gathered about students’ ability to:

• work together in structured teams
• solve problems and make decisions with others
• demonstrate skills in applying knowledge
• take individual and/or shared responsibility for learning during group work
• think critically and creatively, and offer constructive feedback
• analyse, evaluate and synthesise information.

Worked examples

Worked examples are demonstrations of one or more skills, modelled by the teacher, that can help students to know and recognise the standards for which they are aiming. Worked examples can support assessment by allowing students to demonstrate their knowledge, understanding and skills with greater confidence as they know what is required of them. Worked examples can be used to explain the steps required to achieve learning goals, solve problems and support skill acquisition. Presenting students with worked examples or creating worked examples with students can reduce the cognitive load often associated with new learning.

• engaging with annotated exemplars of learning to deepen knowledge, understanding and skills, and/or an understanding of achievement standards
• teacher-and-student joint construction of learning through collaborative discussion and modelling in a range of modes
• collaboratively annotating and/or discussing exemplars of work using criteria.

When worked examples are used for assessment purposes, evidence can be gathered about students’ ability to:

• demonstrate their knowledge, understanding and skills throughout the learning process
• communicate understanding of their own work in relation to the worked example and/or success criteria
• apply a deeper understanding of criteria to their own learning
• transfer knowledge and understanding by using worked examples as models or scaffolds for their own work
• respond to and use explicit instruction and feedback to improve their understanding and skills
• understand where they need to take their learning next and set future learning goals.

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What Is a Formative Assessment? Types, Examples & Strategies

Author & Editor at ProProfs

Michael is a seasoned writer with 12+ years of experience in online learning and training. His work empowers organizations to harness the potential of knowledge in the digital era.

Ever noticed how the most memorable lessons stick with us not because of a final grade, but because of the journey there? 

That’s the magic of formative assessments—they’re not just checkpoints; they’re the secret ingredients that make learning stick. 

This blog post dives into the heart of formative assessments, revealing how they can transform classrooms by turning every lesson into an opportunity for growth and every mistake into a learning moment. 

In this definitive guide, we’ll explore the what, why, and how of formative assessments—from their defining characteristics and purpose to a variety of types and strategies for effective use in the classroom. 

Let’s begin.

What Is a Formative Assessment?

Formative assessment is a strategic approach used by educators to monitor students’ learning progress and adjust teaching methods accordingly. It’s characterized by its real-time application, providing immediate feedback that educators can use to adapt their instruction to meet learners’ current needs. 

Unlike summative assessments that evaluate overall learning at the end of an instructional period, formative assessments are conducted throughout the learning process. 

They can take various forms, including quizzes, interactive discussions, and peer reviews, all aimed at gauging understanding and facilitating continuous improvement.

Watch: How to Create an Online Quiz in Under 5 Mins

What Is the Purpose of Formative Assessment?

The purpose of formative assessment is to enhance the learning process by identifying students’ strengths and areas for growth. This ongoing assessment method allows educators to:

• Modify teaching strategies in real-time to address the immediate needs of their students.
• Support personalized learning, ensuring that instruction is tailored to individual student progress.
• Foster an environment of continuous feedback and growth, encouraging students to engage more deeply with their learning and identify their areas for improvement.

By integrating formative assessment into their teaching, educators can create a dynamic and responsive learning environment that supports student success and promotes a deeper understanding of the material.

Types & Examples of Formative Assessment

Formative assessments come in various formats, each designed to gather feedback on student learning in a way that informs instruction and supports student growth. Here are some common formative assessment tools :

• Quizzes & Mini-Tests: These brief assessments are powerful tools for gauging student knowledge in a focused manner. 

When used regularly, they can highlight trends in student understanding over time, allowing educators to pinpoint specific topics that may require additional instruction or review.

Watch: How to Use Online Quiz Maker for Teachers

• Observations & Check-Ins: This approach involves informal yet purposeful monitoring of students during class activities. 

It offers nuanced insights into how students interact with the material and each other, providing a real-time snapshot of engagement and comprehension levels.

• Interactive Discussions: Encouraging open dialogue about the material not only reinforces students’ understanding but also cultivates critical thinking skills. 

Discussions can unveil diverse interpretations and misconceptions, guiding educators in tailoring subsequent lessons to address these gaps.

• Peer Reviews: Students engage in a reciprocal learning process by evaluating each other’s work. This method not only diversifies feedback but also encourages students to critically engage with the curriculum, deepening their understanding through the lens of their peers’ perspectives.
• Exit Tickets: Simple prompts or questions at the end of a lesson offer immediate feedback on the day’s learning outcomes. Analyzing responses helps educators assess the effectiveness of their teaching and plan necessary adjustments for future classes.
• Learning Journals: Journals that prompt reflection on what was learned and questions that arose during the lesson help students articulate their thoughts and feelings about their learning journey. 

Reviewing these journals gives educators a window into students’ self-perceived progress and areas of difficulty.

Incorporating a mix of these formative assessment types enriches the learning environment and empowers students to take an active role in their education. 

Educators can harness these tools to create a dynamic classroom atmosphere that values growth, encourages engagement, and fosters a deeper connection to the material. 

What Is the Process of a Formative Assessment?

The formative assessment process is a cyclical, interactive approach designed to gauge student understanding, provide feedback, and continuously adapt instruction throughout the learning journey. It’s a dynamic framework that supports teaching and enhances learning. 

Here’s a breakdown of the key steps involved:

Step 1: Identify Learning Objectives 

The first step involves clearly defining what students should learn. These objectives guide the creation of assessment tasks and ensure that the assessment is aligned with instructional goals.

Step 2: Select Appropriate Assessment Methods 

Choose from various assessment methods (e.g., quizzes, discussions, projects) that best suit the learning objectives and the learner’s needs. This diversity allows for a more comprehensive understanding of student learning.

Step 3: Implement the Assessment 

Carry out the chosen formative assessment during the instructional process. This could be through live quizzes, interactive discussions, peer reviews, or individual reflections. The key is to integrate these assessments seamlessly into the learning activities.

Step 4: Analyze Learner Responses 

Review the information gathered from the assessment to identify patterns, strengths, and areas for improvement. This analysis provides insights into each student’s understanding and progress.

Step 5: Provide Feedback 

Offer timely and constructive feedback to students based on their performance. Effective feedback is specific, actionable, and focused on growth, helping students understand what they did well and where they can improve.

Step 6: Adjust Instruction 

Based on the feedback and analysis, adapt your teaching strategies to address the identified learning gaps or challenges. This might involve revisiting specific topics, introducing new resources, or modifying learning activities to suit students’ needs better.

Step 7: Reflect on the Process 

Finally, reflect on the effectiveness of the formative assessment process itself. Consider what worked well and what could be improved in future iterations. This reflection helps refine the assessment process, making it more effective over time.

Throughout this process, the emphasis is on fostering an environment of continuous learning and improvement. By actively engaging in each step, educators can create a responsive classroom atmosphere that supports every student’s growth and achievement.

Strategies for Effective Formative Assessments

To maximize the benefits of formative assessments, educators need to apply strategies that make the feedback loop as effective and seamless as possible. Here’s how to ensure formative assessments contribute positively to both teaching and learning:

• Embed Assessments in Everyday Learning 

Make formative assessments a natural extension of classroom activities. After a science experiment, for instance, ask students to predict the outcome based on the theory they’ve learned. This not only assesses their understanding but also encourages critical thinking.

• Embrace Technology for Interactive Learning 

Modern tools have revolutionized the way we assess and engage with students. ProProfs Quiz Maker, for example, offers an intuitive platform for creating quizzes that are both fun and educational. 

You can create educational quizzes that provide instant feedback, helping students identify areas of strength and those needing improvement, all within an interactive format that captures their interest.

• Foster a Culture of Peer Feedback

Implement structured peer review sessions where students can offer constructive feedback on each other’s presentations or essays. This strategy not only diversifies the sources of feedback but also helps students develop a critical eye for their work and that of their peers.

• Encourage Reflective Practices 

Guide students in reflecting on their learning experiences and outcomes. A reflective journal entry after completing a group project can provide insights into what they learned, the challenges they faced, and how they overcame them, fostering a deeper understanding of the learning process.

• Connect Learning to Real-world Applications 

Design assessments that require students to apply classroom knowledge to solve real-world problems. For instance, in a geography class, students could analyze the impact of climate change on their local community, encouraging them to connect theory with practical, observable phenomena.

• Leverage Exit Tickets for Immediate Insights 

At the end of a lesson, a simple question related to the day’s topic can serve as an exit ticket. This strategy offers quick insights into students’ understanding and retention, informing future instructional decisions.

Implementing these strategies can make formative assessments a powerful tool for enhancing student learning, providing educators with the flexibility to meet each student’s needs while fostering a supportive and inclusive classroom environment.

What Are the Benefits of a Formative Assessment?

Formative assessments offer a wealth of benefits that significantly contribute to both teaching efficacy and student learning outcomes. 

By integrating formative assessments into the educational process, educators and students can experience a more engaged, reflective, and practical learning journey. Here are some of the key benefits:

• Enhanced Learning and Understanding 

Formative assessments help students consolidate their learning by actively engaging with the material. This continuous engagement promotes deeper understanding and retention of the content.

Watch: How Luc Viatour Transformed Education for 1500+ Daily Learners

• Immediate Feedback for Quick Adjustments

The real-time feedback provided through formative assessments allows students to identify their strengths and areas for improvement promptly. This immediacy enables quick corrective actions, fostering a more dynamic and responsive learning environment.

• Personalized Learning Experiences 

Formative assessments identify individual learning needs, enabling educators to tailor their teaching strategies and resources. This personalization ensures that all students receive the support and challenge they need to progress.

• Increased Student Motivation and Engagement 

Active involvement in the learning process increases students’ motivation and engagement. Formative assessments encourage students to take ownership of their learning, leading to higher levels of participation and interest.

• Development of Critical Thinking and Skills 

Through activities like peer reviews and self-assessments, students develop essential skills, including critical thinking, self-reflection, and the ability to receive and apply feedback constructively.

• Support for a Growth Mindset 

Formative assessments emphasize growth and improvement over grades, helping to cultivate a growth mindset among students. This perspective encourages learners to view challenges as opportunities to learn and grow rather than as failures.

• Improved Teacher-Student Relationships 

The continuous interaction and feedback loop foster closer relationships between teachers and students. This rapport builds a supportive classroom atmosphere where students feel valued and understood.

• Data-Driven Instructional Decisions 

Insights from formative assessments give educators a clear view of student understanding, enabling precise, data-driven adjustments to teaching. This targeted approach ensures lessons meet students’ exact needs, optimizing learning outcomes.

• Reduction of Test Anxiety 

Integrating formative assessments throughout the learning journey shifts the focus from high-stakes evaluation to ongoing improvement, significantly easing test-related stress. This frequent, low-pressure feedback mechanism familiarizes students with the assessment process, building their confidence and diminishing anxiety over time.

• Preparation for Summative Assessments 

Regular formative assessments prepare students for summative assessments by ensuring they understand the material and can apply their knowledge effectively. This preparation can lead to better performance on final exams and standardized tests.

Watch: How DMS Boosted Student Scores

How to Create a Formative Assessment Quiz

If you’re using an intuitive quiz tool, such as ProProfs Quiz Maker, the process for creating a quiz is quite straightforward. Here’s how to create a formative assessment quiz in five quick and easy steps:

Step 1: Click “ Create a Quiz ” on your dashboard. 

Step 2: Pick a ready-to-use quiz, create a quiz with AI , or build it from scratch.

Step 3: Add/edit the quiz title, description & cover image.

Step 4: Add/edit questions. 

Employ a variety of question formats to explore diverse knowledge and skill areas, guaranteeing a thorough examination of the topic at hand. 

ProProfs provides an array of question styles, including multiple-choice, fill-in-the-blanks, drag & drop, hotspot, and audio/video responses, facilitating a detailed assessment of learners’ comprehension.

Watch: 15+ Question Types for Online Learning & Assessment

You can add new questions by:

• importing them from 1,000,000+ ready-to-use questions  
• using ProProfs AI to generate questions instantly 
• creating them by yourself

You can add images, videos, audio clips, and docs to your quiz. 

You can also automate the grading of your quizzes to save time and effort, which you can invest in providing individualized support to your learners.   

Watch: How to Automate Quiz Scoring & Grading

You also have the option to offer explanations for answers immediately after a question is answered in the quiz. This instant feedback not only supports the learning process but also enables students to recognize areas requiring improvement.

Step 5: Configure settings.

You can implement several security and anti-cheating measures , including:

• Setting your quiz to be private and secured with a password
• Randomizing the sequence of questions and/or answer choices
• Developing a question pool and drawing a random selection of questions for each participant
• Overseeing the quiz through screen sharing, webcam, and microphone monitoring
• Preventing tab switching, printing, copying, downloading, and repeated attempts

Watch: How to Customize & Configure Your Quiz Settings

You can also change the quiz’s appearance by adjusting the background, colors, fonts, and button text. Plus, you can set the quiz to appear in the participant’s native language.

That’s it. Your formative assessment quiz is ready.

Analyzing the Results

After administering a formative assessment, ProProfs Quiz Maker delivers in-depth analytics that paints a complete picture of every student’s learning progress and overall class performance. This data is essential for modifying instructional strategies to better align with students’ learning needs. 

Apply this insightful feedback to adjust your teaching plans, focusing on clarifying common misconceptions and bolstering areas where students show weaknesses.

Enhance Classroom Dynamics With Formative Assessments

In conclusion, formative assessments are the core of an adaptive and responsive teaching strategy. They offer a clear window into student progress and areas for growth. This approach aligns instruction closely with student needs, significantly enhancing learning outcomes. 

By incorporating tools like ProProfs Quiz Maker, educators can design engaging and insightful assessments that contribute to a tailored learning experience. 

Start elevating your teaching approach by trying out ProProfs Quiz Maker through a free trial or requesting a demonstration today.

Frequently Asked Questions  

What are formative and summative assessments?

Formative assessments are tools teachers use during the learning process to see how students are doing and to adjust their teaching methods. Summative assessments happen at the end of a learning period, like a final exam, to measure what students have learned overall.

