problem solving strategies primary school

Developing Problem-Solving Skills for Kids | Strategies & Tips

We've made teaching problem-solving skills for kids a whole lot easier! Keep reading and comment below with any other tips you have for your classroom!

Problem-Solving Skills for Kids: The Real Deal

Picture this: You've carefully created an assignment for your class. The step-by-step instructions are crystal clear. During class time, you walk through all the directions, and the response is awesome. Your students are ready! It's finally time for them to start working individually and then... 8 hands shoot up with questions. You hear one student mumble in the distance, "Wait, I don't get this" followed by the dreaded, "What are we supposed to be doing again?"

When I was a new computer science teacher, I would have this exact situation happen. As a result, I would end up scrambling to help each individual student with their problems until half the class period was eaten up. I assumed that in order for my students to learn best, I needed to be there to help answer questions immediately so they could move forward and complete the assignment.

Here's what I wish I had known when I started teaching coding to elementary students - the process of grappling with an assignment's content can be more important than completing the assignment's product. That said, not every student knows how to grapple, or struggle, in order to get to the "aha!" moment and solve a problem independently. The good news is, the ability to creatively solve problems is not a fixed skill. It can be learned by students, nurtured by teachers, and practiced by everyone!

Your students are absolutely capable of navigating and solving problems on their own. Here are some strategies, tips, and resources that can help:

Problem-Solving Skills for Kids: Student Strategies

These are strategies your students can use during independent work time to become creative problem solvers.

1. Go Step-By-Step Through The Problem-Solving Sequence 

Post problem-solving anchor charts and references on your classroom wall or pin them to your Google Classroom - anything to make them accessible to students. When they ask for help, invite them to reference the charts first.

2. Revisit Past Problems

If a student gets stuck, they should ask themself, "Have I ever seen a problem like this before? If so, how did I solve it?" Chances are, your students have tackled something similar already and can recycle the same strategies they used before to solve the problem this time around.

3. Document What Doesn’t Work

Sometimes finding the answer to a problem requires the process of elimination. Have your students attempt to solve a problem at least two different ways before reaching out to you for help. Even better, encourage them write down their "Not-The-Answers" so you can see their thought process when you do step in to support. Cool thing is, you likely won't need to! By attempting to solve a problem in multiple different ways, students will often come across the answer on their own.

4. "3 Before Me"

Let's say your students have gone through the Problem Solving Process, revisited past problems, and documented what doesn't work. Now, they know it's time to ask someone for help. Great! But before you jump into save the day, practice "3 Before Me". This means students need to ask 3 other classmates their question before asking the teacher. By doing this, students practice helpful 21st century skills like collaboration and communication, and can usually find the info they're looking for on the way.

Problem-Solving Skills for Kids: Teacher Tips

These are tips that you, the teacher, can use to support students in developing creative problem-solving skills for kids.

1. Ask Open Ended Questions

When a student asks for help, it can be tempting to give them the answer they're looking for so you can both move on. But what this actually does is prevent the student from developing the skills needed to solve the problem on their own. Instead of giving answers, try using open-ended questions and prompts. Here are some examples:

2. Encourage Grappling

Grappling  is everything a student might do when faced with a problem that does not have a clear solution. As explained in this article from Edutopia , this doesn't just mean perseverance! Grappling is more than that - it includes critical thinking, asking questions, observing evidence, asking more questions, forming hypotheses, and constructing a deep understanding of an issue.

There are lots of ways to provide opportunities for grappling. Anything that includes the Engineering Design Process is a good one! Examples include:

• Engineering or Art Projects
• Design-thinking challenges
• Computer science projects
• Science experiments

3. Emphasize Process Over Product

For elementary students, reflecting on the process of solving a problem helps them develop a growth mindset . Getting an answer "wrong" doesn't need to be a bad thing! What matters most are the steps they took to get there and how they might change their approach next time. As a teacher, you can support students in learning this reflection process.

4. Model The Strategies Yourself! 

As creative problem-solving skills for kids are being learned, there will likely be moments where they are frustrated or unsure. Here are some easy ways you can model what creative problem-solving looks and sounds like.

• Ask clarifying questions if you don't understand something
• Admit when don't know the correct answer
• Talk through multiple possible outcomes for different situations 
• Verbalize how you’re feeling when you find a problem

Practicing these strategies with your students will help create a learning environment where grappling, failing, and growing is celebrated!

Problem-Solving Skill for Kids

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Maths Problem Solving At KS2: Strategies and Resources For Primary School Teachers

John Dabell

Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted’s suggested primary school teaching strategies.

Reasoning and problem solving are widely understood to be one of the most important activities in school mathematics. As far back as 1982,  The Cockcroft Report , stated:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. […] At each stage […] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and – along with fluency and reasoning – completes the triad of aims in the 2014 New National Curriculum.

Ofsted’s view on problem solving in the Maths curriculum

Despite its centrality, Ofsted report that ‘ problem solving is not emphasised enough in the Maths curriculum ’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always ‘hit home’. If you’re looking to provide further support to those learners who haven’t yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.

We’ve therefore created a free KS2 resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques:  The Ultimate Guide to Problem Solving Techniques

The context around KS2 problem solving

According to Jane Jones, former HMI and National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:

• Problems do not have to be set in real-life contexts, beware pseudo contexts.
• Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their mathematical thinking for next steps.
• It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
• Pupils of all ability need to learn how to solve problems – not just the high attainers or fastest workers.

The Ultimate Guide to Problem Solving Techniques

9 ready-to-go problem solving techniques with accompanying tasks to get KS2 reasoning independently

How to approach KS2 maths problems

So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:

• Set problems as part of learning in all topics for all pupils.
• Vary the ways in which you pose problems.
• Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
• Make sure you discuss alternative approaches with pupils to help develop their reasoning.
• Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

Perhaps more than most topics in Maths, teaching pupils how to approach problem solving questions effectively requires a systematic approach. Pupils can face any number of multi-step word problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for  approaching  problems.

With this in mind, below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the  Ultimate Guide to Problem Solving Techniques

Models for approaching KS2 problem solving

Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.

Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:

• Understand the problem
• Devise a strategy for solving it
• Carry out the strategy
• Check the result

Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of word problems they are trying to solve. Below are several examples of Polya model acronyms:

C – Circle the question words U – Underline key words B – Box any key numbers E – Evaluate (what steps do I take?) S – Solve and check (does my answer make sense and how can I double check?)

R – Read the problem correctly. I – Identify the relevant information. D – Determine the operation and unit for expressing the answer. E – Enter the correct numbers and calculate

I – Identify the problem D – Define the problem E – Examine the options A – Act on a plan L – Look at the consequences

R – Read and record the problem I – Illustrate your thinking with pictures, models, number lines etc C – Compute, calculate and check E – Explain your thinking

R – Read the question and underline the important bits U – Understand: think about what to do and write the number sentences you will need C –  Choose how you will work it out S – Solve the problem A – Answer C – Check

Q – Question – read it carefully U – Understand – underline or circle key elements A – Approximate – think about the size of your answer C – Calculate K – Know if the answer is sensible or not

T – Think about the problem and ponder E – Explore and get to the root of the problem A – Act by selecting a strategy R – Reassess and scrutinise and evaluate the efficiency of the method

The idea behind these problem solving models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem. You can choose which is most appropriate for the age group and ability of the children you are teaching.

The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way. A far simpler model – that we use in the   Ultimate Guide to KS2 Problem Solving Techniques  – is UCR: Understand the problem, Communicate and Reflect.

You then need to give pupils lots of opportunities to practice this! You can find lots of FREE White Rose Maths aligned maths resources, problem solving activities and printable worksheets for KS1 and KS2 pupils in the Third Space Learning Maths Hub .

You might also be interested in:

• 25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)
• 30 Problem Solving Maths Questions And Answers For GCSE
• Why SSDD Problems Are Such An Effective Tool To Teach Problem Solving At KS3 & KS4

What’s included in the guide?

After reading the  Ultimate Guide to KS2 Problem Solving Techniques , we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques

• Open ended problem solving
• Using logical reasoning

Working backwards

Drawing a diagram

Drawing a table

Creating an organised list

Looking for a pattern

Acting it out

Guessing and checking

Cognitive Activation: getting KS2 pupils in the lightbulb zone

If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The  National Education Research Foundation  (NFER) published ‘ PISA in Practice: Cognitive Activation in Maths ’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.

Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:

• Giving pupils maths problem solving questions that require them to think for an extended time.
• Asking pupils to use their own procedures for solving complex problems.
• Creating a learning community where pupils are able to make mistakes.
• Asking pupils to explain how they solved a problem and why they choose that method.
• Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
• Giving pupils problems with no immediately obvious method of solution or multiple solutions.
• Encouraging pupils to reflect on problems.

Sparking cognitive activation is the same as sparking a fire – once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for independent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).

Read these:

• How to develop maths reasoning skills in KS2 pupils
• FREE CPD PowerPoint: Reasoning Problem Solving & Planning for Depth
• KS3 Maths Problem Solving

That time, effort, and planning will – however – be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life – not just for their SATs.

For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions – don’t forget to download our free  Ultimate Guide to KS2 problem solving and reasoning techniques  resource here.

KS2 problem Solving FAQs

Here are some techniques to teach problem solving to primary school pupils: Open ended problem solving Using logical reasoning Working backwards Drawing a diagram Drawing a table Creating an organised list Looking for a pattern Acting it out Guessing and checking

Ofsted say that teachers can encourage problem-solving by: Setting problems as part of learning in all topics for all pupils. Varying the ways in which you pose problems. Trying to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations. Making sure you discuss alternative approaches with pupils to help develop their reasoning. Ensuring that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

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The Problem-solving Classroom

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• Looking for patterns
• Trial and improvement.

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• mathematical skill.
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• An increased number of speculative responses.
• The number of questions asked by students increases.
• Student - student exchanges increase (volleyball).
• Failures to respond decrease.
• 'Disciplinary moves' decrease.
• The variety of students participating increases.  As does the number of unsolicited, but appropriate contributions.
• Student confidence increases.
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Problem Solving

 A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.

Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.

In a  second video  two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.

Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.

Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

These three resources, from the National Strategies, focus on solving problems.

  Logic problems and puzzles  identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.

Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .

Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.

Primary mathematics classroom resources

Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics

This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.

Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...

8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.

Number Picnic: The problems make ideal starter activities

Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.

Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.

GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.

Examples include:

*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.

*Beach Guest House - Booking guests into appropriate rooms in a hotel.

*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.

*Design a Table - Involving diagrams, measurements, scale.

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

Starting Investigations

The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.

The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.

NRICH Primary Activities

Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!

Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

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How to Teach Kids Problem-Solving Skills

KidStock / Blend Images / Getty Images

• Steps to Follow
• Allow Consequences

Whether your child can't find their math homework or has forgotten their lunch, good problem-solving skills are the key to helping them manage their life. 

A 2010 study published in Behaviour Research and Therapy found that kids who lack problem-solving skills may be at a higher risk of depression and suicidality.   Additionally, the researchers found that teaching a child problem-solving skills can improve mental health . 

You can begin teaching basic problem-solving skills during preschool and help your child sharpen their skills into high school and beyond.

Why Problem-Solving Skills Matter

Kids face a variety of problems every day, ranging from academic difficulties to problems on the sports field. Yet few of them have a formula for solving those problems.

Kids who lack problem-solving skills may avoid taking action when faced with a problem.

Rather than put their energy into solving the problem, they may invest their time in avoiding the issue.   That's why many kids fall behind in school or struggle to maintain friendships .

Other kids who lack problem-solving skills spring into action without recognizing their choices. A child may hit a peer who cuts in front of them in line because they are not sure what else to do.  