Are quizzes summative or formative?

Quizzes can act as both formative and summative assessments. As formative assessments, quizzes are used throughout the learning process to guide both teaching and learning. As summative assessments, quizzes evaluate students’ final understanding at the end of a unit or semester.

Is a worksheet a formative assessment?

Worksheets can serve as formative assessments when used to monitor students’ understanding and inform future teaching strategies. They become practical tools for ongoing learning and adaptation in the classroom, emphasizing feedback over final grades.

About the author

Michael Laithangbam

Michael Laithangbam is the senior writer & editor at ProProfs with 12 years of experience in enterprise software and eLearning. Michael's expertise encompasses online training, web-based learning, quizzes & assessments, LMS, and more. Michael’s work has been published in G2, Software Advice, Capterra, and eLearning Industry.

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Formative vs. Summative Assessment: What’s the Difference? [+ Comparison Chart]

In education, assessments are the roadmap guiding teachers and students to successful outcomes — from navigating subject matter to reaching academic milestones. But not all means of measuring success are the same. In this blog post we’ll explore two of these methods: formative vs. summative assessment.

To maximize teaching effectiveness, it’s important to understand the differences between each assessment type. Keep reading to learn the benefits of tailoring instruction to meet the diverse needs of every learner, plus tips on implementing both techniques.

What Is Formative Assessment?

Formative assessment is not actually a singular method, but instead, a variety of ways for teachers to evaluate student comprehension, learning needs, and academic progress in real-time throughout a lesson, unit, or course. 

These assessments aid in identifying areas where students are struggling, skills they find challenging, or learning standards they have not yet achieved. This information enables teachers to make necessary adjustments to lessons and instructional techniques to better meet the needs of their students. 

Its primary goal is to measure a student’s understanding during instruction; for example, with quizzes, tests, or exams.

As learning and formative assessment expert Paul Black puts it, “when the cook tastes the soup, that’s formative assessment. When a customer tastes the soup, that’s summative assessment.”

What Is Summative Assessment?

Summative assessment, on the other hand, is any type of evaluation that measures a student’s overall comprehension and achievement at the end of a unit, course, or academic period. It typically takes the form of final exams or projects, and aims to gauge what students have learned. Unlike formative assessment, which provides ongoing feedback, summative assessment focuses on determining the extent to which students have mastered the content overall.

This culmination of the learning process helps teachers determine proficiency levels against predefined standards or benchmarks. These assessments — which often carry higher stakes — are used for accountability, such as grading, ranking, and reporting student achievement to parents and school administrators.

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3 Examples of Formative Assessment

For a clearer idea of formative assessment , explore these three examples:

• Exit tickets are brief assessments given to students at the end of a lesson or class period featuring questions that relate to that day’s work. Teachers use exit tickets to gauge student understanding before they leave the class, allowing them to adjust future instruction based on the feedback received. 
• Think-Pair-Share involves three stages: First, prompting students to independently think about a question related to a lesson, then having them pair up with a classmate to discuss their thoughts, before finally asking them to share their discussion with the class. The process encourages active engagement, collaboration, and comprehension.
• One-minute paper is aptly named, allowing students 60 seconds at the end of a lesson or class period to write down the most important concepts from the presented material. Teachers can review these papers to assess how well students understand the material at hand and address any misconceptions.

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3 Examples of Summative Assessment

Likewise, here a few examples of summative assessments:

• Final exams are comprehensive assessments that are typically given at the end of a course or academic year and cover a broad range of topics that were covered over a longer period of time. 
• Standardized tests , such as the SAT and ACT, are administered and scored consistently across a large number of students for comparison purposes. They are also useful for identifying areas for improvement in educational systems and making decisions about student placement or advancement, such as admission into higher education institutions.  
• End-of-unit projects are typically more extensive than regular class assignments and require students to demonstrate their understanding of multiple concepts or skills covered in the unit. Research, originality, collaboration, and presentation are often involved.

How to Grade Formative Assessments

Because of the unique nature of each type of student evaluation, there is also variety in grading summative vs. formative assessments. The following are considerations when grading formative assessments:

• Focus on feedback by prioritizing constructive notes that guide students’ learning and improvement.
• Use rubrics to establish clear criteria for assessment and ensure consistency in grading. 
• Provide descriptive feedback that highlights strengths and areas for improvement.
• Encourage self assessment to promote accountability and reflection as students examine their own work.
• Focus on growth and development over time instead of final outcomes and grades exclusively.
• Track progress to call out student achievement trends over time.
• Use peer assessment to cultivate collaboration and diverse perspectives in evaluation.
• Consider participation and effort in addition to academic achievement in order to take a big-picture look at education and achievement.
• Communicate clearly to facilitate understanding and successful outcomes.

How to Grade Summative Assessments

Consider these methods as you grade summative assessments, keeping in mind a fair and accurate representation of students’ learning outcomes and progress.

• Establish clear criteria to guide students on what is expected and to ensure transparency in assessment standards.
• Use rubrics to keep evaluation criteria structured and promote consistency.
• Assign numerical or letter grades to quantify performance and clearly articulate overall performance.
• Consider weighting grades to reflect the relative importance of different aspects of student performance.
• Provide feedback that is specific and actionable. 
• Ensure fairness and consistency to uphold equitable grading for all students.
• Communicate results clearly so that parents, students, and administrators understand learning outcomes.
• Offer opportunities for review and reflection to encourage students to engage with their assessment and improve moving forward.
• Use assessment data for instructional planning to tailor teaching strategies to student needs.
• Adhere to school or district policies to maintain compliance and consistency.

Formative vs. Summative Assessment Comparison Chart

Understanding these differences is crucial for educators to help students succeed in meaningful and effective ways. When teachers try out different assessment methods and grading styles, they get a better handle on student needs and can create an environment for widespread growth and improvement. 

The best way for teachers to advance their knowledge and understanding of the latest assessment methods is to keep up with professional development opportunities, such as with the University of San Diego’s Professional and Continuing Education (PCE) certificate program. Explore the website to learn more about hundreds of online and independent courses for teachers covering a wide range of subjects.

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What is a Formative Assessment?

Utilize formative assessment to implement feedback loops and create a dynamic learning environment that fosters continuous improvement.

by Michelle Schweikhardt

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Assessments in education often evoke a negative connotation, creating self-doubt and frustration in both students and teachers. Typically, one type of assessment causes this reaction: high-stakes standardized tests otherwise known as summative assessments.

Let’s step back and consider that assessment does have a place in teaching. High-quality formative assessment, when aligned with the curriculum, measuring student growth at all achievement levels, is an essential tool for instruction.

So where’s the disconnect? Not all assessments serve the same purpose, and while there are generally two types of assessments, formative assessments are typically overshadowed by the pressure placed on teachers by standardized (summative) assessments.

The good news is that, in today’s fast-paced educational landscape, formative assessment, implemented effectively, has emerged as a game-changer, offering educators a powerful tool to unlock their students’ full potential and drive academic growth.

By using formative assessment to implement effective feedback loops, educators can create a dynamic learning environment that fosters continuous improvement and inspires them (and their students) to embrace assessment as a catalyst for success.

Formative assessment drives tomorrow’s instruction

What are formative assessments? Unlike summative assessment, which typically evaluates student learning at the end of a unit or course, formative assessment occurs throughout a unit or course and provides real-time feedback to both students and teachers . This approach to assessment allows teachers and students to make mid-stream adjustments and improve understanding in real time.

By regularly assessing student understanding, educators can identify gaps in knowledge, tailor instruction for differentiation, and guide students toward mastery.

Simply put, formative assessment drives tomorrow’s instruction .

Formative assessment is not just about assigning grades or scores; it’s about gathering evidence of learning and using that information to inform instructional decisions.

John Hattie points out that teachers often work from theories and assumptions about student learning. Instead, educators need to concentrate on what students “say, do, write, or make to infer what they understand, know, feel, or think of learning.”

By using formative-assessment practices, educators can gain valuable insights into student progress, identify misconceptions , and adjust their teaching accordingly.

Assessment as learning

Seeing assessment as a formative activity that takes place throughout the learning process sometimes requires a paradigm shift. But when assessment is treated as part of the learning process, students can identify their strengths and weaknesses, and teachers are provided with an effective way to guide instruction.

This view of assessment is often associated with the idea of “assessment as learning,” where students are actively involved in the assessment process and use feedback to develop in their learning journey.

When continuous formative assessment occurs, the feedback creates a cycle of improvement where students can learn from their mistakes, receive targeted support, and make progress toward their learning goals.

Formative assessment strategies for teachers

Observations.

Observing students as they engage in learning activities can provide valuable insights into their understanding and progress. Observation checklists that focus on participation, interactions, or writing can offer evidence of learning, allowing teachers to adjust their instruction accordingly.

Questioning

Asking students well-crafted questions can help to assess understanding and promote critical thinking. Open-ended questions, probing questions, think-pair-share activities , or student conferences are effective ways to engage students in meaningful dialogue and elicit critical thinking. To amplify responses in a whole-group setting, students can answer questions using Talk Moves or every-student-responses .

Exit tickets

Exit tickets are short, quick assessments that students complete at the end of a lesson, activity, or class. They could take the form of a short poll, a reflection prompt, a summary , or a cloze activity . Exit tickets provide a snapshot of student understanding and help teachers gauge the effectiveness of their instruction.

Student self-assessment

Encouraging students to reflect on their learning and assess their progress is an important aspect of formative assessment. Self-assessment activities, such as self-reflection journals, learning logs , or rubrics enable students to take ownership of their learning and develop self-reflection skills.

Peer assessment

Peer assessment involves students giving authentic feedback to their peers. When tightly aligned to learning objectives, this not only provides valuable learning for the student being assessed but also helps the assessing student develop his or her own understanding.

Formative quizzes

Quizzes can be used as a formative assessment tool to check student understanding of factual knowledge, conceptual understanding, or problem-solving skills. They can be administered online or in class and can be designed to provide immediate feedback to both the teacher and students.

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Feedback to learn forward

Equally as important as the assessment itself is the feedback.

Formative assessment nurtures effective feedback. It allows for an immediate response, which is more effective in promoting learning as compared to delayed feedback. And, the more timely, specific, and actionable feedback students receive during the learning cycle, the better they can achieve their goals.

For example, a teacher who uses an exit ticket at the end of a mini-lesson can quickly assess student understanding. This information can then be used to adjust instruction or provide additional support to students.

According to research by John Hattie, “Feedback was among the most powerful influences on achievement. Most programs and methods that worked best were based on heavy dollops of feedback…THROUGHOUT the unit. Not all at the end when it’s too late.”

…the more timely, specific, and actionable feedback students receive during the learning cycle, the better they can achieve their goals.

Feedback is intended to close the gap between where the student is and where they are expected to be. To break the continuous cycle of students underachieving on summative assessments, feedback must be given simultaneously with formative assessments to close the gap.

In truth, figuring out “what” feedback to give and “how” to provide it to students may be more challenging than deciding on the formative assessment. With that in mind, here’s a helpful list of ways educators might consider using feedback to drive student thinking in the learning cycle:

List of ways to drive feedback

• Provide prompts or redirect student thinking toward the intended goal.
• Help students become aware of the strategies they are using or could use.
• Provide information or reteach on misunderstandings.
• Motivate students to feel more invested in their work.

Implementing formative assessment: Assess based on instruction

When teachers are ready to implement formative assessments, the first considerations are:

• What specific types of formative assessment will be used?
• How will data be collected and analyzed?
• How will data be used to adjust instruction?

During the planning process, keep in mind that formative assessment strategies (e.g., exit tickets, digital portfolios , etc.) and feedback methods should be purposefully chosen to match mini-lesson instruction.

Typically, when preparing a unit of instruction, teachers start with the standards, determine the new skills and instruction needed to meet those objectives, and then, decide how to assess student learning.

Teachers ASSESS based on INSTRUCTION.

Therefore, it’s natural to expect that a unit’s skills will be assessed in a final (summative) product or assessment. But, for many, there is a misunderstanding on how to use the days during the unit in preparation for the end of the unit.

Here’s a hint: give formative assessments after each mini-lesson.

Throughout a unit, new instruction is constantly happening. So assessment must be formative. Teachers need to give students numerous opportunities to experiment with isolated, new skills. That’s what makes that time “during” a unit so valuable.

To reach a level of mastery, teachers need to provide students with a scaffold of “practice” (formative) tasks that zero in on specific skills. Remember that formative assessment is simply the You do in the 4-step mini-lesson . So it should be an immediate and authentic application of the skill taught during the I do and We do .

A step-by-step approach to formative assessment

Consider this approach to effectively integrate formative assessment practices throughout a unit:

1. Establish learning goals –Begin by clearly defining the standards-based skills to teach students. What do you want students to know and be able to do? And in what order will you teach skills? By setting clear expectations, you provide a framework for both yourself and your students to assess progress.

2. Choose the You do –With each mini-lesson in a unit, create a You-do task (the formative assessment) that directly aligns with the isolated, mini-lesson skill taught. Choose assessment tasks that are authentic, meaningful, and engaging for students.

3. Communicate expectations –Teachers should communicate the purpose and expectations of formative assessment to their students, providing them with clear guidelines and expectations for participation.

4. Promote self-reflection –Encourage students to reflect on their learning. Provide opportunities for students to assess their progress, identify areas for improvement, and set goals. Help students develop self-reflection skills by asking them to think about how they learn best and what strategies they can use to overcome challenges. Encourage peer assessment and collaborative learning where students can provide feedback to their peers and learn from each other.

5. Provide timely feedback –Feedback is a critical component of formative assessment. Decide ahead of time what kind of feedback to provide and how students will receive the feedback. Effective feedback is specific, constructive, and actionable.

6. Use data to inform instruction –Collect and analyze formative assessment data to inform instruction. This data might be independent student work, written teacher observations, student self-assessments, or data from a digital-response tool. Use the data to identify patterns, trends, and areas of difficulty. Adjust teaching strategies, modify instructional materials, and provide targeted support to address student needs. Formative assessment drives the next lesson.

A formative assessment example

So now you might be asking “Where does formative assessment come into play in my daily lessons? What is a formative assessment in the classroom?”

Here’s an example:

A teacher just finished teaching a 4-step comprehension mini-lesson on how readers make an inference . Now she needs to formatively assess whether students can make an inference while answering a question about a provided text.

After seeing this process modeled in an I do , and again in a We do , it is now time for students to try it out in the You-do phase of the lesson. An effective formative assessment the teacher could use is the Silhouette Head graphic organizer .

Formatively assessing students with a graphic organizer is a strong strategy if the organizer has been modeled multiple times during mini-lesson instruction. With familiarity, the organizer is not something that needs to be explained to students in more detail. Students aren’t wrapped up in how to use the organizer and can simply move into applying their thinking.

The Silhouette Head graphic organizer, for example, allows the teacher to quickly see student annotations and their responses (or inferences) to the question. Feedback can then focus on a variety of facets: the annotations from the text, student connections, or the inference itself.

If time allows, teachers can provide individual feedback, but to help expedite the process and reach every student, they can meet with students to provide similar feedback in small-group conferences during the reader’s workshop.

Formative assessment activities provide educators with real-time insights into what students understand and what they’re missing. Involving students in the formative-assessment process also provides opportunities for more communication and collaboration, critical and metacognitive thinking, and student empowerment.

Formative assessment tools and resources for teachers

Interactive polling and quizzing tools.

Online quizzing and polling tools, such as Plickers , Kahoot! or Quizizz , and Google Forms allow teachers to create interactive quizzes that provide immediate feedback to students. These tools make assessment engaging and fun for students while providing valuable data on student understanding.

Digital exit tickets

Digital exit ticket platforms , like Padlet or Google Jamboard , enable students to submit their responses electronically at the end of a lesson or class. Teachers can quickly review the responses and use the data to inform their instruction.

Digital portfolios

Digital portfolios , created using platforms like Seesaw or Google Sites , provide a space for students to showcase their work and reflect on their learning. Students can upload their assignments, projects, or reflections, and teachers can provide feedback and comments directly within the portfolio.

Online discussion forums

Online discussion forums like Flip (formerly Flipgrid) or Edmodo enable students to engage in asynchronous discussions and share their thoughts and ideas. These platforms provide an opportunity for students to articulate their thinking, respond to their peers, and receive feedback from both their teacher and classmates.

Data analysis tools

Data analysis tools, such as Excel or Google Sheets , can help teachers analyze formative assessment data and identify patterns or trends. These tools can be used to create visualizations, track student progress over time, and make data-driven instructional decisions.

Buying into formative assessment

There’s probably not a teacher that would disagree that formative assessment is necessary and beneficial. Even still, it can be a demanding process for some. It can take extra time to effectively plan formative-assessment strategies and ensure that they are aligned with learning standards and objectives.

Teachers are also up against the clock to provide meaningful feedback to students and ensure that they are using the feedback to guide their learning.

With this in mind, some teachers might think “ If I don’t assign…I don’t have to assess… ” or “ There’s got to be something better .”

But the truth is, the rewards that result from using formative assessment far outweigh the extra time required on the planning side.

Unlock student potential and drive academic growth

To maximize the potential of formative assessment, create a classroom culture that promotes a growth mindset.

• Emphasize the importance of effort, perseverance, and learning from mistakes.
• Encourage students to view assessments as learning opportunities rather than judgments of their abilities.
• Celebrate progress and provide encouragement and support to help students overcome challenges.

By using this approach, teachers can create a classroom environment that values formative assessment as a powerful tool for learning. Remember that formative assessment is an ongoing process, and it requires continuous reflection and refinement—not just for students but teachers as well.

Be open to feedback, reflect on your practices, and be willing to adapt and try new approaches. With time and practice, formative assessment will become an integral part of your teaching toolkit, driving academic growth and unlocking the potential of every student.

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Principles and purposes of assessment in the classroom

• Perspective Article
• Published on: May 12, 2021

• Assessment |
• Curriculum |
• Developing effective learners |
• Promoting good progress |
• Research Engagement

Sarah Earle, Bath Spa University, UK

It might not always feel like it but, as teachers, we are constantly using assessment information to make decisions about what to say, what tasks to set and what to do with task outcomes. Every interaction with students is a potential assessment opportunity, in the sense that such interactions provide us with information about how learning is going, in order to help us to adapt our teaching.

Assessment influences school and classroom culture, impacts on pupil and teacher ideas about learning and determines what is taught and how. According to Stobart (2008, p. 1), ‘Assessment does not objectively measure what is already there, but rather creates and shapes what is measured.’

The effective use of assessment provides both the means to identify whether students have succeeded and the information to help teachers to support those who have not yet ‘got there’. This article will emphasise the use of assessment as we consider principles and purposes. It will explore formative and summative purposes to support meaningful use of assessment, and the principles of validity In assessment, the degree to which a particular assessment m and reliability In assessment, the degree to which the outcome of a particul to inform decision-making.

Formative and summative purposes

In its broadest sense, assessment is an integral part of teaching and includes ‘the process of gathering, interpreting and using evidence to make judgements about students’ achievements’ (Harlen, 2007, p. 11). All interactions with students potentially provide information that could support teachers to make judgements. And students should be included as judgement-makers, involving them in the active monitoring of their own learning.

The purpose of assessment is often hard to define, with information being used by a range of people for a variety of reasons. An important classification concerns formative and summative purposes. It is important to note that it is the use, rather than the activity, that designates the categorisation, because the majority of tasks can be utilised for formative or summative purposes. For example, a multiple-choice quiz can be used formatively to diagnose gaps in understanding or summatively to check understanding at the end of a unit.

Formative purpose in practice

Formative assessment concerns the ongoing classroom assessment practices that inform teaching. This could be something done at the beginning of a topic, to inform planning for the term, or it might be something done in lessons to check whether students need more time on a concept or whether they are ready to move on. In lessons, opportunities for formative assessment can benefit from consideration in advance – for example, deciding on key or ‘hinge-point’ questions or the focus for student recording.

Black and Wiliam (2009) identified the following aspects of formative assessment, which are considered in more detail by Wiliam (2018):

• where the learner is going – clarifying learning intentions and criteria for success
• where the learner is right now – eliciting evidence of student understanding through questioning, discussion and other learning tasks
• how to get there – providing feedback that moves the learner forward
• utilising peer and self-assessment.

These aspects could act as a guide for teachers to prompt reflection on classroom practice and help select which element could be the focus for professional development. For example, if a teacher finds that their questioning is not providing useful information about student understanding, then they may explore ways in which to increase the ‘wait time’ to provide the opportunity for more in-depth discussion and more detailed replies (Black et al., 2004). The aspects listed above are general principles rather than specifics for each lesson because formative assessment is not a list of strategies or a ‘recipe’ to follow; it requires ongoing reflection within and about the lesson. Responsive teachers should utilise their pedagogical content knowledge (PCK) to develop and refine interactions with their students to support learning.

Pupils give feedback about their learning in each verbal or written interaction. When you have identified a need, a gap or a misconception, then the key to formative assessment is to make sure that you do something with this information. For example, you might:

• ask the question in a different way to support understanding
• provide an additional explanation or demonstration
• make a note of a tricky concept to address in a later lesson
• identify those pupils who need some extra support in a particular area
• give verbal feedback to be acted upon in the lesson
• direct pupils to the agreed success criteria to support their self/peer assessment.

Summative purpose in practice

Summative assessment might be based on a ‘snapshot’ – an activity at a particular point in time, like an end-of-term test, or a summary that takes a range of information into account, like an end-of-key-stage teacher assessment (Earle, 2019). Utilising a wide range of information when drawing conclusions ‘by looking at patterns of performance over a number of assessments’ ( DfE Department for Education - a ministerial department responsi , 2019, p. 19) can help us to have more confidence in our judgements, because we are less likely to be focusing on results that are context- or task-dependent. Nevertheless, if all of the assessment tasks are drawn from the same pool, then we may still want to consider how much trust we place in our judgements. For example, written assessments for young children where many of the class cannot yet read fluently may only tell us about reading attainment, rather than knowledge of the topic.

Decisions about purposeful summative assessment should be directly related to the primary aim of reporting or summarising attainment. With this in mind, it is useful to consider the audience: who is the report or summary for? Identifying the audience will help to decide the amount of detail and the language used, since this will vary depending on whether the report is for a pupil, other staff (next teacher, head of department, etc), parents, etc. Nevertheless, assessment that has a primarily summative purpose can still be used in a formative way – for example, to identify gaps to inform the next term’s planning. Teachers may use summative assessment information over a longer period of time to support the development of their practice or the school’s curriculum.

The competing uses of assessment can place the teacher in a ‘conflicted position’ (Green and Oates, 2009, p. 233). Assessment for accountability may seemingly require a different approach to using assessment as part of the learning process. When feeling this ‘conflict’, a discussion with colleagues could be useful to clarify the purpose of the assessment. Teacher assessment literacy is an ongoing and developmental process (DeLuca et al., 2016) and such collaborative reflection can be useful for all colleagues.

The principles of validity and reliability to inform your decision-making

When making decisions about what assessment task to do or what information to gather, a consideration of the principles of validity and reliability can be useful. Both validity and reliability can be examined in great depth; to keep our discussion focused on the classroom, a brief definition for each is presented here, before discussing each in turn:

• validity: whether an assessment is fit for purpose and actually assesses what we want it to – does it merit the inferences that we base on it?
• reliability: trust in accuracy or consistency of an assessment.

Construct validity concerns how well the assessment samples the underlying skill, concept or subject (Stobart, 2009). When deciding on an assessment activity, it is important to consider what you would like to know: which knowledge, understanding or skills should be the focus? Recognising that an assessment activity can only sample a small part of the curriculum, it is worth confirming which part you are wanting to know about (not just the part that is easy to check!). This will help to decide whether the task is fit for your purpose (Green and Oates, 2009) and whether your inferences based on the results are justified. For example, a times tables test can support inferences about a child’s recall of multiplication facts, but not about the child’s attainment in mathematical problem-solving. Checking whether our inferences are justified helps to challenge our preconceived assumptions about our students. We all have preconceived assumptions, which help to make our teaching more manageable – we plan our lessons by second-guessing what students will be able to do – but assessment helps us to check whether they were in fact able to do it or not.

Two threats to validity are useful to consider when exploring the validity of assessment judgements. ‘Construct underrepresentation’ is the name given to issues of limited sampling of the subject, when the assessment is only focused on a small part of what you are interested in. For example, if only the decoding of words is assessed for reading, comprehension of the text will be underrepresented. To alleviate this threat, you need to either broaden the assessment information (broader task or utilising more tasks over time) or limit your inferences to more limited judgements about the sample assessed. The second threat to validity is ‘construct irrelevance’, whereby something gets in the way of the thing that you are trying to assess – for example, if the maths questions were too hard to read or marking is focused more on the neatness of the handwriting than the historical enquiry skills that were the focus for the assessment. Being very clear about the objective(s) being assessed helps to alleviate this threat to validity.

This discussion links to the question of whether the assessment is considering learning or merely performance – for example, has the pupil said the right word to get the mark, even if they have not understood it? One student supplying a correct answer for the class may be a ‘poor proxy for learning’ (Coe, 2013, p. 12). We can only assess the behaviours that we see, so we are reliant on performance to a certain extent. However, by drawing on a range of information and by discussing and questioning further, we can be more confident in our judgements. For example, if pupils use the right word, does that mean that they understand? You may need to question further or ask them to explain. Do they need to ‘say it’ just once? You may need to ask them to demonstrate their learning on more than one occasion, e.g. revisiting the topic later in the term.

Reliability

Reliability concerns the trust that we have in the accuracy or consistency of an assessment (Mansell et al., 2009) – for example, whether we would expect a similar result if we had asked the questions on a different day, or whether we trust the assessment enough to be able to compare between groups (if we need to). This is not just an afterthought; if we do not need to compare with other groups, in particular when we are using assessment formatively, then reliability is less of a concern. If the assessment is primarily about supporting students’ learning, then sitting the task in comparable conditions, etc., is not a priority. Reliability should be more of a concern for assessments with a primarily summative purpose.

Reliability issues can be split into internal and external. Internal reliability concerns the task itself – for example, whether the wording of questions is clear enough to mean the same to everyone, since there may be terms that are reliant on previous knowledge, which could disadvantage some. External reliability concerns issues outside of the task, such as marker consistency, which concerns whether other markers agree with your judgement. In situations where it is important to reach agreement, lists of criteria or mark schemes Criteria used for assessing pieces of work in relation to pa might be developed. These can help markers to be consistent, but they may also narrow the indicators, to a point where the assessment is more about ticking boxes than student attainment. For example, Key Stage 2 English writing assessment tick lists arguably led to a focus on grammatical devices rather than coherent, purposeful writing, with new methods of ‘comparative judgement’ now being explored (for example, by www.nomoremarking.com ) as a holistic alternative to criteria lists.

Reliability can be strengthened by:

• clearly defined criteria, e.g. success criteria, mark schemes, National Curriculum or exam board objectives
• external materials in controlled conditions (if end-of-year/key stage assessments need to be compared across groups)
• standardisation, e.g. compare work to agree the standard
• moderation, which may include standardisation, but also includes broader discussions about what ‘meeting’ and progression look like.

A final point regarding validity and reliability is that they can appear to be at odds with each other: ‘an assessment cannot have both high validity and high reliability’ (Harlen, 2007, p. 23). It is not possible to have highly repeatable, standardised assessment that samples the whole of the subject. Reliability relies on narrowing the task to help markers agree, while validity depends on the opposite: as broad a sampling of the subject as possible. This can be seen as an ‘inevitable trade-off’ (Wiliam, 2003) or a balancing act (Earle, 2017). The aim is to be reliable enough for the purpose, hence the need to be clear about the purpose of the assessment. For example, for primarily formative assessment, the support of learning is more important than standardised conditions, while a snapshot summative task for comparison across the cohort will need to address concerns of reliability.