Or, they may walk out of class when they are being teased because they can't think of any other ways to make it stop. Those impulsive choices may create even bigger problems in the long run.

The 5 Steps of Problem-Solving

Kids who feel overwhelmed or hopeless often won't attempt to address a problem. But when you give them a clear formula for solving problems, they'll feel more confident in their ability to try. Here are the steps to problem-solving:  

• Identify the problem . Just stating the problem out loud can make a big difference for kids who are feeling stuck. Help your child state the problem, such as, "You don't have anyone to play with at recess," or "You aren't sure if you should take the advanced math class." 
• Develop at least five possible solutions . Brainstorm possible ways to solve the problem. Emphasize that all the solutions don't necessarily need to be good ideas (at least not at this point). Help your child develop solutions if they are struggling to come up with ideas. Even a silly answer or far-fetched idea is a possible solution. The key is to help them see that with a little creativity, they can find many different potential solutions.
• Identify the pros and cons of each solution . Help your child identify potential positive and negative consequences for each potential solution they identified. 
• Pick a solution. Once your child has evaluated the possible positive and negative outcomes, encourage them to pick a solution.
• Test it out . Tell them to try a solution and see what happens. If it doesn't work out, they can always try another solution from the list that they developed in step two. 

Practice Solving Problems

When problems arise, don’t rush to solve your child’s problems for them. Instead, help them walk through the problem-solving steps. Offer guidance when they need assistance, but encourage them to solve problems on their own. If they are unable to come up with a solution, step in and help them think of some. But don't automatically tell them what to do. 

When you encounter behavioral issues, use a problem-solving approach. Sit down together and say, "You've been having difficulty getting your homework done lately. Let's problem-solve this together." You might still need to offer a consequence for misbehavior, but make it clear that you're invested in looking for a solution so they can do better next time. 

Use a problem-solving approach to help your child become more independent.

If they forgot to pack their soccer cleats for practice, ask, "What can we do to make sure this doesn't happen again?" Let them try to develop some solutions on their own.

Kids often develop creative solutions. So they might say, "I'll write a note and stick it on my door so I'll remember to pack them before I leave," or "I'll pack my bag the night before and I'll keep a checklist to remind me what needs to go in my bag." 

Provide plenty of praise when your child practices their problem-solving skills.  

Allow for Natural Consequences

Natural consequences  may also teach problem-solving skills. So when it's appropriate, allow your child to face the natural consequences of their action. Just make sure it's safe to do so. 

For example, let your teenager spend all of their money during the first 10 minutes you're at an amusement park if that's what they want. Then, let them go for the rest of the day without any spending money.

This can lead to a discussion about problem-solving to help them make a better choice next time. Consider these natural consequences as a teachable moment to help work together on problem-solving.

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Pakarinen E, Kiuru N, Lerkkanen M-K, Poikkeus A-M, Ahonen T, Nurmi J-E. Instructional support predicts childrens task avoidance in kindergarten .  Early Child Res Q . 2011;26(3):376-386. doi:10.1016/j.ecresq.2010.11.003

Schell A, Albers L, von Kries R, Hillenbrand C, Hennemann T. Preventing behavioral disorders via supporting social and emotional competence at preschool age .  Dtsch Arztebl Int . 2015;112(39):647–654. doi:10.3238/arztebl.2015.0647

Cheng SC, She HC, Huang LY. The impact of problem-solving instruction on middle school students’ physical science learning: Interplays of knowledge, reasoning, and problem solving . EJMSTE . 2018;14(3):731-743.

Vlachou A, Stavroussi P. Promoting social inclusion: A structured intervention for enhancing interpersonal problem‐solving skills in children with mild intellectual disabilities . Support Learn . 2016;31(1):27-45. doi:10.1111/1467-9604.12112

Öğülmüş S, Kargı E. The interpersonal cognitive problem solving approach for preschoolers .  Turkish J Educ . 2015;4(17347):19-28. doi:10.19128/turje.181093

American Academy of Pediatrics. What's the best way to discipline my child? .

Kashani-Vahid L, Afrooz G, Shokoohi-Yekta M, Kharrazi K, Ghobari B. Can a creative interpersonal problem solving program improve creative thinking in gifted elementary students? .  Think Skills Creat . 2017;24:175-185. doi:10.1016/j.tsc.2017.02.011

Shokoohi-Yekta M, Malayeri SA. Effects of advanced parenting training on children's behavioral problems and family problem solving .  Procedia Soc Behav Sci . 2015;205:676-680. doi:10.1016/j.sbspro.2015.09.106

By Amy Morin, LCSW Amy Morin, LCSW, is the Editor-in-Chief of Verywell Mind. She's also a psychotherapist, an international bestselling author of books on mental strength and host of The Verywell Mind Podcast. She delivered one of the most popular TEDx talks of all time.

Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Home > Learning Resources

KS1 and KS2 Maths – Problem solving

• Author: Mike Askew
• Main Subject: CPD
• Subject: Maths
• Date Posted: 20 June 2012

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If children use well worn techniques to solve problems without understanding or modelling the context, their maths skills won't fully evolve

Children, from birth, are proficient problem solvers. By the age of two or three they have solved what are probably life’s two biggest problems - how to walk and how to talk. As they get older they solve practical problems, such as sharing a bag of sweets fairly with others, long before they’ve heard of division. In this article, I look at how we can build on this natural propensity to solve problems in teaching mathematics.

Routine and non-routine problems

Routine problems are problems children know how to solve based on their previous experiences. The sort of thinking required by routine problems can be described as reproductive: the child only needs to recall or reproduce a procedure or method they have previously learnt. A problem like ‘Apples’, for example (see below), is likely to be a routine problem for most children at the upper end of primary school; they know to multiply the two numbers together without having to think deeply about what operation to use.

• Apples on a supermarket shelf are in bags of eight. • If Jane buys six bags, how many apples is that?

In contrast, non-routine problems are where the learner does not immediately have a solution tucked under his belt. The problem solver has to put some effort into understanding the problem and creating, rather than recalling, a solution strategy. Non-routine problems engage learners in productive thinking.

We often think of non-routine problems as needing to be unusual or not having, to us as adults, an immediately obvious method of solution. ‘Stamps’ is typical of this type of non-routine problem.

• Clearing out a desk draw I found a collection of 5p and 6p stamps. • I have a parcel to post that needs 58p worth of stamps on it. • Can I create this exactly using the stamps I found? • If so, is there more than one way of doing this?

In choosing problems to work with, we need to decide whether or not we think a problem will be routine or non-routine for the particular children working on it. In the rest of this article, the problems chosen are being treated as though they are non-routine problems for the children working on them. That’s not to say that I don’t think routine problems have a place in the curriculum - they do. Here, however, I want to deal with some of the issues around teaching and learning non-routine problems.

The importance of context

• Four hungry girls share three pizzas equally. • Eight hungry boys share six pizzas equally. • Does each girl get more pizza than each boy, less or the same?

As a routine problem, the ‘story’ of pizzas and hungry children doesn’t serve any real purpose: children quickly learn to disregard the context, to strip out the mathematics and to work some procedure. The problem could just as easily have been put in the context of builders sharing bricks and many learners would happily say each builder would get 3/4 of a brick, without stopping to question the near impossibility of sharing out bricks.

We can, however, treat ‘Pizzas’ as a non-routine problem and use it to introduce children to thinking about fractions and equivalences. The context of hungry children and pizzas then becomes important. It is not chosen simply to be window-dressing for a fraction calculation. Nor are pizzas chosen because children are intrinsically motivated by food, making the unpalatable topic of fractions digestible. No, the context s chosen because children know about fair shares and slicing up pizzas - they can solve this problem without any formal knowledge of fractions. As the researcher Terezhina Nunes once pointed out, young children would not be able to solve the ‘bald’ calculation 3 divided by 4 but, “show me four young children who, given three bars of chocolate to share out fairly, hand the bars back saying ‘it can’t be done.”

Children have ‘action schemas’ for solving problem like ‘Pizzas’ - they can find ways to solve this with objects, pictures, diagrams and, eventually, symbols. Teaching can then build on the children’s informal solutions to draw out the formal mathematics of fractions. From being one of 20 ‘problems’ on a worksheet to complete in a lesson, ‘Pizzas’ can become a ‘rich task’ taking up the best part of a lesson, if children work on it in pairs and carefully selected solutions are then shared with the class.

Creating mathematical models

Part of the productive thinking in working on rich, non-routine problems requires children to create mathematical models, and we can teach to support this.

• At the supermarket Myprice, milk costs £1.08 per litre. • This is 7 pence less per litre than milk costs at Locost. • How much does 5 litres of milk cost at Locost?

What is missing from this approach is attention to setting up an appropriate model of the problem. Ultimately this could be a mental model of the problem context, but it helps initially to encourage children to put something on paper that can be shared and discussed. In problems involving quantities, like ‘Milk’, simple bar diagrams can help children create the appropriate model. These help children examine the relationships between the quantities (as opposed to simply fixing on specific numbers and keywords).

Setting up a diagrammatic model begins with creating a representation of what is known in the situation. In this example, we know milk at Myprice costs £1.08, so a diagram for this would look like:

MYPRICE £1.08

This provides the basis for talking about what the picture for the price of milk at Locost is going to be. Will the bar be longer or shorter? Where is the bar for the 7 pence to be drawn?

Two different models can be set up and children asked to describe the relationship between the prices at the two supermarkets, to see which diagram fits with the information in the problem. If the diagram for the price at Locost is shorter by 7, then two statements can be made:

MYPRICE £1.08p LOCOST     7p

• Myprice milk costs 7 pence more than milk at Locost.

• Locost milk costs 7 pence less than milk at Myprice.

In comparison, making the bar for milk at Locost longer by 7 gives different comparative statements:

MYPRICE £1.08p 7p LOCOST    

• Myprice milk costs 7 pence less than milk at Locost.

• Locost milk costs 7 pence more than milk at Myprice.

Children can then talk about which of these situations fits with the wording in the problem.

Having established that Locost milk must be £1.15 a litre, children can go on to produce the bar diagram model for this.

Supporting non-routine problem solving

Where the problems were played out as non-routine, three factors identified are worth noting. First, in choosing the tasks, the teachers made sure they would build on learners’ prior knowledge - as I suggest a problem like ‘Pizzas’ can. Second, in contrast to focusing on getting the answer, the researchers observed what they called ‘sustained pressure for explanation and meaning’. In other words, the teachers pressed for children to explain what and why they were doing what they were doing rather than simply focusing on whether or not they had got the correct answer. Third, the amount of time children were allowed to work on the problem was neither too long or too short: children need enough time to ‘get into’ a problem, but too much time can lead to a loss of engagement.

Share good practice

Gather together a collection of problems covering all the years of education in your school (or ask teachers to each contribute two or three problems).

Working together in small groups, teachers sort the problems into three groups:

1. Problems they think would be routine for the children they teach 2. Problems they think would be non-routine for their children 3. Problems they think would be much too difficult for their age group

Everyone agrees to try out a problem from group 2 with their class. Discuss how too much focus on getting the answer can reduce the challenge and stress the importance of pressing children to explain their working. At a subsequent meeting, people report back, focusing in particular on strategies they used to keep the problem solving non-routine.

About the author

Mike Askew is Professor of Primary Education at Monash University, Melbourne. Until recently, he was Professor of Mathematics Education at King’s College, University and Director of BEAM.

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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Let L = the tenth term

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

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Some students may need support to learn effective problem-solving skills. This resource can assist students to think of and evaluate options to a problem or situation. 

You can encourage and support students to use this tool to:

- come up with two options

- write the pros and cons of each option, and

- implement the option they think is best. 