At first glance, it may appear that we just need to ‘get on with it’ when it comes to assessment, with statutory and school structures guiding practice. But as discussed in this article, assessment is an integral part of your teaching and you can make decisions about its implementation and use on a daily basis. Assessment needs to provide value and useful information, which can be put to use to impact the learning of individuals and cohorts.   Pausing for reflection on assessment practice can help us to make assessment opportunities more fruitful and our teaching more responsive.

This is a shortened version of a chapter in The Early Career Framework Handbook , edited by the Chartered College of Teaching and published by SAGE.

Black P, Harrison C, Lee C et al. (2004) Working inside the black box: Assessment for learning Known as AfL for short, and also known as formative assessme in the classroom. Phi Delta Kappan 86(1): 8–21.

Black P and Wiliam D (2009) Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability 21(1): 5–31.

Coe R (2013) Improving education: A triumph of hope over experience. Centre for Evaluation and Monitoring and Durham University. Available at: www.cem.org/attachments/publications/ImprovingEducation2013.pdf (accessed 26 March 2021).

DeLuca C, LaPointe-McEwan D and Luhanga U (2016) Approaches to classroom assessment inventory: A new instrument to support teacher assessment literacy. Educational Assessment 21(4): 248–266.

Department for Education The ministerial department responsible for children’s serv (DfE) (2019) Early Career Framework. Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/913646/Early-Career_Framework.pdf (accessed 26 March 2021).

Earle S (2017) ‘ But I’ve not got time for any more assessment’: Balancing the demands of validity and reliability Impact 1: 44–46.

Earle S (2019) Assessment in the Primary Classroom: Principles and Practice . London: Learning Matters, Sage.

Green S and Oates T (2009) Considering the alternatives to national assessment arrangements in England: Possibilities and opportunities. Educational Research 51(2): 229–245.

Harlen W (2007) Assessment of Learning . London: Sage.

Mansell W, James M and the Assessment Reform Group (2009) Assessment in Schools: Fit for Purpose? London: Teaching and Learning Research Programme.

Stobart G (2008) Testing Times: The Uses and Abuses of Assessment . London: Routledge.

Stobart G (2009) Determining validity in national curriculum assessments. Educational Research 51(2): 161–179.

Wiliam D (2003) National curriculum assessment: How to make it better. Research Papers in Education 18(2): 129–136.

Wiliam D (2018) Embedded Formative Assessment , 2nd ed. Bloomington: Solution Tree Press.

From this issue

Issue 12: Assessment and Feedback

Summer 2021

Impact Articles on the same themes

From the editor

Transforming assessment principles and practices through collaboration: A case study from a primary school and university

The currency of assessment for learners with SEND

Rethinking assessment: How learner profiles can shift the debate towards equitable and meaningful holistic assessment

Assessing progress in special schools: Reviews and recommendations

• Original Research

Classroom assessment in flux: Unpicking empirical evidence of assessment practices

The role of frequent assessment in science education at an international school in Singapore

• Teacher Reflection

Teaching creativity: An international perspective on studying art in the UK

Improving academic resilience and self-efficacy through feedback: Moving from ‘what’ to ‘how’

Mind the gap: What are national assessments really telling us about vocabulary and disadvantaged students?

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K–12 policies and resources

• Student assessment

Understanding K–12 assessment

The following information outlines the K–12 assessment position of the Queensland Curriculum and Assessment Authority (QCAA) and provides a foundation for building and clarifying knowledge and understanding of assessment literacy. It is intended to support and guide the processes integral to quality teaching, learning, assessment and reporting.

Understanding K–12 assessment (PDF, 307.3 KB)

All Queensland teachers and students deserve to benefit from their assessment experiences. Assessment should provide timely and useful information that can be used by teachers and students alike to improve how teachers teach and how and what students learn. Assessment is an essential component of effective teaching and learning.

Assessment:

• improves teaching by providing information on what students know and can do
• helps students progress in their learning by giving them feedback to inform their next steps in learning
• provides meaningful information on students’ strengths, learning needs and achievements.

Principles and attributes of assessment

The following principles form the foundation of beliefs about assessment practices.

Principles of quality assessment (QCAA 2017a) should be:

• aligned with curriculum and pedagogy
• equitable for all students
• evidence-based , using established standards/continua to make defensible and comparable judgments about students’ learning
• ongoing , with a range and balance of evidence compiled over time to reflect the depth and breadth of students’ learning
• transparent , to enhance professional and public confidence in the processes used, the information obtained and the decisions made
• informative of where students are in their learning.

Quality assessment (QCAA 2017b) is characterised by three attributes:

• validity , through alignment with what is taught, learnt and assessed
• accessibility, each student is given opportunities to demonstrate what they know and can do
• reliability , assessment results are consistent, dependable or repeatable.

Assessment is the ongoing process of gathering, analysing and reflecting on evidence to make informed judgments about the achievement or capabilities of individuals and cohorts.

Assessment plays an integral role in improving learning and informing teaching. Its fundamental purpose is to establish where learners are in an aspect of their learning at the time of assessment (Masters 2014).

The literature uses different terms about assessment, including assessment for, as and of learning, diagnostic, formative and summative.

Assessment for, as and of learning

Assessment for learning, assessment as learning and assessment of learning (Earl 2013) are purposes for which evidence is gathered about student progression to improve teaching and learning. Assessment for these purposes can involve both teachers and students, providing opportunities for them to give and receive feedback and inform future planning. The principles and attributes described above should be considered when planning any assessment.

Assessment for learning

Assessment for learning occurs throughout the learning process and could be diagnostic [1] and/or formative [2] .

Assessment as learning

Assessment as learning places the student central to the processes of assessing and learning. Students monitor their own learning and use formal and informal feedback and self-assessment to determine the next steps required to meet learning outcomes/objectives. Assessment as learning encourages students to take responsibility for their own learning.

Assessment of learning

Assessment of learning is often referred to as summative [3] assessment and can include formal assessment tasks, internal or school-devised assessment and external assessment.

Uses of assessment

Assessment information has multiple uses, including:

• evidence of students’ strengths, ways of learning, areas of development, the depth of their knowledge, and their conceptual understandings, which informs the teacher, so they know what students can do, and what subsequent teaching is required to progress student learning
• identification of students’ learning needs across a range and balance of assessments that enhances teachers’ ability to establish where students are in their learning and to help them attain higher levels of performance
• clear, specific, meaningful and timely feedback, allowing reflection on the learning process and collaboration to support future learning and development
• evidence of student learning and advice for further progress, underpinning the provision of meaningful reports/statements to parents/carers and others
• development of lifelong learners by enabling students to identify and reflect on the progress they are making, which is crucial to building self-evaluation, self-efficacy and self-responsibility for in-depth and long-term learning
• refinement of quality teaching, by supporting teacher reflection and professional learning
• provision of information for certification
• measurement and evaluation of policies, programs, interventions and teaching strategies to provide better understanding of student achievement and growth.

Assessment literacy

What is assessment literacy.

Assessment literacy is defined as the skills and knowledge teachers require to design, evaluate and quality assure assessment performances to support student learning (DeLuca 2016).

Teachers who are assessment literate:

• produce quality assessment
• demonstrate the required knowledge and skills to validly and reliably assess students’ learning
• apply standards/descriptions consistently to, and make judgments about, students’ learning/work
• interpret and apply the feedback and data from assessment to improve teaching and learning.

As students move through the phases of schooling, they become increasingly assessment literate, with the ability to:

• understand the purpose of what they are doing
• understand the basis on which judgments will be made
• demonstrate this understanding through their engagement with assessment
• reflect on feedback and apply it in the future.

School assessment policies

School assessment policies provide guidelines for teachers and expectations for all staff and students for assessment. These policies support schools in promoting equitable and credible outcomes, including academic integrity.

Academic integrity

Academic integrity requires academic responsibilities to be approached in an honest, moral and ethical way. Schools, parents/carers and others who support students in their learning are responsible for promoting and maintaining academic integrity.

When students genuinely demonstrate their learning, they achieve results based on their own work and effort. Students will become increasingly more aware of their responsibility in demonstrating academic integrity as they progress through the phases of schooling.

Quality assurance

Assessment-literate teachers use quality assurance processes to develop a shared understanding of the expected quality of learning performance (Willis & Adie 2016). This assists teachers to improve teaching and inform assessment processes.

Quality assurance processes involve teachers:

• engaging in in-depth conversations and/or professional learning prior to teaching about what standards will look like in practice
• collaborating to design assessment tasks aligned with the principles and attributes of quality assessment
• sharing learning intentions/objectives and standards/marking criteria with students
• engaging in feedback, moderation and professional conversations and activities.

Moderation of assessment is a process in which teachers engage in focused dialogue to share their observations and judgments in order to:

• improve the consistency of their decisions
• ensure their judgments are as valid, reliable and fair as possible.

Conversations should occur before judgments about the quality of work are given to learners. This provides students and parents/carers with confidence that the decisions made are an accurate judgment of achievement.

Quality assurance processes for Senior schooling

The QCAA operates quality assurance processes for internal assessment in Applied, Applied (Essential), General, General (Extension) subjects and Short Courses.

The QCAA quality assurance processes support schools to develop and administer assessment instruments and ensure consistency of judgments about student responses. The processes support the continual improvement of assessment practices in schools.

Purpose of feedback

The purpose of feedback is to provide meaningful information about a student’s strengths and areas for improvement to support them to progress towards their learning goals.

How teachers and students make use of assessment information is vital to understanding and improving learning. Effective feedback encourages self-reflection, allows students to actively monitor and evaluate their own learning, and facilitates self-direction and motivation. Together assessment and feedback support continuous, collaborative, active and self-directed learning.

Characteristics of effective feedback

To support evaluation, self-reflection and improved understanding, feedback should be:

• individualised
• specific to the teaching, learning and assessment related to the standards/descriptions
• clear, and in language that is readily interpreted by the intended audiences
• timely, so that students can act on it and adjust their learning
• collaborative, so that students, teachers and parents/carers all support and participate in the students’ learning
• delivered in a way to support the learner to reflect, act on the feedback and build their capacity for self-assessment.

Schools should refer to their sector policies for reporting requirements.

Purpose of reporting

The purpose of reporting is to communicate assessment information, formally or informally, to help students, parents/carers, teachers and education authorities make decisions about what students know and can do, including recommendations for their future learning.

Reports/statements may provide:

• information about progress and achievement to parents/carers and students
• summaries of the school’s achievements and progress for school communities
• statewide and national statistical information and analyses to broader educational communities.

Characteristics of effective reporting

To support the effective communication of achievement, areas for improvement, and actions that the student, school and parents/carers might take, reports/statements should be:

• aligned with the curriculum and assessment
• defensible, comparable and based on clearly defined achievement standards
• in plain English so they are easy to interpret and understand.

The National Education Agreement (Australian Government 2015) underpins the legal obligations of schools and teachers in relation to reporting.

Australian Government 2018, The National School Reform Agreement: https://www.dese.gov.au/quality-schools-package/national-school-reform-agreement

Earl, L M 2013, Assessment as learning: Using classroom assessment to maximise student learning 2nd edn, Corwin, California, USA, ISBN 978-1-4522-4297-2

DeLuca, C, LaPointe-McEwan, D & Luhanga, U 2016, ‘Approaches to classroom assessment inventory: A new instrument to support teacher assessment literacy’, Educational Assessment , vol. 21, issue 4, pp. 248–266, https://doi.org/10.1080/10627197.2016.1236677

Masters, G N 2014, ‘Assessment: Getting to the essence’, Designing the Future , issue 1, Centre for Assessment Reform and Innovation, www.acer.org/cari/articles/assessment-getting-to-the-essence

Queensland Curriculum and Assessment Authority (QCAA) 2020, QCE and QCIA policy and procedures handbook v2.0 https://www.qcaa.qld.edu.au/senior/certificates-and-qualifications/qce-qcia-handbook

Queensland Curriculum and Assessment Authority (QCAA) 2018, Understanding K–12 assessment, www.qcaa.qld.edu.au/k-12-policies/student-assessment/understanding-assessment

QCAA 2018a, Principles of quality assessment, www.qcaa.qld.edu.au/k-12-policies/student-assessment/understanding-assessment/principles-quality-assessment

QCAA 2018b, Attributes of quality assessment, www.qcaa.qld.edu.au/k-12-policies/student-assessment/understanding-assessment/attributes-quality-assessment

Willis, J & Adie, L 2016, ‘ Developing teacher formative assessment practices through professional dialogue: Case studies of practice from Queensland, Australia’, paper presented at the 2016 Annual Meeting of the American Educational Research Association,Washington DC, 8–12 April, https://eprints.qut.edu.au/98412

[1] Diagnostic assessment gathers evidence on a student’s strengths or discrete knowledge and skills. This evidence can inform further support, differentiation or intervention to teaching and learning.

[2] Formative assessment is undertaken throughout the teaching and learning process to determine progress on achieving learning outcomes/objectives. Formative assessment provides the basis for feedback that is used to adjust teaching and learning and can help teachers to differentiate instruction.

[3]Summative assessment is undertaken at defined key points of the teaching and learning process to indicate standards achieved and informs reporting/certification. Summative assessment provides sufficient evidence of learning to make defensible and comparable judgments about the quality of student responses against predetermined standards/objectives.

• Principles of quality assessment
• Attributes of quality assessment
• Syllabus development
• Cultural Capability Action Plan 2024–26
• Perspectives Statement 2017–20
• Equity statement
• Building relationships
• Ethical research
• Inside and outside knowledge
• Working with guest speakers
• Acknowledgment of Country
• Welcome to Country
• Indigenous Cultural Intellectual Property (ICIP)
• Aboriginal ceremonies
• Aboriginal lore
• Australian Curriculum cross-curriculum priority
• Knowledge frameworks
• Mathematics as storytelling
• Oral histories
• Relationships to Country/Place
• Seasons and stars
• Spirituality and religion among Torres Strait Islanders
• Storytelling
• Visual art and Aboriginal knowledges
• Visual art and Torres Strait Islander knowledges
• Yarning circles
• Equity resources
• Academic Integrity and Artificial Intelligence
• Assessment Design and Artificial Intelligence
• Digital Literacy and Artificial Intelligence

Purposes and types of assessment used in education and training

Table of Contents

This paper delves into the various assessment methods employed in educational settings, spanning initial interviews to diagnostic, formative, and summative evaluations. Special emphasis is placed on the benefits and drawbacks of each method, as well as the accommodations provided for students with special needs, to ensure an equitable assessment environment.

Introduction

Initial assessment and interview process.

The first assessment that a student faces upon joining the course is an initial assessment in the form of an interview, during this interview the student’s A level results will be checked to ensure they meet the minimum requirements of the course. This is also the ideal opportunity to ascertain why the potential student has applied for the course and what they are hoping to achieve, along with any specific additional support needs. When teaching a level 3 course it is also essential for students to have a Maths or English qualification, if one of these qualifications has not been obtained they will not be able to join the course and a lower level course will be required. The initial assessment that is used to interview students is far from perfect, there will be aspects of the student’s ability that are missed, possibly resulting in a place on the course not being offered.

Diagnostic Assessment: Unearthing the Gaps

Formative assessment: observations and discussions.

During teaching I am continuously checking learning in the form of formative assessment, the two primary methods I use are observations and discussions. Using observations as an informal performance monitoring method of tasks is excellent for gauging how much information students have retained. Observations clearly show how well students are able to complete practical tasks. There are negatives to observations, many students will become nervous when I am observing their work and may not perform at their highest level. Another formative assessment method is discussions, which allow students to talk about a specific subject with varying degrees of freedom. A discussion requires careful management to ensure the conversation remains on topic and all students are involved, this can be a major issue when using discussion as an assessment method as shy students will do their best to remain silent. Discussions suit learners with aural learning preference and can also be used to support learners with visual impairment

Summative Assessment: Exams and Their Implications

Accommodations for students with special needs.

When I am exam invigilator I provide additional time for students with dyslexia, the exam papers are also available in different colours and coloured overlays are available for students if required. The same exam paper is also available in a larger font to assist students with visual impairment and a digital copy is provided in order to be used with computer screen readers for students with severe visual impairment.

Further reading

Assessment for learning: putting it into practice by paul black, christine harrison, clare lee, bethan marshall, and dylan wiliam., inclusive assessment and accountability: a guide to accommodations for students with diverse needs by sara e. bolt and andrew t. roach..

This book provides comprehensive information on inclusive assessment practices, especially for students with special needs.

How to Create and Use Rubrics for Formative Assessment and Grading by Susan M. Brookhart.

Assessment for learning project, national center on educational outcomes (nceo).

NCEO provides research and resources on educational assessments, especially focusing on students with disabilities and English Language Learners. They have a plethora of publications on inclusive assessment practices.

Learning Forward

What is the purpose of assessment, what are the 7 principles of assessment.

The seven principles of assessment are foundational guidelines ensuring assessments are effective and equitable. These principles include: clarity of purpose, relevance, validity, fairness, reliability, manageability, and continuous reflection and review. Collectively, they ensure that assessments are meaningful, accurate, and promote genuine understanding and improvement in the learning process.

What are the 5 purposes of assessment in education?

How do cultural differences and backgrounds impact the effectiveness and fairness of assessments, what are the long-term impacts on students who consistently perform poorly on standardised assessments.

Students who consistently perform poorly on standardised assessments may experience diminished self-esteem, leading to decreased motivation and engagement in their educational journey. Over time, they might internalise these negative outcomes, developing a fixed mindset about their abilities and potential, which can limit future academic and career opportunities. Furthermore, consistent underperformance can result in missed educational interventions or supports, leaving underlying learning challenges unaddressed and perpetuating the cycle of struggle.

How do digital technologies and online learning environments impact traditional assessment methods and their effectiveness?

Are there alternative assessment methods that might better cater to diverse learning styles than the ones mentioned, how do educators ensure that the assessment tools themselves remain up-to-date with the ever-evolving curriculum and teaching methodologies.

Educators frequently review and revise assessment tools in collaboration with curriculum developers, ensuring alignment with current learning objectives and teaching strategies. They also participate in professional development and training sessions, staying informed about the latest educational research and best practices in assessment. By gathering feedback from students, peer educators, and utilising data-driven insights, they can refine and adapt assessments to better match the evolving educational landscape.

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Special Education and Inclusive Learning

Mastering Formative and Summative Assessments in the Classroom

Understanding and utilising different types of assessments in education.

As educators, we use various forms of assessment to evaluate student learning, inform our instruction, and provide feedback. Four key types of assessment are formal, informal, summative, and formative. Understanding the distinctions and appropriate uses of each is crucial for effective teaching and learning. According to a 2019 National Center for Education Statistics study, schools that regularly use formative assessments saw a 10-15% improvement in overall student performance on standardized tests.

Formal vs. Informal Assessments

Formal assessments are structured, standardized evaluations that measure specific learning outcomes. These typically include tests, quizzes, projects, presentations, and other planned assessments that all students complete in the same manner. Formal assessments provide concrete data on student performance and progress.

Informal assessments, on the other hand, are more fluid and occur naturally throughout the learning process. These can include observing students during activities, listening to their discussions, reviewing their classwork, asking questions, and gauging their participation. Informal assessments give teachers valuable insights into student understanding and engagement on an ongoing basis.

While formal assessments are often graded, informal assessments usually are not. However, this is not a hard and fast rule – some informal assessments may be graded and some formal ones may not be. The key distinction is the level of structure and standardization.

Formative vs. Summative Assessments

Formative assessments are used to monitor student learning and provide ongoing feedback during the instructional process. Their primary purpose is to identify areas where students are struggling so teachers can adjust their teaching and provide targeted support. Examples include quick quizzes, exit tickets, draft essays, and practice problems.

• Pop quizzes
• Peer evaluations
• One-minute papers

Summative assessments evaluate student learning at the end of an instructional unit against a standard or benchmark. They are used to determine grades, measure progress, and assess cumulative knowledge. Examples include final exams, term papers, capstone projects, and standardized tests.

• Final exams
• Research papers
• Capstone projects

Contrary to some misconceptions, formative assessments can be graded, though they often are not. Summative assessments are typically graded, but this is not always the case. The key difference is when and how they are used in the learning process.

Nuances and Overlap

While these categories are useful, there is often overlap between them. For example:

• A unit test could be both summative (assessing mastery of that unit) and formative (informing instruction for the next unit).
• A graded homework assignment may be formal in structure but formative in purpose.
• An end-of-year standardized test is summative for that year but may be used formatively to plan for the next year.
• Informal observations can provide formative feedback to both students and teachers.

Assessment Type Comparison Chart:

Cultural Considerations: When designing assessments, be mindful of cultural biases. Ensure that questions and examples are inclusive and relevant to all students’ backgrounds.

Assessment Validity and Reliability:

• Validity: Ensure your assessment measures what it’s intended to measure.
• Reliability: Strive for consistency in results across different times or scorers.

Ethical Considerations:

• Maintain student privacy when sharing assessment results.
• Be aware of potential biases in assessment design and scoring.
• Ensure equal access to assessment preparation materials.

Differentiation Strategies:

• Offer multiple formats (e.g., written, oral, visual) for assessments.
• Allow extended time for students who need it.
• Provide scaffolding or simplified language where appropriate.

Assessment Issues Troubleshooting Guide:

Best Practices for Using Assessments

• Use a variety of assessment types to get a well-rounded picture of student learning.
• Align assessments closely with learning objectives and instructional methods.
• Use formative assessments frequently to monitor progress and adjust teaching.
• Provide clear expectations and criteria for formal and summative assessments.
• Use assessment data to inform instruction and provide targeted support.
• Involve students in the assessment process through self-evaluation and peer feedback.
• Balance the use of graded and ungraded assessments to motivate without overstressing students.
• Consider the purpose of each assessment when deciding whether to grade it.
• Use summative assessments as opportunities for students to demonstrate mastery in authentic ways.
• Reflect on assessment results to improve both teaching and assessment practices.

Effective use of various assessment types is crucial for supporting student learning and improving instruction. By understanding the nuances of formal, informal, formative, and summative assessments, teachers can create a comprehensive assessment strategy that provides valuable insights and promotes student success. Remember, the ultimate goal of any assessment should be to enhance the learning process and outcomes for all students.

Actionable Steps:

Audit your current assessment practices. Incorporate at least one new assessment type into your next unit. Collect student feedback on assessment methods. Collaborate with colleagues to share effective assessment strategies. Regularly review and adjust your assessment approach based on student outcomes.

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Mathematics teaching, learning, and assessment in the digital age

• Survey Paper
• Open access
• Published: 10 July 2024

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• Hans-Georg Weigand   ORCID: orcid.org/0000-0001-6099-1318 1 ,
• Jana Trgalova 2 &
• Michal Tabach 3  

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The role of teaching, learning, and assessment with digital technology has become increasingly prominent in mathematics education. This survey paper provides an overview of how technology has been transforming teaching, learning, and assessment in mathematics education in the digital age and suggests how the field will evolve in the coming years. Based on several decades of research and educational practices, we discuss and anticipate the multifaceted impact of technology on mathematics education, thus laying the groundwork for the other papers in this issue. After a brief introduction discussing the motivations for this issue, we focus our attention on three lines of research: teaching mathematics with technology, learning mathematics with technology, and assessment with technology. We point to new research orientations that address the issue of teaching with technology, specifically describing attempts to conceptualise teachers’ mathematical and digital competencies, perspectives that view teachers as designers of digital resources, and the design and evaluation of long-term initiatives to support teachers as they develop innovative teaching practices enhanced by digital technologies. Our examination shows that learning with technology is still marked by new conceptualizations raised by researchers that can further our understanding of this complex issue. These conceptualizations support the recognition that multiple resources, ranging from paper and pencil to augmented reality, participate in the learning process. Finally, assessment with technology, especially in the formative sense, offers new possibilities for offering individualised support for learners that can benefit from adaptive systems, though more tasks for conceptual understanding need to be developed.

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Avoid common mistakes on your manuscript.

1 Introduction

The widespread availability of digital educational technologies and resources will increasingly influence mathematics teaching and learning in the coming years. How will this growing influence affect teachers and students of mathematics? Which digital and analogue resources will be used in the classroom? How will the use of digital technology affect the theory of mathematics education and the implementation of ideas in the classroom? And finally, what are the consequences for ongoing and final classroom assessments? These questions have been discussed extensively over the last decades in diverse mathematics education journals (see especially ZDM issues 55(1), 2023; 52(7), 2020; 52(5), 2020; 49(5), 2017; 44(6), 2012; 42(7), 2010; 41(4), 2009; 34(3), 2002) and at many conferences, especially the biennial Congress of the European Society for Research in Mathematics Education (CERME), which began in 1999. In 2018, a group of participants who were deeply involved in the CERME Thematic Working Groups on Technology took the initiative to launch the ERME Topic Conference for Mathematics Education in the Digital Age (MEDA). This conference sought to expand discussion of theoretical and practical knowledge and experience in the context of digital technologies and to look ahead at how mathematics education ought to be shaped in the coming years. The articles in this issue are significantly influenced by the three MEDA conferences and in particular are based on papers given at the 2022 MEDA3 conference held in Nitra, Slovakia (Weigand et al., 2022 ).

We begin by explaining the terminology we use in this article, followed by our methodological considerations. The literature uses various terms and expressions to refer to digital devices and digital content for mathematics teaching and learning, the most common of which are digital tools, digital technology, digital resources, and digital media. Because these terms are often used interchangeably, here we discuss each of them briefly to support our decision regarding the terms we use in this paper. Monaghan et al. ( 2016 ) broadly define a tool as “something you use to do something” (p. 5), thus distinguishing a tool from an artefact, defined as an object (material or symbolic) made by humans for a specific purpose. According to these authors, “an artefact becomes a tool when it is used by an agent, usually a person, to do something” (ibid., p. 6). Hence, according to the instrumental approach a tool is called an instrument (Rabardel, 2002 ) in that it cannot be conceived without considering a user and a purpose. The term digital technology usually refers both to tangible devices such as computers or tablets and to intangible means such as software. In the previous conceptualization, digital technology was considered an artefact or a tool when someone used it to achieve a given goal. In the last decade, researchers have begun referring to resources available for teachers and students rather than to technology: “Resources might be software, computers, interactive white-boards, online resources, but also traditional geometry tools and textbooks” (Trgalová et al., 2018 , p. 146). The term resource was conceptualized by Adler ( 2000 ), who suggested thinking of it “as the verb re-source, to source again or differently” (p. 207). This perspective emphasizes the user-resource relationship in which the user’s activity is nourished by the resource and, in turn, the resource can be modified and adapted by the user. Yet another perspective views mathematical knowledge as mediated by artefacts (Vygotsky, 1978 ). To stress the mediating role of a digital artefact, some researchers use the term digital media . Borba et al. ( 2023 ) suggest considering media in a broad sense; for them “computers, videos, paper-and-pencil, regular classrooms, homes, and libraries are examples of media” (p. 2). According to the theoretical construct of “humans-with-media”, digital technologies are thought “to be coparticipants in the production of mathematical knowledge” (ibid., p. 3).

In this paper, we use the term digital technology to refer to hardware or software. Furthermore, in referring to other objects used in mathematics education, such as videos, e-textbooks, and interactive whiteboards, we have chosen to adopt the term resources (whether digital or non-digital) that is widely used in mathematics education research.

After defining our terminology, we can now explain our methodological approach to the topics of teaching, learning, and assessment in the digital age. Like any survey, this survey paper must set the boundaries of what to retain and what to omit. In setting these boundaries, we have adopted two guiding principles. On the one hand, we have attempted to avoid repeating information from recent publications. One example is the chapter on “Technology and Resources in Mathematics Education” (Trgalová et al., 2018 ) in the book Developing Research in Mathematics Education (Dreyfus et al., 2018 ), released to celebrate the 20th anniversary of the European Society for Research in Mathematics Education (ERME) and its tenth congress (CERME). The chapter reviews the last 20 years of technology use in research and practice, describing the development of technology and resources and the design and implementation of digital mathematical tasks and theories and approaches concerning technology and resources. Another example is the book Mathematics Education in the Digital Age (Clark-Wilson et al., 2021 ), which emerged from the intense communication and collaboration during and after the MEDA1 conference. Finally, the recently published handbook on Digital Resources in Mathematics Education (Pepin et al., 2023 ) “presents the state-of-the art scholarship on theoretical frames, mathematical content, learning environments, pedagogic practices, teacher professional learning, and policy issues related to the development and use of digital resources in mathematics education” (p. 2). On the other hand, we have sought to be sensitive to the contributions appearing in this special issue. These two considerations reflect our view of the purpose of this paper: to position the contributions of the special issue in the broader context of the field. We categorised these contributions into three topics inspired by the recent MEDA3 conference: teaching, learning, and assessment with technology. These contributions propose new theoretical developments for tackling emergent issues and employ a variety of research methods, leading to further methodological elaborations: case studies and other qualitative methods; quantitative studies; and mixed methods. In the survey we have also taken into consideration publications from the last five years in journal papers and at leading conferences such as CERME, ICTMT, and MEDA.