In high school settings, some students may respond better to a short conversation. For these students, you can use the first page of the guide as a prompt sheet to facilitate talking through a problem. Short notes in a workbook of a student’s choosing as a reminder of decisions made may also be helpful.

School Excellence Framework alignment

Australian professional standards for teachers alignment.

Standard 1: Know students and how they learn

Primary teachers, SLSOs

This resource can be used to support students to think of and evaluate options to a problem or situation. It includes a template for students to consider and compare two potential solutions.

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Problem-Solving in Elementary School

Elementary students practice problem-solving and self-questioning techniques to improve reading and social and emotional learning skills.

In a school district in New Jersey, beginning in kindergarten each child is seen as a future problem solver with creative ideas that can help the world. Vince Caputo, superintendent of the Metuchen School District, explained that what drew him to the position was “a shared value for whole child education.”

Caputo’s first hire as superintendent was Rick Cohen, who works as both the district’s K–12 director of curriculum and principal of Moss Elementary School . Cohen is committed to integrating social and emotional learning (SEL) into academic curriculum and instruction by linking cognitive processes and guided self-talk.

Cohen’s first focus was kindergarten students. “I recommended Moss teachers teach just one problem-solving process to our 6-year-olds across all academic content areas and challenge students to use the same process for social problem-solving,” he explained.  

Reading and Social Problem-Solving

Moss Elementary classrooms use a specific process to develop problem-solving skills focused on tending to social and interpersonal relationships. The process also concentrates on building reading skills—specifically, decoding and comprehension.

Stop, Look, and Think.  Students define the problem. As they read, they look at the pictures and text for clues, searching for information and asking, “What is important and what is not?” Social problem-solving aspect: Students look for signs of feelings in others’ faces, postures, and tone of voice.

Gather Information . Next, students explore what feelings they’re having and what feelings others may be having. As they read, they look at the beginning sound of a word and ask, “What else sounds like this?” Social problem-solving aspect: Students reflect on questions such as, “What word or words describe the feeling you see or hear in others? What word describes your feeling? How do you know, and how sure are you?”

Brainstorming . Then students seek different solutions. As they read, they wonder, “Does it sound right? Does it make sense? How else could it sound to make more sense? What other sounds do those letters make?” Social problem-solving aspect: Students reflect on questions such as, “How can you solve the problem or make the situation better? What else can you think of? What else can you try? What other ideas do you have?”  

Pick the Best One.  Next, students evaluate the solution. While reading, they scan for smaller words they know within larger, more difficult words. They read the difficult words the way they think they sound while asking, “Will it make sense to other people?” Social problem-solving aspect: Students reflect on prompts such as, “Pick the solution that you think will be best to solve the problem. Ask yourself, ‘What will happen if I do this—for me, and for others involved?’”

Go . In the next step, students make a plan and act. They do this by rereading the text. Social problem-solving aspect: Students are asked to try out what they will say and how they will say it. They’re asked to pick a good time to do this, when they’re willing to try it.

Check . Finally, students reflect and revise. After they have read, they ponder what exactly was challenging about what they read and, based on this, decide what to do next. Social problem-solving aspect: Students reflect on questions such as, “How did it work out? Did you solve the problem? How did others feel about what happened? What did you learn? What would you do if the same thing happened again?”

You can watch the Moss Elementary Problem Solvers video and see aspects of this process in action.

The Process of Self-Questioning 

Moss Elementary students and other students in the district are also taught structured self-questioning. Cohen notes, “We realized that many of our elementary students would struggle to generalize the same steps and thinking skills they previously used to figure out an unknown word in a text or resolve social conflicts to think through complex inquiries and research projects.” The solution? Teach students how to self-question, knowing they can also apply this effective strategy across contexts. The self-questioning process students use looks like this:

Stop and Think. “What’s the question?”

Gather Information. “How do I gather information? What are different sides of the issue?”

Brainstorm and Choose. “How do I select, organize, and choose the information? What are some ways to solve the problem? What’s the best choice?”

Plan and Try. “What does the plan look like? When and how can it happen? Who needs to be involved?”

Check & Revise. “How can I present the information? What did I do well? How can I improve?”

The Benefits

Since using the problem-solving and self-questioning processes, the students at Moss Elementary have had growth in their scores for the last two years on the fifth-grade English language arts PARCC tests . However, as Cohen shares, “More important than preparing our students for the tests on state standards, there is evidence that we are also preparing them for the tests of life.”

Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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• Published: 18 July 2023

Fostering twenty-first century skills among primary school students through math project-based learning

• Nadia Rehman   ORCID: orcid.org/0000-0002-4172-625X 1 ,
• Wenlan Zhang 1 ,
• Amir Mahmood 1 ,
• Muhammad Zeeshan Fareed 2 &
• Samia Batool 3  

Humanities and Social Sciences Communications volume  10 , Article number:  424 ( 2023 ) Cite this article

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• Development studies

In today’s modern world, students must be equipped with twenty-first century skills, particularly those related to solving real-life problems, to ensure competitiveness in the current global economy. The present study employed project-based learning (PBL) as an instructional tool for teaching math at the primary level. A convergent mixed-methods approach was adopted to determine whether the PBL approach has improved students’ twenty-first century skills, including collaborative, problem-solving, and critical thinking skills. Thirty-five students of the experimental group were treated with PBL, while 35 students of the control were treated with the traditional teaching method. ANCOVA test for “critical thinking skills” showed a significant difference between the experimental and control group ( F  = 104.833, p  = 0.000 < 0.05). For collaborative skills, results also showed a significant difference between the two groups ( F  = 32.335, p  = 0.000 < 0.05). For problem-solving skills, the mean value of experimental (25.54) and control group (16.94) showed a high difference after the intervention. The t -value (8.284) and the p value ( p  = 0.000) also showed a highly significant difference. Observations of the classroom also revealed the favorable effects of employing PBL. PBL activities boosted the level of collaboration and problem-solving skills among students. Students could advance their collaboration abilities, including promoting one another’s viewpoints, speaking out when necessary, listening to one another, and participating in thoughtful discussions. During the PBL project, students’ active participation and effective collaboration were observed, significantly contributing to its success.

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Introduction.

Learners of the twenty-first century need to equip with the core knowledge and necessary skills to perform in various situations to succeed. There are many different educational philosophies, each of which contains essential elements for human development (Parrado-Martínez and Sánchez-Andjar 2020 ). In 2017, Alif Ailaan published a report entitled “Powering Pakistan for the 21st -Century,” highlighting the dismal state of math and science education nationwide. Report data showed that, on average, fourth graders earned 433 out of 1000 points in math on the National Education Assessment System exam. The survey concluded that students performed exceptionally poorly in mathematics and geometry (Ailaan 2017 ). Most students in public schools are not actively involved in their education because of the teacher-centered nature of the classroom. In teachers’ eyes, students’ knowledge, passions, and individuality are irrelevant (Rehman et al. 2021 ).

The National Education Policy of 2009 states that teachers should adapt their teaching methods according to the need of the students and situation. The National Curriculum for 2006 also emphasizes a significant shift in the teacher’s role, from information transmitter to classroom environment maker, to assist students in gaining a sound knowledge of mathematical topics. Several factors affect how effectively the math curriculum is put into practice. These factors include the school setting, student demographics, and instructional resources (Mazana et al. 2018 ). Teachers must adopt cutting-edge practices to ensure their students are well-equipped for the twenty-first century. Using ICT, these novel methods may assist teachers in honing these abilities and adapting instruction to meet the moment’s needs (Muthukrishnan et al. 2022 ).

PBL and twenty-first century skills

In the twenty-first century, cognitive abilities are an unquestionably reliable measure of a student’s success (Saduakassova et al. 2023 ). Students of this generation need to be aware of how the world is changing and prepare themselves with the skills necessary for a more challenging way of life (Wongdaeng and Hajihama 2018 ). Students need to be able to engage in critical thinking to survive in this competitive era. It will enable them to take the initiative and devise meaningful solutions to emerging problems (Suwastini et al. 2021 ). Students need to have strong communication skills and the ability to work effectively with others to succeed in today’s world when networking is essential to one’s career (Akcanca 2020 ). Students must have an imaginative and creative mindset to keep up with the rapid advances. The terms “communication”, “cooperation”, “creativity”, “problem-solving skill”, and “innovation skills” are often referred to as “the 4Cs” that PBL supports; in the present study, the author only focused on the three skills, collaborative, critical thinking and problem-solving that has more influence in math learning (Almazroui 2023 , pp. 125–136).

Educational professionals have recognized the importance of the 4Cs to student success. They have proposed that PBL as an instructional design can improve students’ mastery of the 4Cs (Kurniahtunnisa and Wowor 2023 ). According to Moghaddas and Khoshsaligheh ( 2019 ), PBL is a teaching strategy that falls under the constructivist approach and centers on having students participate in a series of research-oriented activities that require their collaborative actions to achieve the goal. By participating in these activities and interacting with others, students’ critical thinking, communication, collaboration, and creative abilities can be enhanced (Papanastasiou et al. 2019 ).

There are several problems with Pakistan’s educational system, including a lack of funds, inefficient program execution, and poor management and instruction (Shah Bukhari et al. 2022 ). As a result, most of our educational institutions continue employing more conventional instruction modes. Math is the most powerful tool for acquiring knowledge that exists in the world (Sithole et al. 2017 ). Math is the discipline in the scientific world that focuses on developing individuals’ perceptual and cognitive abilities. History shows that every ancient civilization placed a high value on mastering arithmetic. History also shows that every ancient civilization greatly valued becoming proficient in arithmetic (Alsaad et al. 2023 ). Students who are not good at math struggle academically due to their lack of enthusiasm for studying the subject since they either do not find it interesting or challenging. Children lose interest in understanding complex concepts such as algebra, arithmetic, or geometry at a young age when teachers force them to learn without focusing on the twenty-first century skills (Abramovich et al. 2019 ). The present study investigates the impact of PBL on students’ twenty-first century skills, including problem-solving, critical thinking, and collaborative skills.

Reasons for implementing project-based learning in math

One of the main reasons for implementing PBL in math is to address the low math scores of Pakistani students, as reported by TIMSS 2019 and Alif Ailaan reports ( 2017 ). Finland has improved its ranking in PISA by implementing PBL in its education system, which has helped to promote student-centered learning, collaboration, and problem-solving skills and to develop a deep understanding of the subjects studied, resulting in improved academic performance. PBL can help students to develop a deeper understanding of mathematical concepts and skills through hands-on, real-world problem-solving activities. For technology-deprived classrooms, PBL effectively engages students in active learning experiences, such as group projects and case studies. Technology integration is impossible in many public schools due to a lack of access to basic infrastructure such as electricity and internet connectivity. Implementing PBL in math can promote student motivation, collaboration, and creativity, essential for developing twenty-first century skills and preparing students for future careers. PBL can shift the focus from teacher-centered instruction to student-centered learning, allowing students to take ownership of their learning and develop critical thinking skills.

Research question

Q1. Is there any statistically significant difference in the students’ collaborative skills between the experimental and the control group?

Q2. Is there any statistically significant difference in the students’ problem-solving skills between the experimental and the control group?

Q3. Is there any statistically significant difference in the students’ critical thinking skills between the experimental and the control group?

Q4. How do students collaborate with group members during classroom project learning?

Literature review

Pbl and collaborative skills.

Collaborative learning (CL) is a fundamental component of the twenty-first century skills. It involves students collaborating to exchange ideas, solve an issue, or achieve a common objective (O’Grady-Jones and Grant 2023 ). In math education, CL’s popularity skyrocketed in the 1980s, but it has continued to develop since then (Simon 2020 ). The educational strategy known as collaborative learning tries to improve students’ education by having them work on projects together in groups (Vogel et al. 2016 ). This method encourages students to construct their meaning from various sources of knowledge rather than relying solely on memorizing facts and figures. To complete a wide range of class projects and assignments, students work together in small groups to better grasp complex ideas and concepts (Roldán Roa et al. 2020 ). Primary factors determining the efficacy of collaborative work are students’ level of involvement in the learning process and teachers’ readiness to evaluate project outputs (Kaendler et al. 2015 ).