Despite highlighting these three main aspects—teaching, learning, and assessment with technology—we are aware of other fields of interest related to technology in mathematics education. While we do not explicitly refer to these, we do touch upon them when relevant to this issue, e.g., technology and curriculum design, technology in instruction processes, technology and embodiment, and technology and beliefs of teachers and students. Moreover, many published studies have focused on young students working with digital technology, especially with tablets and special apps (e.g., Cavalletti et al., 2023 ; Kortenkamp et al., 2020 ) using Scratch or TouchCount (Bakos, 2023 ). In this issue, we concentrate on the use of digital resources in secondary education as all the papers in this special issue address this school level.

We begin our discussion with an overview of recent developments in teaching with technology , with specific emphasis on teachers’ digital competencies in using technology effectively in the classroom and on the role of teachers as designers of digital resources. The section on learning with technology begins with an overview of the use of multiple resources while learning mathematics and then discusses new developments such as augmented reality and video technology. The section on assessment with technology emphasizes the meaning of formative and summative assessment and discusses automatic feedback and adaptive assessment, conceptual understanding, and task design in the development of assessment profiles. In discussing each of these topics, we anticipate the possible future developments emerging from the present state of research to provide further perspective on the use of digital resources in the digital age.

2 Teaching with technology

In a recent survey paper on teaching mathematics with digital technology, Clark-Wilson et al. ( 2020 ) noted that in the last two decades, the focus of research studies has shifted from how technology can foster students’ learning to “how teachers can make practical use of different types of digital technology to provide students with activities that will enhance their mathematical learning” (p. 1223). This shift reflects researchers’ acknowledgement of the fact that “of all the factors influencing student activity it is the teacher who most influences learning” (ibid.).

Topics that address teaching with digital technology and resources include the investigation of obstacles and levers to digital technology integration (e.g., Thomas & Palmer, 2014 ), teachers’ knowledge, beliefs, and competences and the way these influence their digital practices (e.g., Remillard et al., 2024 ), digital task design to support teachers’ use of technology (Mariotti et al., 2023 ), design and evaluation of teacher education, and professional development programs (e.g., Thurm et al., 2024 ).

In this section we provide an overview of three ‘hot’ research topics in the area of teaching mathematics with digital technology that are also the focus of papers in this special issue: teachers’ digital competencies, teachers as designers, and innovative teaching practices leveraged by digital technology.

2.1 Teachers’ digital competencies

The belief that teachers are one of the most important factors influencing student learning when it comes to integrating digital technology in mathematics classrooms led researchers to studying teachers’ practices (e.g., Hennessy et al., 2005 ; Haspekian, 2014 ), knowledge, and skills needed for effective use of digital technology (e.g., Niess et al., 2009 ; Rocha, 2013 ), obstacles to technology integration (e.g., Jones, 2004 ), and affective aspects such as beliefs or personal orientations (e.g., Thomas & Palmer, 2014 ). Considering both cognitive (knowledge) and non-cognitive dimensions (e.g., affective, motivational) underscores the need to focus on teachers’ competencies, as Carr ( 1993 ) points out:

It is argued that we need teachers who are not just knowledgeable or well-informed about education , but whose knowledge and understanding is expressed or exhibited in their abilities - teachers, in short, who are competent by virtue of the intelligent application of their knowledge and understanding in effective practice (p. 254, author’s emphasis).

Hence, the notion of digital competency emerged in the context of digital technology. Various frameworks are available that describe this competency, mostly in institutional documents such as the European Commission Digital Competence Framework for Educators (Redecker & Punie, 2017 ) or the UNESCO ICT Competency Framework for Teachers (Butcher, 2018 ) at the international level. These frameworks Footnote 1 are general and apply to any subject matter and school level.

In their recent literature review of teachers’ professional digital competence (TPDC), Skantz-Åberg et al. ( 2022 ) point to the scarcity of conceptualizations, stating that almost 75% of papers reviewed do not provide a clear definition of the terms they use. The authors express regret that the view of technological competence as “a set of basic technological skills” or “something that applies mainly to teachers’ handling of digital technology” (p. 10) is the most prominent pedagogical view and that its development is considered to be the responsibility of individual teachers. The authors conclude by claiming that

the conceptualisation of TPDC needs to be directed away from the strong focus on the technological competence and basic hands-on skills of individual teachers to a focus on a collective responsibility and accountability for TPDC (p. 16).

In a similar study that examines teachers’ digital competencies in higher education, Basilotta Gómez‑Pablos et al. ( 2022 ) note that the various conceptualizations in the literature converge in “the need for teachers to have didactic and technological knowledge that allow them to make use of digital technologies in their professional practice” (p. 2). The authors call attention to emerging lines of research, among them the necessity “to rely on frameworks and theoretical reference models that identify the dimensions and components of digital competence” (p. 8, authors’ emphasis) and to develop methods for assessing teachers’ digital competencies, since currently most methods are based on “teachers’ self-perception” (p. 9).

Gonscherowski and Rott ( 2023 ) also recently noted that self-assessment is a dominant instrument for assessing teachers’ digital competencies. Indeed, at CERME12 (Clark-Wilson et al., 2022 ) mathematics teachers’ digital competences emerged as one of the “hot” topics in the field of research on teaching mathematics with digital technology and resources. Conceptualising these competences requires considering relevant theoretical frameworks to provide an operational definition of their dimensions and components and to elaborate research methods for capturing and assessing them.

Recent mathematics education research includes initiatives toward defining teachers’ digital competencies that consider specificities related to teaching mathematics. Based on the assumption that the distinction between students’ mathematical and digital competencies tends to fade away, Geraniou and Jankvist ( 2020 ) contend that mathematical and digital competencies must be articulated for teaching as well. These authors use a network of four theoretical frameworks—the Danish KOM framework of mathematics teachers’ competencies (Niss & Højgaard, 2011 ), mathematics knowledge for teaching (Ball et al., 2008 ), TPACK (Mishra & Koehler, 2006 ), and instrumental orchestration (Trouche, 2004 )—to conceptualise mathematical digital competencies for teaching (MDCT). According to Geraniou et al. ( 2022 ), MDCT are “the competencies teachers need (or have) to select and implement technology in their practice in pedagogically productive ways” (p. 167). In this issue, Geraniou et al. ( 2024 ) further elaborate on these competencies by drawing on the concept of mathematics digital competence for students (Geraniou & Jankvist, 2019 ). They rely on the theory of instrumental orchestration, the KOM framework, and the documentational approach to didactics (Gueudet & Trouche, 2009 ; Trouche et al., 2018 ), illustrating their arguments with the case of an experienced teacher.

Dilling et al. ( 2024 , this issue) adopt a different approach. Extending the TPACK framework (Mishra & Koehler, 2006 ), these authors propose the media, pedagogy and content model (MPC) to describe mathematics teachers’ professional media competencies, which they define as “competencies that enable a teacher to evaluate and select digital technologies and use them in the mathematics classroom effectively”. Although these two conceptualizations—MDCT and MPC model—draw on different theoretical frameworks, they share the view that digital competencies allow teachers to identify the affordances and limits of digital tools and consequently select the appropriate ones to be used in support of students’ mathematics learning.

2.2 Teachers as designers

Many researchers have acknowledged the importance of tasks in mathematics teaching and learning. Sierpinska ( 2004 ) considers “the design, analysis and empirical testing of mathematical tasks, whether for the purposes of research or teaching, as one of the most important responsibilities of mathematics education” (p. 10). Watson et al. ( 2013 ) claim that “task design is core to effective teaching” (p. 8). In relation to digital technology, tasks appear even more critical, as “some of the key affordances arising from technology use emanate from the tasks we use with it” (Thomas & Lin, 2013 , p. 109). The introduction to the proceedings of the ICMI study 22, which is devoted to task design in mathematics education , define a task as follows:

anything that a teacher uses to demonstrate mathematics, to pursue interactively with students, or to ask students to do something. Task can also be anything that students decide to do for themselves in a particular situation. Tasks, therefore, are the mediating tools for teaching and learning mathematics (Watson et al., 2013 , p. 10).

Teaching thus includes the selection, adaptation, design, enactment, and evaluation of tasks (ibid.). Acknowledging that interactions with tasks are an important facet of teachers’ professional activity led researchers to consider teachers as designers or partners in task design, rather than merely as task implementers (Brown, 2009 ; Jones & Pepin, 2016 ). Hence, teaching design is gaining increased interest in mathematics education research.

Two emerging research trends can be observed in recent research studies in relation to teachers as designers of their instruction. On the one hand, researchers’ attempts to understand and describe the requirements of designing and using (digital) tasks in terms of teachers’ competencies have led to a focus on teacher design capacity. On the other hand, the emergence of communities engaged in collective task design, such as communities of practice (Wenger, 1998 ), communities of inquiry (Jaworski, 2014 ), or teacher design teams (Handelzalts, 2009 ), has initiated a new research field in teachers’ collaborative work that may be accompanied and supported by facilitators.

Teacher design capacity. During the last two decades, researchers have begun exploring teachers’ interactions with curricular materials, for example by considering teaching as a design process (Brown, 2009 ) and by viewing curriculum materials as resources supporting such a process. Researchers agree on the existence of a mutual influence between teachers and resources, such that resources affect teacher practice and teachers modify resources to adapt them to their own context and needs. Examining such teacher-resource interactions necessitates understanding “pedagogical design capacity”, defined as a teacher’s “skill in perceiving the affordances of the materials and making decisions about how to use them to craft instructional episodes that achieve her goals” (Brown, 2009 , p. 29). Pepin et al. ( 2017 ) further conceptualised Brown’s pedagogical design capacity as “teacher design capacity” that incorporates three main components: (1) an orientation or a goal for the design, (2) a set of design principles, and (3) “reflection-in-action” (p. 802). Building on existing conceptualisations of teacher design capacity, Trgalová and Tabach ( 2024 , this issue) propose a framework that incorporates the specificities of mathematics and the use of digital technology, yielding a definition of teachers’ digital resource design capacity (DRDC). The authors then elaborate a conceptualisation of mathematics teachers’ DRDC, which they illustrate using two case studies from a course for pre-service mathematics teachers aimed at developing participants’ design capacity based on the DRDC conceptualization.

Teacher design teams . In their ICME13 survey paper, Robutti et al. ( 2016 ) claim that “the notion of mathematics teachers’ working and learning through collaboration … gains increasingly more attention in educational research and practice” (p. 651, authors’ emphasis). They point to “ever-increased interest in exploring and examining different activities, processes, and the nature of differing collaborations through which mathematics teachers work and learn” (p. 652). Their paper provides three emblematic examples to illustrate various forms of mathematics teachers’ collaboration: (1) a school-based collaborative lesson study in Japan that relies on iterative teacher processes of planning, teaching, lesson observation, and post-lesson discussion and reflection; (2) collaborative teacher projects in England involving schools and an “expert other” (p. 655), aimed at producing resources, planning, implementing, and evaluating an intervention, and providing professional development for other teachers; (3) mathematics learning communities in Norway involving teams of researchers and teacher educators in partnership with schools and based on “three layers of inquiry” (p. 656): in students’ mathematical activity, in mathematics teaching, and in the research process during the collaboration.

The 25th ICMI study devoted to teachers of mathematics working and learning in collaborative groups (Borko & Potari, 2020 ) confirms the growing interest in this topic. The emergence of new theoretical frameworks during the last decade has allowed researchers to address collective aspects in teachers’ professional activities and to consider how these aspects have affected teachers’ learning and professional development. Examples include the documentational approach to didactics (Gueudet et al., 2013 ) and the meta-didactical transposition theory (Arzarello et al., 2014 ) of collaboration between two communities: teachers and researchers or teacher educators. Most research studies focus on in-service mathematics teachers engaged in collaborative work. Other examples include the collective design of e-textbooks by an association of teachers (Sabra, 2016 ), the documentation workmates initiative in which a pair of teachers designed new resources for teaching algorithms and programming (Wang, 2018 ), and collaborative work on scenario design to consider possible enactments of classroom activities within a professional development programme (Cusi et al., 2020 ). Yet very little research has considered collaboration among pre-service and in-service teachers. To fill this gap, Dilling et al. ( 2024 , this issue) report on a collaborative project between pairs of teachers made up of an in-service teacher and a pre-service teacher trained to assist the in-service teacher in integrating digital technology in the classroom. The paper highlights the importance of a sound distribution of responsibilities within the teacher pairs so as to divide the workload.

2.3 Innovative teaching practices leveraged by digital resources

In the current digital age, mathematics teachers are provided with a profusion of digital resources, mainly available through the Internet. Consequently, much research in mathematics education has focused on teachers’ interactions with resources. Indeed, these interactions are thought to form the core of their professional activity (Remillard, 2005 ; Gueudet & Trouche, 2009 ). As noted above, the consensus is that teachers’ interactions with resources have the potential to affect both the resources themselves as they are modified and combined with other resources and the teachers’ practices that are shaped by the resource use. Hence, it is legitimate to expect that innovative digital resources will lead to innovative teaching practices. Indeed, as Clark-Wilson ( 2017 ) notes, digital resources have the potential to offer learners an environment in which they can explore mathematical ideas:

The advent of dynamic mathematical digital resources in the early 1990s promised a transformation of the teaching and learning mathematics as the technology enabled teachers and learners to experience and explore difficult mathematical ideas in more tangible ways.

Yet Clark-Wilson also notes that despite their potential, such technologies remain underused, mostly because of the complexity of integrating them into teachers’ practices. Research projects examining teachers’ professional development have sought to help teachers overcome barriers to technology use. One of these is the UK Cornerstone Maths project, which aimed to exploit the dynamic and visual affordances of digital technology and provide students an environment in which “to explore and solve problems within structured activities” (Clark-Wilson et al., 2013 , p. 13). Teachers’ appropriation of specifically designed resources was accompanied by professional development programs. Likewise, Naftaliev and Barabash ( 2024 , this issue) orchestrate teachers’ interactions with a specific type of digital resources known as technology-based interactive resources to foster the evolution of in-service teachers’ practices toward teaching experimental mathematics.

Digital technology has also been explored as a vehicle for the development of creativity, which is considered a 21st century skill, for example in the book Creativity and Technology in Mathematics Education (Freiman & Tassel, 2018 ). The European MC2-Mathematical creativity squared project demonstrated that digital technology can support social creativity in the design of digital resources (Kynigos et al., 2020 ) and at the same time can foster students’ creative mathematical thinking (Trgalová et al., 2018b ; Kolovou & Kynigos, 2017 ). Ye et al. ( 2024 , this issue) observe and analyse the mathematical creative actions of in-service teachers engaged in problem solving activities with Scratch, alongside their development of mathematics and programming knowledge.

To summarize, the above survey demonstrates several emerging trends and research evolutions in teaching mathematics with digital technology, which are further discussed in the concluding section: a shift from reporting on the complexity of digital technology integration in mathematics classrooms to exploring what teachers need to use digital tools effectively in terms of mathematical and digital competencies ; viewing teachers as designers of (digital) resources rather mere resource implementers; development of innovative teaching practices enhanced by digital technologies; and the need for long(er) term support for teachers in integrating digital technology in their classrooms.

3 Learning with technology

In her paper “Solid Findings in Mathematics Education: The Influence of the Use of Digital Technology on the Teaching and Learning of Mathematics in Schools”, Hoyles ( 2014 ) stated: “Digital tools have the potential for transforming teaching and learning mathematics in ways not possible with other tools” (p. 50). Indeed, according to Drijvers ( 2019 ), learning mathematics with technology was found to be beneficial for student learning, though the average effect size was small to moderate. At the same time, Hoyles stated:

In order for the potential for transforming mathematical practice through the use of digital technologies for the benefit of all learners to be realised, teachers, teachers’ practice and their beliefs about learning must form part of the process ( 2014 , p. 50).

Taken together, these quotations tell the story of integrating technology in the mathematics classroom and student learning: on the one hand, a clear vision of new opportunities that are realised to some extent, and on the other hand acknowledgment of the practical complexity involved in “making good use” of these opportunities for the benefit of all students.

The issue of student learning with technology raises many questions. For example, what do we know about learning with technology in different mathematical domains? Does learning algebra differ from learning geometry? How does learning algebra in a CAS environment differ from learning algebra in a graphical environment? What is the influence of tasks provided to students which use the same technological tools? How does learning mathematics in technological environments in elementary school differ from high school? Some of these questions are discussed in depth in the chapters of the newly published handbook titled Digital Resources in Mathematics Education (Pepin et al., 2023 ). For example, Leung et al. ( 2023 ) explore how digital technology enhances geometric skills, Haspekian et al. ( 2023 ) study algebra education with digital resources, and Biehler et al. ( 2023 ) question the impact of digitalization on content and goals of statistics education.

In the following concise review, we were guided by the issues emerging from the papers in this issue. We chose two themes that on the one hand go beyond mathematical topics and on the other hand are linked to recent developments in our field. We begin by discussing the use of multiple resources while learning mathematics—a conceptualization that may shed new light on our understanding of learning with resources. We then refer to a new adoption of technologies for learning mathematics that is influenced by developments in hardware, software, and accompanying pedagogy. In each subsection we first describe the topic based on the literature and then refer to the papers in this issue.

3.1 Learning with multiple resources

It is clear today that digital resources do not replace paper and pencil resources, but rather are used alongside them. Acknowledging the fact that learning mathematics takes place both with analogue and with digital resources, Geraniou et al. ( 2023 ) asked

how students (and subsequently teachers) conceptualise mathematics as they make transitions when using digital resources, involving different mathematical representations and different semiotic systems that may be using ‘new’ representations of mathematical concepts? (p. 1).

According to these authors, the use of graphs, symbolic expressions and numerical data can be considered as dynamic realisations of the same mathematical idea or as a dynamic and connected means of bridging between virtual concrete-like phenomena and their abstract counterparts. The authors further define transitions while working with digital and other resources using the words “within, beyond and across” (ibid., p. 1).

A transition is considered “within” a resource if several different representations of the same mathematical object or concept are available for students, who need to make sense of them. Bach ( 2023 ), for example, examines pairs of students who interacted with a dynamic geometry environment and were also asked to report individually in a paper environment. Bach noted:

‘Transitions within a digital tool’ concern the coordination of representations presented in a digital tool, which may be related to different content areas. ‘Transitions beyond a digital tool’ include the coordination of digital tool representations to paper-based representations. Such a transition may be evident even when it is not undertaken (p. 344).

Thus, observing learners as they interact with resources can shed light on transitions, as can researchers’ expectations regarding whether such transitions will take place, which may be absent in students’ work. For example, while working with a spreadsheet, students need to write expressions using such Excel-cell notations as 2*A2, whereas in a paper environment they would use 2*x, 2x or 2*A.

A transition is considered to be “across” resources when the opportunity is provided to navigate between two or more digital resources. In such cases, mathematical knowledge about a concept or an object is learned with one resource and then used with a different resource, possibly also with different representations. For example, Panorkou et al. ( 2023 ) studied students’ covariation thinking while using several resources (simulation, table, and graph) and described their transition across the resources as “messy”. Specifically, the researchers “provide an insight into the nature of the synergy of artefacts that offers a constructive space for students to shape and reorganise their meanings about covarying quantities” (p. 131).

Four papers in this issue describe cases of transitions within, across, and beyond resources. Radmehr and Turgut ( 2024 , this issue) analyse online video resources for studying the topic of derivation. The authors look for representations [realisations in their terminology] of mathematical objects in the video. These representations provide learners opportunities to make transitions within the video resource for the same mathematical object.

Jaber et al. ( 2024 , this issue) studied students working in an augmented reality environment in the mathematical context of covariational change. The authors offer learners the possibility to make transitions across carefully designed physical phenomena and their mathematical representations (tables and graphs).

Brnic et al. ( 2024 , this issue) studied students’ transitions across resources such as digital textbooks, dynamic visualisations, feedback formats, and digital tools, while they learned about conditional probability. The authors also studied students’ transition beyond resources by analysing students’ work on a paper and pencil test. They compared the achievements of students who learned with non-digital resources to those who learned with the digital resources and also compared gender differences.

Finally, Bach et al. ( 2024 , this issue) studied students’ transition beyond resources, moving from working with dynamic geometry resources to oral and written communication concerning the dynamic aspects of the mathematical objects observed.

3.2 Technological developments adopted for school mathematics

A different line of research examining students’ learning with digital resources is related to technological hardware and software developments and their influence on the uses of innovative technologies for teaching and learning mathematics. For example, augmented reality (AR) was first introduced by the US Air force in the early 1990s. AR can be defined as a system that incorporates three basic features: real and virtual worlds, real-time interaction, and accurate 3D registration of virtual and real objects (Wu et al., 2013 ). For mathematics education, AR is “a mixed reality technology that contains virtual objects that are implemented or ‘augmented’ with the real world” (Ahmad & Junaini, 2020 , p. 107). That is, AR technology facilitates design in which virtual elements can be added for the viewer while looking at real world objects such as tables or graphs.

In a systematic review of the use of AR in mathematics education, Palancı and Turan ( 2021 ) found an increased number of reports since 2010 that mainly used qualitative research methods. The researchers note that the use of AR

supported learning and motivation and enhanced the spatial abilities of students. Additionally, the most frequent disadvantages of AR in mathematics education were that it caused technical inconveniences and it is difficult to develop materials through AR (p. 89).

As this AR example shows, it is less accurate to speak about “new” and “old” technologies. Rather, we look for technological developments accompanied by new ways of exploiting hardware and software that have the potential to benefit students’ mathematics learning (Hoyles & Lagrange, 2010 ).

Another example is the use of video technology to capture live images by electronic means. This technology was first developed for commercial television in the early 1950s to capture live images by electronic means. As is the case with other technical tools, these videos were adopted for educational purposes. Specifically, video recordings were adopted for professional teacher development in that the instruction of actual teachers in the classroom was recorded as a basis for discussions and reflections at a professional development meeting (Jaworski, 1990 ). Teacher educators who are also mathematics education researchers used recordings of professional development meetings as an opportunity to reflect on their own practice and research (Coles, 2014 ; Tirosh et al., 2014 ). Video technology was also adopted as part of learning while engaging with (serious) video games (e.g., dragonbox algebra Footnote 2 for learning to solve linear equations, see Kapon et al., 2019 ). Indeed, it is hard to imagine flipped classrooms or MOOCs without the use of videos (Lo et al., 2017 ).

Kay ( 2012 ) identified two main factors that facilitated a tremendous increase in the use of instructional videos for learning aims: one is the YouTube platform, launched in 2005, that allowed users to upload and watch videos with ease; the other is the increasing size and availability of bandwidth, influencing the quality of what one might learn by watching such media. Kay and Kletskin ( 2012 ) identify two kinds of videos for use in mathematics higher education—algorithm presentations and problem-based demonstrations—claiming that problem-based demonstrations were less prevalent in our field. There is still no consensus regarding how to design an instructional video or how to measure its effectiveness (Netzer & Tabach, 2023 ). Some researchers use indirect methods such as students’ course grades, course dropout rate, and student feedback, while others examine the actual way in which learners use the video (Kim et al., 2014 ).

Three papers in this issue describe cases of using AR or video technology.

As noted above, Jaber et al. ( 2024 , this issue) designed special software that students could use to experiment with a physical phenomenon: while a cube slid down an inclined plane (Galileo experiment) students observed the covariation of time-distance in a table and in graph representations. They also observed the elongation of a physical spring under various masses, where the stiffness of the spring served as a parameter (Hooke’s Law). The AR technology enabled juxtaposing the view of the physical experiment and the mathematical representations, allowing students to discuss and make sense of these covariation phenomena.

Radmehr and Turgut ( 2024 , this volume) took advantage of the YouTube platform to identify online instructional video on derivation by using the number of views for the video they chose to analyse as an inclusion criteria (more than 3.2 million views!). The starting point of the analysis was that this highly observed resource provides learning opportunities for the students who watch it.

Finally, Wirth and Greefrath ( 2024 , this issue) designed a video resource that students worked on in pairs to learn how to handle modelling problems. The authors made use of our knowledge as a research community regarding the use of written examples and implemented this knowledge in their instructional video. This video was shown to 18 pairs of students without prior experience in modelling; each pair worked individually with the video to make sense of the modelling process. The authors examine the students’ perceived advantages and pitfalls following this experience.

In summary, although learning with technology has already been examined for several decades, the above survey provides evidence that the field is far from reaching stability. It is still characterised by new conceptualizations that researchers have raised to further our understanding of this complex issue. It is interesting to note how much time it is taking the education system to adopt technological innovations for research purposes, not to mention how much time it is taking for these innovations to be implemented in mathematics classrooms as an everyday reality.

4 Assessment with technology

Digital assessment also offers new types of affordances for assessment, such as automated scoring, feedback, and adaptivity. These affordances provide new opportunities with respect to developed tasks and assessment problems as well as styles of performing tasks and means of solving problems (e.g., see Drijvers & Sinclair, 2023 ). Interactive software such as Computer Algebra Systems (CAS), Dynamic Geometry Systems (DGS), and spreadsheets offer opportunities for carrying out interactive and dynamic tasks that are not possible using paper and pencil means, as do films, animations, and simulations. Assessment can be individualised in that feedback can be adapted to individual learners. Nevertheless, problems and difficulties associated with digital assessment must be considered. One such problem is the possibility that problems will become more complex due to a greater variety in representations. Another is the need to assess conceptual knowledge in addition to procedural knowledge, a form of assessment that is generally thought to be more difficult. Moreover, media use in the classroom and on examinations can change many or even all aspects of assessment.

There are new possibilities for the ways in which tasks are selected for use in assessments, in the way they are presented to students, in the ways that students operate while responding to the task, in the ways in which evidence generated by students is identified , and how evidence is accumulated across tasks. (Stacey & Wiliam, 2013 , p. 722)

In the following section, we begin with some general observations on the use of digital technologies in formative and summative assessment. We then discuss specific aspects we expect to be more important in the coming years: automatic feedback and adaptive assessment, assessment of conceptual understanding, and task development for digital assessment.

4.1 Digital technologies in formative and summative assessment

Assessment in mathematics education is characterised by a well-accepted duality between large-scale or summative assessment on the one hand and classroom or formative assessment on the other. Summative assessment refers to the assessment of learning that is associated with evaluation of student knowledge and learning at the end of a course or teaching unit, quite often with the aim of assessing students’ proficiency level. In contrast, formative assessment is assessment for learning that entails gathering information about a student’s current state of knowledge and learning to guide teachers and students in subsequent teaching and learning (e.g., Stacey & Wiliam, 2013 ). Digital technology has been and will continue to be used to enhance both summative and formative assessments.

Assessment is further marked by another duality: assessment with digital technologies and assessment through digital technologies (Stacey & Wiliam, 2013 ). Footnote 3 Assessment with digital technologies is characterised by traditional paper-based learning methods in which learners have access to digital learning opportunities such as software and videos (Drijvers et al., 2016 ; Fahlgren et al., 2021 ). In many countries today, especially in the West, handheld technology is allowed to be used or is even mandatory in examinations. In contrast, in assessment through technology or technology-based assessment (TBA), technology serves as a testing environment.