In PBL, students are encouraged to work in groups of two or more pairs or classes to discover common ground, develop ideas, define concepts, or generate an end product (Rizkiyah et al. 2020 ). Students attentively follow the teacher’s instructions and diligently interpret and apply their understanding of the course material, demonstrating their grasp through study and application (Qureshi et al. 2021 ). The usage of CL has brought about a profound shift away from the old classroom atmosphere centered on the teacher delivering lectures. The ways of taking notes, listening to a lecture, and simply observing may only partially disappear in a classroom setting, emphasizing collaboration. However, they coexist with other strategies for promoting active learning and student conversation regarding the course content (Kollar et al. 2014 ). Teachers who employ interactive teaching methods perceive themselves not merely as transmitters of expert knowledge to students but, more significantly, as mentors or coaches facilitating a mature learning process. They see their role as expert designers of the cognitive experiences their students engagement. This shift in perspective allows them to engage students better in the learning process (Lim et al. 2023 ).

Recent research has shown that both meaning and behavior influence the process of learning. During collaborative learning activities, the students are encouraged to overcome challenging obstacles. Immersive learning activities often begin with topics in which students must supply particular facts and perspectives (Almazroui 2023 ). Contrarily, traditional classrooms typically initiate by providing information and concepts before transitioning into a practical application (Markula and Aksela 2022 ). In this setting, teachers expect students to quickly evolve from their roles as preliminary researchers, dealing with questions and answers or problems and solutions, to becoming competent experts. It requires them to employ higher-order thinking and problem-solving strategies (Brown et al. 1989 ). Despite the term “collaborative learning” being widely applied across various fields and disciplines, it still needs universal approval. Though many may still need to grasp the concept fully, certain commonalities tend to emerge (Qureshi et al. 2021 ). In the twenty-first century, there was a rise in working together. Because the focus has shifted from individual actions to group efforts and from the individual to society, it is more vital than ever for people to think about and collaborate on significant issues (Laal et al. 2012 ).

PBL and problem-solving skills

Project-based learning is an approach to education in which students demonstrate mastery of a topic by developing and presenting their solutions to real-world problems (Chiang and Lee 2016 ). In the planning stage, students must evaluate the needs for product development, identify issues with current products, and modify these products based on the principle of creative problem-solving. PBL can benefit students’ knowledge, skills, attitudes, and creativity in problem-solving capacities (Andanawarih et al. 2019 ). However, unlike conventional teaching methods, project-based education can be challenging to put into practice. Tee ( 2018 ) stated that students must communicate effectively to ensure the success of project-based learning projects. The students struggled through the project planning phase to apply the concept of creative problem-solving, which is essential when building a product (Artama et al. 2023 ). Therefore, educators are encouraged to craft a guide for innovative problem-solving by harnessing student-generated product concepts. However, the current student knowledge and abilities level can challenge the effective implementation of project-based learning (DeCoito and Briona 2023 ). Students are to fault for this since they need more practice solving problems or participating in project-based learning. The students’ incapacity to apply strategies for overcoming creative obstacles while learning contributes to the low quality of their work (Kiong et al. 2022 ). Therefore, it is essential to emphasize the use of creative problem-solving strategies in PBL to provide students with the means to finish the projects associated with each chapter with relative ease and better prepare them for higher education (Devanda and Elizar 2023 ).

PBL and critical thinking skills

In addition to content knowledge, PBL fosters skills like critical thinking, creativity, lifetime learning, communication, teamwork, flexibility, and self-evaluation (Artama et al. 2023 ). Creating science and mathematics curricula aims to train students to think more critically. Analytical and critical thinking is examining data, making inferences, articulating ideas, and assessing claims. However, the student’s critical thinking skills are still formative (Mutakinati et al. 2018 ). For this reason, schools must implement programs that help students develop their abilities in areas like creativity and critical thinking, which are in high demand in the modern workplace. Project-based learning is an effective method of teaching and learning in the contemporary era. This approach in the education sector offers equal treatment of real-world issues. At the outset of each lecture, students examine problems from the real world, which are then recast as problems for them to solve in pairs or small groups (Pan et al. 2023 ).

Critical thinking is an essential life skill. Future success requires students to have strong communication and critical thinking skills. Critical thinking is analyzing and evaluating one’s thinking to make constructive changes. Nadeak and Naibaho ( 2020 ) identified six levels of critical thinking: unreflective thinker, challenged thinker, novice, practicing thinker, advanced practitioner, and master. When we talk about “critical thinking”, we are talking about the ability to analyze information, evaluate its relevance, and comprehend problems. Analyzing, evaluating, reasoning, and reflecting are part of the process (Rati et al. 2017 ).

The Paul–Elder Framework for critical thinking defines critical thinking as a self-reflective and disciplined process involving constant self-monitoring and correction. This framework encourages an analytical approach to personal thought processes to enhance them. The unreflective thinker, the challenged thinker, the novice thinker, the experienced thinker, the expert thinker, and the master thinker are the six stages of critical thinking (Paul and Elder 2008 ). According to Paul and Elder ( 2008 ), there are eight parts to a thinking process: an objective, a set of questions, a body of data, a set of interpretations and interferences, a set of ideas, a set of assumptions, some potential outcomes, and a point of view (Fig. 1 ). The intellectual standards outline the criteria for good critical thinking (Mutakinati et al. 2018 ).

The author made this figure based on the framework provided by Paul and Elder ( 2008 ).

Math education incorporates many skills, including self-awareness, the ability to plan and organize learning, and the capacity to think critically. The assessment of students determines the accuracy, credibility, and relevance (or applicability) of the provided materials. Critical thinking and mathematics are deeply intertwined; one must integrate both to understand the discipline truly. Every child must learn and practice arithmetic and logic. Therefore, any program that teaches critical thinking should incorporate strategies that cater to diverse student populations (Holmes and Hwang 2016 ).

Previous studies on PBL

PBL has gained recognition worldwide as an alternative approach to traditional teacher-centered education, emphasizing hands-on, collaborative, and inquiry-based learning activities (Yang et al. 2021 ). Previous studies have shown that PBL can effectively promote student learning, engagement, and achievement across various subjects, including math and science. For example, a study by Paryanto et al. ( 2023 ) found that PBL improved student achievement and attitudes toward learning in engineering education.

However, some studies have also criticized the effectiveness of PBL in specific contexts, highlighting the challenges of implementing PBL and potential limitations. For instance, a study by Loyens et al. ( 2023 ) found that PBL had a limited impact on students’ cognitive and metacognitive skills in medical education. The authors suggested that the lack of clear guidelines and support for PBL implementation and the complex and dynamic nature of medical education may have contributed to these results (Saqr and López-Pernas 2023 ). Furthermore, some researchers have argued that the effectiveness of PBL may depend on various factors, such as the level of student readiness, teacher training and support, curriculum alignment, and assessment methods. For example, a study by Jincheng and Chayanuvat ( 2020 ) found that PBL is more effective when integrated into a comprehensive curriculum reform program than used as a stand-alone intervention. Additionally, the authors emphasized the importance of aligning PBL with clear learning objectives, providing appropriate scaffolding and support, and using valid and reliable assessments to measure student learning (Szalay et al. 2023 ). While PBL has shown promise as a practical approach to teaching and learning, its implementation and effectiveness may depend on various factors, and caution should be exercised in its application (Jincheng and Chayanuvat 2020 ).

Constructivist theory

The social constructivist approach is consistent with project-based learning since it stresses students’ involvement in the learning process through group work and instructor guidance (Huang et al. 2022 ). Therefore, educators should foster classroom environments where students can take charge of their learning. Students in project-based learning classes are encouraged to participate actively in their education and develop critical transferable skills while working on real-world projects (Le et al. 2023 ). Interpersonal learning occurs when individuals participate in groups, share information, and work together to overcome obstacles (Dolmans 2019 ). Students develop essential life skills in groups where they take full responsibility for their education (Harden 2018 ). Students’ ability to think creatively and fill the gap between their knowledge and talents is aided by acquiring these new life skills. It highlights the significance of PBL, which brings transformative experiences, facilitates long-term knowledge retention, and nurtures students’ commitment to an inclusive and participatory society (Mielikäinen 2022 ).

In addition, the multiple intelligence theory developed by Howard Gardner fits well with the approach taken in project-based education (Owens and Hite 2022 ). Gardner highlighted that all humans possess eight types of intelligence, each manifested in a unique set of skills and abilities, and he discriminated between these types in the context of students. Due to these differences, teaching and learning styles vary. By incorporating a wide range of activities, project-based courses may effectively accommodate students with a wide range of learning preferences (Radkowitsch et al. 2022 ).

The experiential learning theory (ELT) developed by Kolb ( 1984 ) served as the theoretical foundation for PBL (Sevgül and Yavuzcan 2022 ). The ELT works well with the principles of PBL, and it proposes that young children have an innate interest in the scientific method and want to know how the things they meet in their everyday lives function. Sevgül and Yavuzcan ( 2022 ) argued that children are naturally curious and continually engaged in meaningful interactions with the world around them. They learn to think critically and solve difficulties by interacting with one another. Consultation with adults, peers, and educators promotes collaborative learning. Like experience, growth is a continuous process, with each step having its distinct logic and psychology that prime the learner for the next level (Rajabzadeh et al. 2022 ). The principles of PBL exemplify Kolb’s ELT due to their emphasis on fostering a learning environment that resonates with students and a real-world audience. Students must provide classroom activities that enable them to benefit from real-world applications and cultivate meaningful relationships with their peers. Students gain a sense of belonging to something greater than themselves when they work together toward a common objective (Sevgül and Yavuzcan 2022 ). The study focused on understanding how learning occurs in PBL, and Kolb’s ELT provided a framework for doing so based on meaningful and authentic experiences. Students can only engage in meaningful learning if they can build on their existing knowledge and participate in projects with personal and global significance (Erstad and Voogt 2018 ).

Methodology

In the present study, the researcher adopted a convergent mixed-methods approach to determine if the problem-based learning (PBL) method has enhanced students’ twenty-first century skills, including collaboration, problem-solving, and critical thinking. A quasi-experimental design was used for the quantitative part, and a non-equivalent control group pre-test-post-test design was employed. This design remains prevalent in educational research (Cohen et al. 2017 ). For the qualitative part, students were observed during intervention using the collaborative framework to understand the students’ involvement during their project work. Students in 5th grade were selected as the object of the study, one section (35 students) was selected as an experimental, and others (35 students) were selected as a control group. The experimental group was treated with PBL intervention, while the control group was treated with the traditional teaching method. Random sampling was not possible due to fix schedule of the school. It was a 6-week project, and the detail of the PBL project is provided in Table 1 . In the control group, teachers implemented the same content traditionally. Before and after the intervention, collaborative, critical thinking, and problem-solving were measured in both groups of students.

Instruments

The researcher adopted a collaborative scale Tibi ( 2015 ) developed to answer the research questions. This scale was used to evaluate the students in the control and experimental groups to see how well they could work together (see Table 2 ). The questionnaire consisted of 37 five-point Likert-style statements. To assess problem-solving skills math test was designed, which contains twenty items. To measure the students’ creative and critical skills, the researcher adopted Gelerstein et al. ( 2016 ), Yoon ( 2017 ), Sumarni and Kadarwati ( 2020 ) open-ended questionnaire. The study collected data using a critical thinking skills test comprising ten problems. These problems measured sub-skills, including interpretation, analysis, evaluation, inference, explanation, and self-regulation. Table 1 presents the instruments used for this critical thinking test.