Computer-based tests and (final) examinations have been in use for many years at the university level, e.g., in medicine and engineering studies (Iannone, 2020 ). Recently, computer-based examinations have begun to be introduced in school mathematics. Computer-based versions of the PISA test have been offered since 2012; by 2015, PISA’s primary mode of assessment of students’ skills was computer-based and tasks were coded automatically (Jerrim, 2016 ). One part of the national assessment of 18-year-old high school students in Finland is a computer-based test using the Abitti system. In this system, students work in an environment isolated from the digital world yet still have access to mathematical tools like GeoGebra, Maxima, Casio ClassPad or TI-Nspire (Drijvers, 2018 ). The Dutch Ministry of Education developed a diagnostic test for 15-year-old students used on final examinations in lower secondary mathematics education (ibid.).

In addition to summative assessment, in recent years formative assessment has gained importance in assessing classroom work and supporting the learning process, especially while using digital technologies (Aldon et al., 2017 ; Dalby & Swan, 2019 ; Olsher, 2019 ; Cusi & Morselli, 2024 ). In 2009, Black and Wiliam ( 2009 ) provided a widely accepted specification of formative assessment:

Formative assessment (FA) is conceived as a method of teaching in which evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have taken in the absence of the evidence that was elicited (p. 7).

In addition to the key areas and moments in which formative assessment is used, the European Formative Assessment in Science and Mathematics Education project ( FaSMEd , Aldon et al., 2017 ) emphasises three main elements or technology functionalities of formative assessment: sending and displaying ; processing and analysing ; and providing an interactive environment (Cusi, 2022 ). These functionalities should be integrated into the whole teaching and learning process. They are especially represented in classroom communication (e.g., with systems like MOODLE or ILIAS), in feedback (e.g., with systems like STACK), and in interactive work with digital technology (e.g., with systems like GeoGebra). In this ZDM-issue, two contributions refer to specific questions concerning formative assessment. Cusi and Morselli ( 2024 , this issue) investigate the specific roles played by teachers when making conscious in-the-moment decisions during classroom discussions to foster the development of effective formative assessment processes. Hershkovitz et al. ( 2024 , this issue) evaluate the use of feedback on the topic of reflective symmetry in digital learning environments among 9- to 12-year-old elementary school students.

4.2 Automatic feedback and adaptive assessment

Feedback is perhaps the most important aspect of teaching and learning (Hattie & Clarke, 2018 ). Feedback with digital technologies, and particularly computer algebra systems like GeoGebra-CAS, Mathematica or STACK, are best suited for algorithmic calculations. When these technologies are used for learning, two types of use-software interactions are important: system input and system output. In the case of input, users must be confident with the question to be answered and its representation in the technical input scripts. In the case of output, users must to be able to interpret the system feedback and validate it with respect to the posed problem. Even though the calculations are done automatically, the feedback system developer, the task designer or the teacher must construct the kind of feedback required in advance. For example, STACK generates automatic differentiated feedback from student solutions. For each task, the designer must define relevant and possible outputs in advance, which will then be checked vis-à-vis the task or problem solution. Various forms of feedback can provide verbal, numerical, graphical or algebraic information about students’ answers (Pinkernell et al., 2019 ). Students in technical and science fields use the interactive adaptive assessment system OPTES (or its follow-up system DigikoS) as supplementary materials to repeat school mathematics in the introductory phase of their studies (see Roos et al., 2019 ). In OPTES, STACK tasks are used to develop an adaptive learning and training system (Wankerl et al., 2019 ), making it possible to select appropriate exercises for individual learners. These kinds of adaptive systems will become increasingly meaningful in the coming years.

An important issue in current research is how to help teachers make productive use of the results of digital learning assessments in the classroom (Dalby & Swan, 2019 ). Klingbeil et al. ( 2024 , this ZDM-issue) describe the development and evaluation of the online formative assessment system SMART, which is designed improve mathematics learning among upper primary and junior secondary school students. The system provides teachers an informative diagnosis of students’ conceptual understanding (Stacey et al., 2009 ; Haspekian, 2020 ; Fahlgren et al., 2021 ). Each SMART test is individually evaluated and identifies students’ understanding, misconceptions, and knowledge gaps. Further, it provides teachers useful information about possible future steps, tasks to solve, or instructions to improve. In SMART, only the teacher receives the results of the test because the teacher is considered the initiator of the developmental process.

Individualisation of the learning process requires more than individual feedback on solutions and solution processes. Indeed, the problems of the next learning step must also be individualised and individual learning trajectories must be adaptive. Since the time teaching and learning machines were first introduced, adaptive assessment was always an important aspect of individual learning (Olsher et al., 2023 ). OPTES, for example, categorises a special mathematical field, e.g., algebra or calculus, based on a didactical reference model concerned with particular aspects of knowledge. Problems in one category are more closely related than problems from different categories. All problems in this field are arranged in a graph with special transformation probabilities. If a learner does not solve a problem, the probability of getting a similar problem is higher than if the problem is solved correctly. The transformation probabilities are calculated in a training process with a large number of users (Wankerl et al., 2019 ).

4.3 Digital assessment and conceptual understanding

Competency assessment is a central but demanding task for which digital technologies are increasingly being used in different contexts. In assessing procedural knowledge—i.e., knowing how to use procedures like transformations of terms, how to solve equations with formulas or how to calculate square roots with the Heron algorithm—computer algebra systems such Mathematica or STACK are adequate tools that allow the development of fully automated examination evaluation and grading. The assessment of conceptual understanding is far more complex for it entails assessing the understanding of mathematical concepts and the adequate application of mathematical concepts in internal and external mathematical problem-solving situations. This assessment is best accomplished by oral tests, interviews or any kind of project work. Concerning digital assessment, Olsher et al. ( 2023 ) note the risk that this kind of assessment “is not commonly testing competencies that match what it means to ‘do mathematics’ in the 21st century” (p. 21). Hoogland and Tout ( 2018 ) even see “mathematics education… at risk of focusing too much on assessment of lower order goals, such as the reproduction of procedural, calculation based, knowledge and skills” (p. 675). Nevertheless, in the context of the increasing importance of digital assessment, means must also be developed for assessing conceptual understanding.

The so-called Basic Mental Models (in German “Grundvorstellungen”) (vom Hofe & Blum, 2016 ) can serve as a good basis for the development of conceptual understanding. A Basic Mental Model (BMM) of a mathematical concept is a conceptual interpretation that gives it meaning. Yet BMMs still need to be developed and empirically validated (Greefrath et al., 2021 ), as do appropriate assessment tasks.

Some empirically based suggestions for the use of digital technologies in developing conceptual understanding have already been proposed. Weigand and Günster ( 2022 ) used digital tools (GeoGebra) to develop the dynamic view of functions on these levels of understanding. Ruchniewicz and Barzel ( 2019 ) developed a digital tool for student self-diagnostics as they work with different representations of functions. Yerushalmy and Olsher ( 2020 ) and Popper and Yerushalmy ( 2022 ) developed a digital tool for the development of reasoning while working with and classifying quadrilaterals.

4.4 Task design for digital assessment

Task design is a crucial element in mathematics education (Watson et al., 2013 ; Watson & Ohtani, 2021 ). Digital assessment raises a number of questions concerning task design: What new kinds of questions do digital tests allow (e.g., how to integrate films, simulations or interactive applets into the questions)? How do working styles in digital tests differ from those of paper-and-pencil tests (e.g., doing preliminary considerations and sketches on paper alongside the digital test, using interactive programs like GeoGebra or hand-held-technology in addition to the digital test)? How do the test questions influence the general classroom work (e.g., does the use laptops, hand-held devices or computer programs in examinations influence the need for hand calculations with paper-and-pencil)?

Concerning the development of tasks in digital assessment systems, four aspects need to be taken into consideration: (1) the task representation; (2) the way students or learners should work (in relation to software functionality); (3) the evaluation of students’ work and answers, and (4) the feedback on students’ solutions. A major theory has evolved regarding principles of designing assessment tasks for both summative and formative assessment. Suurtamm et al. ( 2016 ) believe that the principles underlying these two forms of assessment are similar because “large-scale and classroom assessment interact with one another in different ways” (p. 25). Still of major importance is the emphasis in the NCTM assessment standards ( 1995 ) “that both large-scale and classroom assessment should take into account not only content but also mathematical practices, processes, proficiencies, or competencies” (p. 5). Yet many questions concerning task design in digital environments still remain: Who designs the problems? Who has control over the assessment platforms (e.g., to what extent can individual teachers write their own assessments)? Which tools are allowed? (e.g., Nortvedt & Buchholtz, 2018 ).

Questions with verbal answers are clearly better suited for assessing higher order mathematics skills than multiple choice tests, as these questions enable students to express themselves more freely. Yet assessing handwritten questions is often challenging. Moons et al. ( 2024 , this issue) developed a “checkbox grading system” that (human) assessors can use to assess handwritten mathematics exams as “atomic feedback”. The idea is to combine pre-defined answers for test problems by using a list of checkboxes for classification. The system then automatically calculates the grade and provides individualised feedback to students.

A great deal of experience has accumulated regarding assessment with technology, especially using CAS-systems. For example, CAS-supported examinations have been in use in Great Britain, France, Germany and the Scandinavian countries for many years (Bach, 2023 ). Leigh-Lancaster and Stacey ( 2022 ) give an overview of the 20 years in which CAS-calculators were used in Australia, showing that the availability of sophisticated digital technologies does not necessarily make assessment easy.

One reason for digital assessment is pragmatic: it offers an effective means of designing and implementing tests and examinations. Moreover, the use of digital technologies in tests and examinations is known for allowing enhanced experimental and heuristic work in problem-solving phases and for providing opportunities for realistic modelling tasks (Fahlgren et al., 2021 ). Yet this experimentation requires sufficient time to try out different methods and pursue them thoroughly, which is very difficult to implement within the confines of the time-limited tests that have been the predominant form of examination up to now. Yet, aligning learning activities in the instructional learning process with assessment activities is a crucial part of the learning process: “Any course needs to be designed so that the learning activities and assessment tasks are aligned with the learning outcomes that are intended in the course. This means that the system is consistent” (Hattie, 2009 , p. 6). The issue of the use of digital media in examinations must therefore also be accompanied by a discussion of alternative forms of examination, such as portfolios, individual studies, and project work (Ball et al., 2018 ).

In summary, in the coming years assessment with and through technologies will play an important and increasing role in formative and summative assessment. During the pandemic, many teachers were exposed to new possibilities for digital assessment (e.g., online quizzes or digital interactive learning trajectories) and later adapted some of these in their traditional teaching (Cusi et al., 2023 ; Engelbrecht & Borba, 2023 ). Some current developments will surely influence assessment in the coming years. Inputting symbolic expressions using a formula editor is still not very convenient and “limits the expressivity of ideas due to the efforts of communicating them. Here technological developments such as optical character recognition (OCR) may provide useful solutions” (Olsher et al., 2023 , p. 22). Furthermore, the issue of how to use Virtual and Augmented Reality not only in the classroom but also in assessment situations remains an open question (Wu, 2013 ; Palancı & Turan, 2021 ).

5 Conclusion

Teaching, learning, and assessment are closely related in learning environments, especially in mathematics classrooms. Hence, they must be oriented towards goals in terms of mathematical knowledge and general competencies. On the one hand, digital technologies and resources must be selected with a view to achieving these goals, while on the other hand, digital technologies and resources also influence the way in which these goals are achieved. This interrelationship, along with new developments in digital resources such as artificial intelligence products (e.g., adaptive digital learning systems or generative artificial intelligence systems like chatbots) make planning for the future very difficult or even impossible. In the digital age, all stakeholders in the educational system—politicians, school administrators, teachers, and students alike—must be flexible and prepared for continuous adaptations and corrections in the educational process. Moreover, in view of the diversity of educational systems, together with different national and regional peculiarities and traditions and diverse convictions and emphases, it is unlikely that generally accepted strategies for dealing with digital technologies and resources in mathematics education will emerge.

Nevertheless, based on the experience of the last decades and on the discussion in the above sections about teaching, learning, and assessment with technologies, we can still make some comments, suggestions, and recommendations regarding the use of digital technologies and resources in the digital age:

Despite major expectations on the part of the public, the use of digital technologies is not an end in itself. Rather, these technologies must be critically evaluated in the context of the intended goals of mathematics learning.

Digital technologies for new curriculum developments, task design, and the development of new problems and tasks for teaching, learning, and assessing are continually being explored.

Current digital technologies should be integrated into all levels of pre- and in-service teacher education. Nevertheless, this integration must be flexible and open to further technical developments and must not focus on special hardware or software.

As we show in the section devoted to teaching with digital technology, the mathematics education research community has demonstrated growing interest in conceptualising mathematics teachers’ professional competencies, with the goal of using digital artefacts in classrooms effectively. The current lack of consensual conceptualization highlights the diverse opinions regarding what makes mathematics teachers competent users of digital artefacts in their instruction.

As discussed in the section on assessment with digital technology, formative assessment could benefit from the potential offered by digital technologies, especially concerning individual feedback as a crucial element of mathematics learning and teaching.

The development of digital technologies for tests, examinations, and summative assessment should be intensified, especially concerning conceptual understanding. The fact that examination problems set standards for learning and teaching in the classroom is well-known.

Most recent research studies, including those in this volume, highlight the need for networking theories to address complex issues related to the use of digital artefacts in mathematics teaching, learning, and assessment. Likewise, the field requires large-scale studies using quantitative methods to complement the qualitative research methodologies dominating the research field.

Embodiment and embodied cognition, especially in connection with virtual and augmented reality, will become increasingly important. Hence, research on this topic as well as adequate classroom examples that go beyond the equipment debate need to be developed.

Finally, it is reasonable to assume that Artificial Intelligence will exert a major influence on educational systems. For the time being, the topic of how language generation models such as ChatGPT will influence teaching, learning, and assessment remains an open question.

Despite the ubiquity of digital technology and resources, this issue demonstrates that old but still relevant themes require further theoretical and methodological investigation.

An analysis of these frameworks can be found in (Tabach & Trgalová, 2019 ).

https://dragonbox.com/about .

The use of the word “with” in this paper has a narrower interpretation than the word “with” in the rest of this paragraph.

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