Ventista ( 2018 ) also used this questionnaire in his study. The scale’s reliability was determined to be 0.76 using the Cronbach alpha test. In conclusion, higher-order cognitive skills emerged from metacognitive processes (Coskun 2018 ). This finding agreed with prior work published by Sumarni and Kadarwati ( 2020 ) on developing test items to gauge students’ creative abilities. The critical thinking instrument used in this research exhibited high validity and reliability, making it possible to assess students’ critical and creative thinking skills in the context of math.

The math test was designed to check how well students can solve problems. This test uses content from three chapters of a 5th-grade math teacher’s guide to see their improvement. The test consisted of 20 questions and aimed to gauge fifth-grade students’ problem-solving abilities in angle measurement and geometry. The test consists of ten questions related to each category. The first ten questions measured students’ problem-solving skills related to angle measurement, while the second set measured their geometry-related skills. Test questions are crafted carefully to assess the students’ understanding of these concepts and their ability to apply them to real-world scenarios. The test was administered to the students, and the results were analyzed to determine their proficiency in problem-solving skills related to these topics (see Table 2 ).

The study utilized the “ITEMAN” tool to perform item analysis on these data (Ramadhan et al. 2019 , pp. 743–751). The results showed that the difficulty index might range from 0.33 to 0.85, and the discrimination index may range from 0.31 to 0.82. According to the findings of Susanto and Retnawati ( 2016 ), We considered an item to be of generally high quality if its difficulty index ranged from 0.31 to 0.89 and had a discrimination value of at least 0.22.

The classroom observations tool served as a source for gathering qualitative data. Before the observational activities, participants received information about the researcher’s intentions. The study utilized a collaborative framework tool to monitor students’ behavior and engagement in the experimental classroom. Before initiating data collection, the instrument underwent a validation process.

Stages of the experiment

Before the intervention, homogeneity of the 5th-grade math students was established. Both groups were randomly allocated as the 5-B experimental and 5-A as the control group. Before the intervention, we examined all the experimental and control variables, including collaborative, critical thinking, and problem-solving skills.

Before the intervention, twenty-first century skills were measured as a pre-test from both groups.

In the experimental group, PBL was used as an instructional tool for delivering math content. Different lesson plans and modules are prepared concerning the “Measurements of angels, geometry, and decimal concept”. A control group was treated with a traditional method with the same content (see Table 3 ).

Lesson schedule (6 weeks, 5 h weekly, for 30 class hours), lesson plans, and modules were designed before intervention. Lessons planning followed Math Core standards.

Before the intervention, AV aids were prepared for classroom activities. Students worked in the classroom in groups of six girls (five groups) in each session.

For assessment, teachers used worksheets and projects at the end of the session and followed the operational stages mentioned by “Buck Institute” Kaptan and Korkmaz ( 2000 ).

After the intervention, both groups implemented the “math attitude, creativity, and problem-solving test” as a post-test.

During the project work, experimental group students were observed to assess their engagement and collaboration with peers and groups.

PBL project implementation

A hands-on project.

During this procedure, the students worked on creating a new product. They discuss and present an actual model.

For the present study, students constructed a project after 4 weeks of lessons and presented it at the end of the experiment. All group members participated and presented their work to the class (see Fig. 2 ).

Students’ group activity in PBL in the classroom.

Driving questions

During this procedure, students strive to provide a solution to an open-ended question. For the present study, the instructor prepares different open-ended questions for students to answer. The best part was that every member was participating. Every classroom consists of average, below-average, and high achievers. PBL encouraged every category student to get participated in project-making.

Q1. Identifying Right, Obtuse, and Acute Angles?

Q2. Name the marked angle.

(a) Name the vertex of the angle.

(b) Name the arms of the angle

Q3. Classify the following angles into acute, obtuse, right, and reflex angles:

(i) 35°(ii) 185°(iii) 90°(iv) 92°(v) 260°

Q4. Observe the given figure with a protractor and give the measure of each of the angles.

New information

As a result of participating in this process, students acquire new mathematical information. This task also helped students to review previously learned knowledge. For the present study, the teacher introduces the new concept with examples, like percentages, discounts, and real value.

Student-driven elements

The teacher performs indirectly as a facilitator while the students direct their learning. Throughout the lesson, the teacher acted as a facilitator, and it was the first time for students to learn math with different teaching strategies; so, at every step researcher and the trainer acted as a facilitator and provided a zone of proximal development (ZPD), throughout their learning process.

Realistic goals and outcomes

Students work on a realistic project, and it has some objectives. It is appropriate both for the age of the students and aligned with course standards. PBL is appropriate for primary-grade students; PBL helps them strengthen their foundation and make concepts more precise and practical.

Application to the real world

The mathematical concepts involved things that learners might encounter outside the classroom. All the essential elements are followed rigorously (see Table 4 ).

The effect of PBL improving students’ collaborative skills

The study uses one-way ANCOVA for the pre-and post-test on the experimental and control groups to check the effectiveness of PBL in improving the 5th-grade students’ collaborative skills. Before proceeding to a one-way analysis of covariance, a homogeneity of variance test analysis is performed to ensure the data aligns with the fundamental premise of ANCOVA (see Table 5 ).

Levene’s test result, shown in Table 5 , demonstrates no difference between the experimental and control groups before the intervention ( F  = 0.806, p  = 0.0373 > 0.05). The data analysis aligns with the primary hypothesis of ANCOVA. That means that the two groups’ variations are identical to one another. Therefore, the two samples originate from populations with the same variance.

Table 6 represents a result of one-way ANCOVA for the students about collaborative skills. Results show a significant difference between the experimental and control groups ( F  = 253.564, p  = 0.000 < 0.05). This indicates that PBL activities impact the fifth-grade students’ collaborative skills during project learning. Students in the intervention group developed collaborative skills during the math project compared to the control group students.

The effect of PBL improving students’ critical thinking skills

One-way, ANCOVA compares the pre-and post-test results of the “critical thinking skills” of the treatment and control groups for the fifth-grade math students. In determining whether the data are consistent with the fundamental premise of ANCOVA, a homogeneity of variance test analysis is performed before a one-way analysis of covariance (see Table 7 ).

Table 7 represents a result of Levene’s test, which revealed no significant difference between the two groups ( F  = 3.711, p  = 0.58 > 0.05). The fundamental premise of ANCOVA applies once the data analysis is complete.

Table 8 represents the result of one-way ANCOVA for the students’ “critical thinking skills”. Results showed a significant difference between the treatment and control groups ( F  = 23.281, p  = 0.000 < 0.05). The intervention group’s critical thinking skills improved compared to control group students. PBL helps the students to develop twenty-first century skills and involve them in critical thinking during their project learning.

The effect of PBL improving students’ problem-solving skills

Problem-solving skills.

An accomplishment exam was developed to evaluate students’ problem-solving skills in math. This test required students to respond to 10 questions (20 marks) chosen and crafted according to the math curriculum’s standards-based learning objectives (SLO). Before and after the experiment, the test was given to students of both groups to know the difference.

Table 9 represents the mean scores of the experimental and control group students’ problem-solving test results. The mean value of the experimental group before the intervention was 12.46, and after the intervention was (25.54). While the pre-mean value of the control group was (11.80) and after was (16.94). The data reveals an increase in the mean value for both groups. However, the experimental group, which received instruction through the PBL method, exhibited a more substantial increase than the group taught math using the traditional method. The p value also shows that before the intervention, the p value was ( p  = 0.421), which is greater than 0.05, which means there was no significant difference between the experimental and control group. While after the intervention, the p value ( p  = 0.00) shows that there is a significant difference.

To check the difference in the mean scores between the control and experimental group before and after the experiment, an independent sample t -test was applied.

Table 10 represents the result of the independent sample t -test; the mean value of the experimental group (12.46) and the control group (11.80) shows a minor difference in both groups before the intervention. The t -value (0.809) and the p value ( p  = 4.22) also show no significant difference. The results of this table show that group of experimental group and control group performed the same on achievement and problem-solving skills before the intervention; there was no significant difference between experimental and control group students. The p value ( p  = 4.22) is more significant than 0.005. That specified no significant difference between the experimental and control groups before the treatment.

Table 11 represents the result of the independent sample t -test; the mean value of the experimental group (25.54) and the control group (16.94) show a high difference in both groups after intervention. The t -value (8.284) and the p value ( p  = 0.000) also show a highly significant difference. This table shows that the experimental group performed better on problem-solving skills than the control group, which was not treated with PBL. PBL as an instructional tool was suggested as one of the best teachings for teaching math at the primary level. Cohen’s d value of 1.82 specified a big difference between the group treated with the PBL instruction method and those treated through traditional teaching methodology.

Paired sample t -test was applied to check the difference between the pre-and post-scores of the experimental and control group.

Table 12 shows the results of paired sample t -test. Paired sample t -test is applied to the pre-post-test of the experimental and control group to know the difference before and after the intervention. The mean value of the scores showed that there were highly significantly different. As the p value is smaller than 0.05 ( p  = 0.005), the probability value is highly significant, and there is a difference in the mean scores of the experimental group. PBL helps the students develop more problem-solving skills than the control group. On the other hand, the mean value of the control group’s scores showed a minor difference, and the p value is more significant than 0.05, which means that the traditional method did not significantly affect the students’ problem-solving skills.

Qualitative analysis

All experimental group members were observed using a collaborative scale framework during project work. Students were observed under the project’s four themes: individual accountability, social skills, and group processing. This method is widely used in social sciences (Pleşan 2021 ). The instructor divided the students into seven groups (five girls in each group) with varying abilities and potential. The students were able to acquire various skills in these diverse groups to enhance them as well as intragroup interpersonal interactions. Classroom observations were conducted several times a week over 6 weeks. The study utilizes two inductive and deductive reasoning cycles during the coding process (Ridder 2014 ). Four themes were generated from the observational data: student group work, a student, shared duties, the interdependence of the student’s work and their decision-making

Students’ group work

During the PBL, students collaborated in groups from the project planning stage to creating the product and project presentation. Students collaborated in groups to discuss statistical applications in their classrooms throughout the project preparation stage. Then, they discuss further the project’s title, description, and objectives, the project’s implementation steps, the project schedule, and each group member’s responsibilities. Additionally, observations revealed that students leveraged social media platforms, such as WhatsApp group chats, for discussions outside school hours.

Students shared responsibilities

Each group assigned its members a task and set a deadline, ensuring students appropriately shared duties. Therefore, the students were expected to finish the related activities before the due date. When it was their chance to speak on what they had discovered about angles, how they are measured, and how these angles differ from one another, the students were sharing responsibility. This circumstance demonstrated that each group member must collaborate to develop their awareness of many aspects and apply them to their project. Additionally, each student took part in constructing the presentation of their work on hard copy paper and outlining the presentation materials for their project presentation in front of the entire class. The project tasks involved cutting paper, measuring angels, and sketching various shapes with various angles and were shared among the pupils to produce the final items.

The students made decisions regarding the theme of the project, the activities they would undertake, the project’s timeline, individual roles within the group, the final product, and the materials and tools required for the project. They also determined the most effective method to present their project results to others. When making substantial judgments about the project’s topic, process, and output, students always hold an initial conversation to address individual ideas collectively. To influence the choice, the students bargained their thoughts. The observation revealed that the student gained confidence in her ability to voice her opinions during the group assignment. When students encountered divergent viewpoints among group members regarding the process of making important decisions, they conducted voting and arrived at a consensus opinion.

Additionally, the researcher discovered that one student needed help developing the project’s product, particularly the finished item. The student expressed concern about the final product’s adornment, which she feared would be overdone and lower its esthetic worth. These data demonstrate that the student and her team were making crucial design decisions that impacted the result.

Students’ interdependent work

From the observations, it is clear that the task required each group member to create a unique set of presentation materials on angles, which were to be assembled into a cohesive presentation on stiff chart paper. Therefore, if any group member does not complete their tasks in time, it may cause a delay in the final presentation chart’s completion. This circumstance demonstrated the interdependence of the student’s contributions to the PBL. The researcher observed and documented students’ collaborative efforts in a project-based learning environment, and the following are excerpts from these observations. In addition, each group member was assigned to prepare and bring the tools and supplies required to complete the project. The manufacturing process is improved if one team member gets the necessary tools or materials. That demonstrated how student effort is interdependent and dramatically impacts the project. This requirement enables students to comprehend and be conscious of the significance of their part in completing the project. Students were able to apply the concept of an angel to everyday problems through the completion of their mathematics project. In this project, students worked in small groups to gather and describe the data using their knowledge and observations. Subsequently, they transformed the angles into visual representations. The student’s final projects, displayed in the counseling room, the students’ club room, and the school wall magazine, served as references for significant school statistics.

The findings above conclude that applying PBL in mathematics enhances students’ teamwork skills. When students share responsibility equitably, make crucial decisions, and produce an interdependent project product, they attain level 5 according to the criteria for twenty-first century students’ collaboration skills.

The present study’s findings contribute to the growing body of literature on PBL and its potential for promoting students’ twenty-first century skills, particularly in Math education. The results showed that students who received PBL instruction developed collaborative, critical thinking, and problem-solving skills, as measured by various assessment tools, including questionnaires, tests, and classroom observations. These skills are essential for preparing students for the complex challenges of the twenty-first century, such as global competition, technological advancements, and social and environmental issues. It aligns with previous research highlighting the benefits of PBL for promoting critical and creative thinking (Darling-Hammond et al. 2020 ). However, students in Pakistani government schools need to become more accustomed to engaging in critical thinking while solving arithmetic problems, as reported by the TIMSS study. That is a big challenge for teachers seeking to improve math and Science Education (Ahmad et al. 2022 ).

The study sheds light on implementing PBL activities in classrooms and how they can enhance students’ critical thinking, problem-solving, and collaborative abilities. This finding can help teachers reevaluate how students gain from participating in PBL activities and restructure their instructional approaches to achieve student-centered learning. The study’s results are consistent with previous research, suggesting that PBL can help students build collaborative skills through group projects (Chistyakov et al. 2023 ). Collaboration abilities are crucial for success in today’s interconnected working environment and global culture. PBL is one educational activity that can help students build these skills, as it demands that students collaborate in small groups to solve problems and produce products. PBL is an ideal method for teaching mathematics at the primary level. It helps students recognize the relationships between different mathematical concepts and develop a conceptual understanding of the subject. It can help students identify partial order in the collection of mathematical notions, an essential aspect of mathematical concept development.

However, it is essential to note that the effectiveness of PBL may depend on various factors, such as teacher training and support, curriculum alignment, assessment methods, and student readiness. For instance, Loyens et al. ( 2023 ) research revealed that PBL minimally influences students’ cognitive and metacognitive abilities within medical education. The researchers posited that the absence of well-defined guidelines and assistance for PBL implementation might have yielded these findings in conjunction with medical education’s intricate and ever-changing landscape. Furthermore, implementing PBL may require significant time, resources, and training for teachers and students, posing challenges in specific educational contexts. Therefore, further research is needed to explore the effectiveness and feasibility of PBL across different subjects, grade levels, and cultural contexts and identify the optimal conditions for its implementation.

In conclusion, this study provides empirical evidence of the potential benefits of PBL for promoting twenty-first century skills in math education, including collaboration, critical thinking, and problem-solving. The findings underscore the importance of student-centered, inquiry-based, and authentic learning experiences that can prepare students for the complex challenges of the twenty-first century. The study’s results inform the development of practical pedagogical approaches that promote student learning and engagement and contribute to the ongoing dialog on educational reform and innovation.

This study has a unique contribution to the context of the Pakistani educational landscape. While the literature is abundant with studies on the benefits of project-based learning (PBL), this study specifically addresses the implementation and effectiveness of PBL in teaching mathematics to 5th-grade students in Pakistan. By providing detailed insights into the local context, including the cultural, social, and educational factors that may influence the adoption and outcomes of PBL, we have enriched the understanding of PBL’s applicability and potential benefits in diverse settings. Furthermore, the interpretation of our results highlights the development of twenty-first century skills, collaborative abilities, problem-solving aptitude, and creative thinking skills among the participating students, demonstrating the value of PBL as an instructional tool within the Pakistani context. This original contribution advances the global understanding of PBL’s effectiveness. It offers practical implications for educators and policymakers in Pakistan seeking innovative ways to improve learning outcomes and foster essential skills in their students. Moreover, in Pakistani public schools where technology integration is not feasible, PBL can be an effective alternative for math teaching by utilizing low-tech resources such as manipulatives, posters, and group activities. Teachers can create engaging and collaborative problem-solving experiences for students, fostering critical thinking skills even in technology-deprived classrooms.

Data availability

The data supporting this study’s findings are available on request from the corresponding author. These data are part of a large project, and only a portion is available for the following reasons: (1) Some participants in the study requested complete anonymity, which restricts the availability of specific datasets to protect their privacy and confidentiality. We have taken all necessary steps to ensure no personal or identifiable information is included in the available data. (2) Additionally, some of the data are reserved for future publication. It ensures the integrity of ongoing analyses and prevents potential overlap in research findings. We understand the importance of data availability in promoting transparency, reproducibility, and open science, and we commit to making as much of the data available as possible within these constraints. Data are available at https://doi.org/10.7910/DVN/YJY0FI and accessed with the author’s permission.

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NR: made significant contributions to the conception and design of the study, writing, data collection, analysis, and interpretation. WZ: provided valuable insights into the theoretical framework conceptualization, resources, supervision, validation, and proofreading. AM: writing, review, and editing. MZF: actively participated in the manuscript revising for scientific accuracy and ensuring clarity in the “Methodology” section. SB: review and editing. All authors read and approved the final manuscript.

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Rehman, N., Zhang, W., Mahmood, A. et al. Fostering twenty-first century skills among primary school students through math project-based learning. Humanit Soc Sci Commun 10 , 424 (2023). https://doi.org/10.1057/s41599-023-01914-5

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Exploring the significant problems confronting secondary schools history education: a baseline study

• Open access
• Published: 14 May 2024
• Volume 3 , article number  52 , ( 2024 )

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• Fekede Sileshi Fufa   ORCID: orcid.org/0000-0001-6035-8205 1 ,
• Abera Husen Tulu   ORCID: orcid.org/0000-0002-0408-9028 2 &
• Ketebo Abdiyo Ensene   ORCID: orcid.org/0000-0001-8492-9340 1  

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The purpose of this baseline study is to determine the significant problems confronting history education in secondary school. The researchers employed qualitative research methods and case study design. The techniques that were employed to acquire credible data were document analysis, interviews, and classroom observation. Six experienced history education teachers and eight top-ten students from Sebeta town public secondary school were interviewed, and academic achievement statistics of 174 students in history education were analyzed. In addition eight lesson observations were carried out to validate the information gleaned from the interviews and document analysis. The study's findings show that the primary challenges influencing history education in Sebeta town public secondary schools were teaching strategy, a lack of awareness about implementing participatory teaching methods, a lack of comprehensiveness of the contents of history education teaching materials, and the issue of the bulkiness and scope of history education texts being covered on time. The findings also indicate the significance of training history education teachers to use participatory teaching tactics, as well as the need for curriculum experts to better coordinate the range of history education content and teaching strategies. The findings of this study will help teachers, practitioners, scholars, policymakers, and educational professionals find solutions to significant problems in secondary school history education, as well as develop effective techniques for teaching history education in secondary schools that involve twenty-first century skills and abilities.

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1 Introduction

History education as an academic discipline has a long history in the world. In the nineteenth century a German historian Leopold von Ranke an indispensable contribution to modernizing history writing [ 1 , p. 2, 2 , p. 171]. Ranke (1795–1886) not only established history as a major discipline, but he also established the idea that all accurate history must be based on primary sources and rigorous methodology [ 1 , p.13, 3 ]. As a result, he is regarded as the father of modern historiography [ 1 , p. 2]. Since the nineteenth century, history education has developed as an independent discipline across the world.

In terms of teaching strategies, evidence shows that teaching approaches play an important role in any subject of study in enhancing students' academic achievements [ 4 , p. 601, 5 ]. Many research findings demonstrate that the approach employed to develop any operation significantly determines the end product [ 6 , p. 7]. Several factors influence students' academic achievement; evidence suggests that teachers are the most essential ones in terms of students’ education and achievements [ 7 , pp. 2633–34]. According to the research findings conducted on student learning, the way teachers engage their pupils is crucial in the teaching and learning process [ 8 , p. 39]. The approaches used by the teacher should be matched to the demands of the students [ 6 , p.7]. Students’ motivation and achievement are mostly dependent on the teachers’ activities [ 9 , p. 15). Several researches have indicated that among the subjects offered in schools, students do have not much interest in history education [ 10 , p. 45]. According to a study conducted on secondary schools, history education has been taught through lectures rather than participatory and student- centred strategies [ 11 , p. 1). According to Kiio [ 11 , pp. 1–2], effective implementation of participatory teaching and learning methodologies can increase students' interest in history education. Issar [ 10 , p. 49] also emphasized the significance of learning history education, stating that learning history education should help students understand the complexities of human lives, the diversity and relationships between different groups, the changes and continuities and connect the past, present, and future events.

Scholars confirm that constructive learning approaches allow students to participate actively in the lessons [ 12 , p. 35]. Since 1980, the theory of social constructivism has been advocated as an effective way of learning and teaching [ 12 , pp. 35–36]. It is a theory developed by Russian psychologist Lev Vygotsky (1896–1934), which holds that individuals are active participants in the creation of their knowledge [ 13 , p.783]. Vygotsky’s social constructivism focuses on pedagogies that encourage active learning, effective and meaningful learning, constructive learning, and learning by doing [ 13 , p.783]. Current research in the field of history education supports the notion that participatory approaches to teaching the subject at the secondary school level are the preferred method for developing the skills required to handle the world's future historiographical needs [ 14 , p. 81]. In several works of literature, interactive teaching approaches are vital in increasing student academic achievement. The purpose of this baseline study is to investigate the significant problems confronting history education in Sebeta government secondary schools.

2 Statement of the problem

History education is frequently a source of public debate, a source of unrest, and a site of struggle over what and how should be taught in schools in Ethiopia [ 15 , p. 2]. National history is taught as a compulsory subject in different countries. Several countries believe that knowing the country’s history is a requirement for all citizens [ 16 , pp. 1–2]. In the case of history education teaching in Ethiopia, for the first time, a history syllabus was included in the education curriculum after 1943 [ 17 , p.87]. However, no specific research on significant problems confronting history education in Ethiopian secondary schools has been conducted. Researchers who have studied the problem of education in Ethiopia have directly and indirectly addressed the issue of history education [ 18 , pp.18–19].

According to research conducted by Resource and Guide [ 19 , p. 8], teaching is important by incorporating 21st-century skills such as critical thinking skills, problem-solving, language proficiency, communication and collaborative skills, cognitive skills, adaptability skills and the ability to make decisions. Furthermore, student-centred teaching method fosters students' comprehension, deep learning, problem-solving, critical thinking, and communication [ 20 , p. 4]. Research conducted on history education has discovered a link between teaching approaches and students' attitudes towards history education [ 21 , p. 3]. A scant study has been conducted on significant problems confronting history education in Ethiopian secondary schools and on approaches more appropriate for teaching history.

This motivated the researchers to conduct research on major problems confronting history education in Ethiopian secondary schools in Sebeta town. To fill this gap, the researchers used a variety of tools to analyze significant problems confront history education in Ethiopian secondary schools in general, and Sebeta town public Secondary School in particular.

Thus, this study attempts to answer the following questions:

What are the most significant problems facing history education at Sebeta town public secondary school?

What are the most common teaching strategies employed at Sebeta town government secondary school?

How is the student’s academic achievement in history at Sebeta public secondary school?

3 Objectives of the study

To find out the most significant problems facing history education at Sebeta Town Government Secondary School.

To identify the most common teaching strategies employed at Sebeta town government secondary school.

To determine a student’s academic achievement in history at Sebeta government secondary school.

4 Literature review

Any research project needs theory to provide direction and help on how things are implemented. Theoretical foundation aids in deciphering the way phenomena happen and the basis of specific actions [ 22 , p. 75]. This research is founded on Vygotsky’s social constructivist learning theory, which supports historical thinking. According to a social learning theory developed by Russian psychologist Lev Vygotsky (1896–1934), individuals are active participants in the development of their knowledge [ 23 , p. 395]. This social constructivism approach places a strong emphasis on pairs and small groups [ 24 , pp.13–15]. According to this theory, students learn primarily through interactions with their classmates, instructors, and parents, whereas teachers are expected to facilitate dialogue in the classroom [ 25 , p. 243]. According to Richard [ 26 , p. 380], good teaching and learning are strongly reliant on interpersonal interaction and conversation, with the primary focus on the student’s understanding of the topic.

Scholarly works reveal that there is very little study on the significant problems confronting history education. The existing scholarly works on teaching approach and students’ learning, on the other hand, demonstrate that there are strong relationships between the effects of teaching strategies and students’ achievement. Sugano and Mamolo [ 27 , p. 827] conducted a study on the “Effects of Teaching Methodologies on Students’ Attitude and Motivation,’’ found that teaching methods had an enormous positive impact (Cohen’s d = 0.379) on student attitude. The study also found that cooperative learning had a greater power than traditional teaching methods in improving students’ positive attitudes, motivation and interest.

History teaching should not only be mastery of the basic content (substantive knowledge) but also enhance the acquisition of subject skills and competencies that will make students learn on their own and manage their own lives and carry it through the adversities of life in society [ 26 , 28 ]. Luka [ 14 , p. VII] discovered in his study, “The Impact of Teaching Methods on Attitudes of Secondary School Students Towards Learning of History in Malawi,” that students in secondary schools have negative attitudes towards learning history. One of the reasons he highlighted is that student-centred techniques of teaching are not regularly used in the subject of history education ( Ibid , [ 29 ]).

Moreover, Mazibuko [ 30 , p. 142] revealed that teaching methods in history education greatly contributed to students' negative perceptions of the subject. He discovered that traditional methods of teaching history utilized by teachers contributed to students decreasing interest in the subject ( Ibid ). Besides, Zhu and Kaiser [ 31 , p. 191] discovered that teaching methods influence students’ motivation, attitudes towards school, willingness to do homework, and confidence in their learning.

In his study on effective teaching in history, Boadu [ 8 , p. 39] discovered that effective teaching of history should bring the subject closer to students’ lives, hearts, and minds. He argued that effective teaching cannot emerge from traditional history teaching, because the teacher lectures on the subject intensely, and students are forced to take and memorize notes.

Silver and Perini [ 32 , p. 16) argued that teachers who use a variety of teaching techniques have well-behaved and motivated students, resulting in high student academic achievement.

Adding to this, according to [ 33 , p. 74], the quality of teaching strategies influences student learning and contributes to a 15 to 20 times improvement in student achievement. These researches highlighted that effective teaching strategies played a crucial influence on student motivation, developing students’ positive attitudes, and improving students’ academic achievement more than traditional teacher-centred approaches. There has been no research undertaken in Ethiopian secondary schools to determine which methodologies could be better appropriate for teaching history. Using the designed study instruments, the researchers examine and determine the significant problems confronting history education in Sebeta government secondary schools.

5 Research methodology

The study was conducted using the constructivist paradigm view with the qualitative research approach. In this study, the researchers utilized a qualitative research approach. The qualitative research approach allows the researchers to conduct an in-depth investigation of the problem under study [ 34 , pp. 177–179, 35 , p. 12]. The qualitative research approach has different specific designs. These are Phenomenology, Ethnography, Narrative inquiry, Case study, Grounded theory and Historical research [ 36 , p. 49]. In this study, the qualitative case study design was used. Case studies are ways to explain, describe, or explore phenomena. According to Hatch [ 37 , p. 37], case studies are the type of qualitative work that investigates a contextualized contemporary phenomenon within specific boundaries. This study was carried out using document analysis, interviews, and classroom observation techniques.

The researchers received the accreditation letter from their institution and submitted it to the relevant authorities to confirm the legality of the research. The letter was then submitted to the Sebeta town’s education office and Sebeta secondary schools to acquire authorization to collect primary data from sampled respondents. The data collection process was started after getting all relevant permits from the authorities. Before interviews with respondents, the researchers described the goal of the study to the participants to acquire their permission. The researchers told participants that the study's primary aim was to collect data for the research titled "The significant problems confronting history education in history education in Sebeta town public secondary schools, Ethiopia." After extensive verbal discussions with the respondents, interviews were conducted with those who expressed full interest in participating in the study.

5.1 Sampling procedure

This study employed a purposive sampling technique. In the first stage, the study site was chosen purposively, which is Sebeta town. In the following step, this baseline study was confined to two out of four government secondary schools in Sebeta town with similar standards, a higher number of students and staff than the others. The schools that were purposely selected for the study are those that have been in existence for a long time, have more experienced staff than others, and are expected to provide firsthand information. Purposive sampling was used to select knowledgeable research participants [ 38 , pp. 512–513]. Because it allows the researcher to select the research participants who were believed informed sources of information, thoughtful, informative, articulate, and experienced with the problem under the study [ 35 , p.142, 39 , pp. 100–114]. The researchers selected individuals who have a good source of information about the issue under study (history education teachers and students [ 39 , p. 100]. In the selected two secondary schools, there are six history education teachers, five males and one female. These teachers were purposefully included in the study. The researchers believed that the experienced teachers who were chosen were useful as a primary source of data because they were familiar with the subject's contents, as well as its problems. Eight top-ten grade ten students from the two schools also took part in the study directly. The researchers believed the top-ten students were able to explain the area of study more accurately than the others. Grade ten students were purposefully chosen for the study. The following are the grounds for choosing grade ten students: First history education in Ethiopia begins in grade nine. Students began studying history education grade nine onwards. Because it is assumed that grade ten students know more about history education contents than grade nine students. Second, it is assumed that grade ten comprises all types of students (higher achievers, moderate, and slow learners), as well as grade 10 students who will choose a major (social sciences and natural sciences) in their future grade eleven. As a result, the researchers opted to gather the finest information from grade ten students to establish their perspectives toward history.

6 Results and discussions

6.1 what are the significant problems facing history education in sebeta town government secondary school, 6.1.1 interviews analysis.

For explanation, the abbreviation SSST stands for “Sebeta Secondary School Teacher”, similarly, BSSST stands for “Burka Sebeta Secondary School Teacher” and the numbers denote the order. As shown in Table  1 , six history education teachers were interviewed for this study. Of the six teachers interviewed, five had more than 15 years of teaching experience. Five of these teachers hold a bachelor's degree and one has an MA in history. Five of the teachers interviewed were male and one was female. During the interviews, the teachers revealed to the researchers that three of the six teachers had an MA in another academic discipline (Table 2 ).

For clarification, the abbreviation SSSS stands for, “Sebeta Secondary School Student”, BSSS, “Burka Sebeta Secondary School Student” and the numbers represent the order. Eight students’ four males and four females from both schools were chosen for the interview of this study.

An interview is one of the data collection instruments that were used to explore the significant problems confronting history education in government secondary schools. An interview allows the researchers to gather information that is directly related to the research objectives [ 40 , p. 411]. It is typically conducted one-on-one with informants who have firsthand experience with the research topic [ 25 , p. 144]. An interview was conducted with six experienced history education teachers, and eight secondary school students to gather adequate data about the topic under investigation.

The researchers began their interview with teachers by asking, “What are the significant problems facing history education in Sebeta town government secondary school?” The researchers interviewed teachers concerning the organization of the history education curriculum. Teacher SSST1’s response to this question is as follows: “I have been teaching history education for 18 years but I have never seen or read the curriculum of history education until today.’’ Furthermore, BSSST1 shared the same point of view saying: “So far, I have not read any history education syllabus or seen what it contains except students’ textbook. There is no available history education syllabus in secondary school for teachers. ” Teacher SSST2 also made a similar note: “We do not have a history syllabus, and the teaching materials that we use to teach students are only students’ textbooks.”

All of the teachers interviewed stated that they did not have a history curriculum and had never utilized it. The researchers found that teachers do not see contents, structures, recommended teaching aids, and methodologies in the history education syllabus and teachers’ guide.

Teachers explained that the history education textbook is divided into three parts: world history, African history, and Ethiopian history. According to the teachers interviewed, the history of the Ethiopian peoples are not written inclusively in students’ textbooks, and Ethiopian history education does not adequately addressed the political, social, and economic history of the Ethiopian people (BSSST1, BSSST2, SSST1, SSSS2, SSST3). However, research work suggests that in multi-ethnic countries, all students should be able to learn about themselves and their culture from the books they learn from Hodkinson et al. [ 41 , p. 3] stated that “all learners must be able to find themselves and their world represented in the books from which they learn.”.

In addition, teachers were asked as history education teaching materials in the same way as other Subjects. To this question, all of the teachers interviewed consistently said no. Teachers claim that “since our country’s political changes, textbooks for all disciplines have been updated three to four times, but history education has not been updated in the same way” (BSSST1, BSSST2, SSST1, SSSS2, SSST3, SSSST4). They demonstrated this to the researchers by referring to the textbook they were using. In this instance, a history grade 10 students’ textbook was published in 2002 GC/1994, reprinted in 2005/1997 and renewed in 2023 after 18 years. According to the teachers interviewed, there has been no detailed reform of history education in terms of adding or removing content, implementing new teaching strategies, or keeping up with the 21st-century world. One interviewed teacher said, ‘’I have been teaching history for 18 years and have not observed any changes in history education contents since I started teaching history education.’’ (SSST1).

The researchers continued their interview with teachers by asking, is the content of the history education curriculum appropriate for the student's abilities? This question is to gather evidence to understand that the content of the history curriculum is appropriate for the student's abilities. Teachers and students were asked this question. When asked about the content of history education in grade ten, teachers made two comments:

Students who did not study history as a subject in elementary school (1st grade to grade eight) may find it more difficult when they begin studying history education as a subject in grade nine (SSST1 and SSST2).

They have been studying in their mother tongue in primary school (grades 1 to 8) and studying in English from grade 9 onwards will make it difficult for students to understand the contents (SSST1 and SSST2). The students interviewed strongly agree with the latter. According to the students, “the content of history is very difficult to understand, history is not like other subjects, it requires proper knowledge of English” SSSS1, SSSS2, BSSSS1 and BSSS2).

Follow-up questions were also raised for teachers, to determine the teaching methods included in the history education curriculum. However, teachers were unable to respond to this question because they were not implementing the teaching practices outlined in the history education curriculum due to a lack of a history syllabus. A well-designed teaching strategy has a crucial role in improving students' academic achievement [ 42 , p. 51–64]. Therefore, teachers teach history using their own teaching and learning methods. When asked what teaching method they used, the teachers stated that they used the lecture teaching method (SSSS1, SSSS2, BSSSS1 and BSSS2). The reason they use lecture methods more than other teaching and learning methods is that the content of history lessons is extensive and the time allocated for history lessons is 80 min per week (SSSS1, SSSS2, BSSSS1 and BSSS2).

6.1.2 Classroom observation analysis

The researchers used lesson observations to obtain firsthand and ‘real' facts and data about the significant problems confronting history education in Sebeta government secondary schools. This is because many people do not want to discuss all topics during an interview [ 43 , p. 117]. The researchers employed the lesson observation checklist, which included activities such as the teacher's teaching strategies, teacher and student activities throughout the session, teacher-student interaction during the lesson, student seating arrangements, and teaching aids used. Using this checklist, the researchers observed the teacher’s teaching practice during the lesson. The researchers observed four different classrooms. The primary aim of this observation was to strengthen the data obtained from teachers and students during an interview. The teachers in all of the classrooms first ask students what they learned in their last class. Aside from that, they only used to give notes and lectures to the students in every class.

Another point that the researchers visited in the classroom was the teachers’ and students’ activities during the lesson. The teachers gave notes, and lectures and many students were busy writing notes. When the teachers lecture the content some students do not pay attention and instead take notes. Some students do not take notes, do not listen and look elsewhere. As observed by the researchers, teacher-student interaction during the lesson is very weak. Based on the observation students' seating arrangements were traditional in that three students' seats occur on a wave which is not convenient for group discussion, group work and collaborative learning.

During classroom observation, there are no teaching aids used in all classrooms visited by the teachers to make the lessons practical.

Finally, based on the findings of the study through classroom observation, traditional methods of teaching and learning in history classrooms are still the dominant teaching strategies in the twenty-first century. Researchers who research teaching strategies confirm that participatory teaching is an effective way to improve students’ academic achievement. Madar and Baban [ 42 , pp. 51–64] also discovered that participatory teaching is a good strategy to develop students’ skills and increase their academic achievements. They added that participatory teaching strategies put students at the centre of the teaching and learning process (p. 51). However, through interviews with teachers, students, and lesson observation, the researchers discovered that teachers are not employing student-centred approaches that are fitting for students' learning and achievement.

The responses of teachers and students are consistent with the literature on strategies for teaching. Researchers who conducted studies on teaching strategies found that the teacher- centred method is a traditional strategy that is not very effective in enhancing student achievement. The findings of this study also agree with Mohammed [ 44 , p. 11] who conducted a study on, “strategies in the teaching of geography …” , and stated that the lecture method of teaching has a negative effect on students’ creativity, critical thinking, ability to produce new ideas, and academic achievement of students. Similarly, this study’s findings also concur with Ezurike [ 45 , pp. 1120–124] conducted a study on, “The Influence of Teacher-Centered and Student-Centered Teaching Methods on Academic Achievement of Students,” which discovered that poor methods, mostly teacher-centred and conventional teaching methods used by teachers, are one of the major factors contributing to students’ poor achievement.

Finally, it is better to conclude that teaching strategies can positively and negatively influence students' academic achievement. If teachers only employ the lecture approach without involving students in the lesson, it may result in low student academic achievement in contrast if teachers employ student-centred strategies students can understand the main point of the lesson and enhance the academic achievement of students.

6.2 How do teaching strategies influence students' academic achievement in Sebeta secondary schools?

To answer this question, the researchers conducted interviews with teachers and students, as well as document reviews and classroom observations. This issue was addressed by both teachers and students. Methods of teaching have a wide range of effects on the academic success of learners. When asked this question, they all had similar answers. According to teachers, good teaching strategies play a significant role in improving students’ academic achievement. They state this as follows:

Using collaborative teaching practices can significantly improve students' academic achievement. Because collaborative instruction is a teaching technique in which students learn together by assisting one another. Higher achiever students support the low achiever learner in this instructional learning process. However, if teachers utilize traditional teaching methods without involving students in the teaching-learning process, students' academic achievement may suffer (BSSST1, SSST2, and SSST3).

However, for a variety of reasons, teachers do not use collaborative teaching strategies to improve the academic achievement of their students. Rather than focusing on improving the academic achievements of students’ teachers are only concerned with completing their content. Furthermore, the student stated that teaching strategy can positively and negatively influence students' academic achievement. According to students:

…if teachers employ interactive teaching strategies during teaching lessons, students can understand the main point of the lesson and profit much from it. In contrast, if teachers exclusively employ the lecture approach without involving students in the lesson, it may result in low student achievement in the subject. Furthermore, students responded with two statements: excellent teaching strategies encourage students’ interest in the subject and are also, critical for improving students' academic achievement (BSSSS1, BSSSS2, SSSS1, SSSS3, and SSSS6).

The teachers were interviewed about teaching methods they implement when teaching a history education lesson. The teachers were asked to mention teaching methods that they always use in teaching history. The majority of the teachers claimed to use lecture approaches when teaching history education lessons. Teachers noted: “huge class sizes and low time allotted to history subjects, making it difficult to apply participator/student-centred methods (BSSST3, SSST, and SSST2). Furthermore, when asked about their teachers’ teaching methods in history class, students stated that “teachers only use teacher-centred strategies (lecture, dictation, note-giving and reading notes on the blackboard)” (BSSSS3, SSSS1, SSSS2).

During the interview all interviewed teachers acknowledged the use of the lecture method in their teaching. The justifications provided for the use of the lecture method include saving time, the convenience of covering content on time and the nature of students. Teachers said, “A lecture method helps the teacher to cover a lot of content in a short period” (SSST1, SSST2, SSST3, SSST4, BSST1, and BSST2). The findings of this study are consistent with the findings of a study conducted by Luka [ 14 , p. 30] on the topic of “the impact of teaching methods on attitudes of secondary school students towards learning of history in Malawi,” which discovered that teachers use boring lecture methods to complete their courses rather than focusing on students' results.

History teachers' perceptions of the use of the participatory approach were very low. Based on the interview conducted with history education teachers they were not interested in using student-center teaching strategies (BSSST1, BSSST2, SSST1, SSST2, SSST3, and SSSST4). Teachers claimed that participatory teaching strategies were time-consuming and unsuitable for large-class settings ( Ibid ). Instead of using participatory teaching strategies teachers choose teacher-centred methods to cover a large portion within a given time.

The researchers interviewed history teachers at Sebeta secondary schools about the challenges that they confront when implementing the participatory approach. The interviewed teachers stated that the time allotted for history education did not correspond to the content (BSSST1, BSSST2, SSST1, SSST2, SSST3, and SSST4). They were unwilling to utilize student-centred teaching methodologies because they believed it would be time-consuming and difficult to cover the contents of the student’s textbooks within the academic year. According to the teachers, the time allotted to history education every week was only two periods (80 min), although history education included more than 246 pages ( Ibid ). Students also stated that teachers frequently employ lecture methods when teaching history lessons. Both teachers and students agree that collaborative learning methods are more beneficial than traditional teaching methods in improving students’ academic achievement (SSST1, SSST2, SSST3, SSST4, BSST1, and BSST2). Teachers claim that "due to the wide range of topics covered in history education, we use lecture methods of teaching rather than participatory approaches" (SSST1, SSST3, BSST1, and BSST2).

6.3 How is the student's academic achievement in history at Sebeta government secondary school? To answer this question, the researchers used document review

6.3.1 document analysis.

Document analysis is part of the qualitative data collection strategy that every researcher engages in throughout the research period. In this research researchers reviewed, history education students’ textbooks, published articles and roasters of students (students’ mark list). The history education achievement of 174 Sebeta government secondary school students scored in grade 9 in 2020/2021 was compared to look at their achievement in grade 10 in 2021/2022. As a result, one student achieved less than 50% out of 100%, 39 students’ scores ranged from 50 to 60 out of 100%, 98 students scored from 61 to 70 out of 100%, 27 students scored between 71 and 80 out of 100%, 8 students scored between 81 and 90 out of 100%, and 1 student scored between 91 and 100, in grade nine. In grade 10, 11 students scored below 50, 103 students scored between 50 and 60, 45 students scored between 61 and 70, 9 students scored between 71 and 80, 4 students scored between 81 and 90, and 2 students scored between 91 and 100 out of 100%.

Based on this analysis, we can witness students’ achievement in two ways. The first is that in grade 9, 138 out of 174 students scored less than 70% out of 100% and the results of students scoring from 70 to 100% declined significantly. The second point to mention is that student achievement in history education has been highly declining at the subsequent grade level. In Grade 10, the number of students scoring less than 50% grew, and 159 out of 174 students scored less than 70% in history education. This indicates students' achievement in history in grade 9 decreased in grade 10. This suggests that students' achievement in history education was inadequate. Following the analysis of student achievement, interviews were conducted with students and teachers to identify why students' achievement in history education was so low.

7 Conclusion and recommendations

Research shows that teaching strategies are a crucial aspect in successful learning because they enable learners to learn, create, and take a proactive attitude towards learning. The significant issues confronting history education have been identified were teaching strategy, a lack of awareness about implementing participatory teaching methods, a lack of comprehensiveness of the contents of history education teaching materials, and the issue of the bulkiness and scope of history education texts being covered on time and Lack of teachers’ understanding of employing creative teaching strategies to improve students’ academic progress. Despite this, the study found that teachers in Sebeta government secondary schools use the teacher-centered lecture approach rather than interactive or student-centered strategies, which are recommended for students' learning. Teachers were cognizant of student-center teaching and learning improved student achievement. Conversely, teachers are hesitant to adopt participatory teaching methodologies due to the vastness of history textbooks and the lack of time provided to history education to cover bulky texts. As a result, they employ teaching approaches that they believe will allow them to complete the history education contents in the allocated time rather than focusing on enhancing students' academic achievement.

Furthermore, the study also found out that teachers are reluctant to use participatory student-centred learning methods because the two periods per week allocated (80 min) to teaching history education are not enough to cover a wide range of history education content. They believe participatory student-center teaching is ineffective in large classrooms and takes more time than the lecture method. Such thinking stems from a lack of understanding (imparting knowledge) on the use of innovative teaching strategies. The researchers examined the lecture teaching approach that students had learned as well as their results. Several students' achievement in history education shows below 70% out of 100% at Sebeta government secondary schools. The main reason for this low achievement is the teachers’ teaching strategies (the use of teacher-centred approach) to teaching history education to complete a wide content within the allotted time. Teachers do not consider which strategies could improve students’ achievement rather than focus on completing their content. This has also resulted in students’ negative attitudes towards the subject.

The outcomes of this study can serve as the foundation for future research in academic and professional studies. This discovery is notable for the fact that teaching and learning approaches influence students' academic achievement in both directions. Accordingly, if teachers only employ the lecture approach without involving students in the lesson, it may result in low student academic achievement in contrast if teachers employ student-centred strategies students can understand the main point of the lesson and enhance the academic achievement of students.

Thus, for future studies intervention exprimental research in history education is required to measure the extent to which participatory methods of instruction increase the academic achievement of students over teacher-centred strategies. More research, according to the researchers, should be conducted using participatory teaching methods in one classroom and lecture methods in others to determine to what extent participatory teaching methods improve the academic achievement of students when compared to teacher-centred strategies. Following the findings, researchers provided the following recommendations: national and regional education experts should collaborate closely in making history education content inclusive, as well as training history education teachers in the use of participatory teaching approaches. Curriculum experts should effectively organize the breadth of history education contents. To ensure that students learn successfully, the relevant authorities should rigorously monitor the state of the teaching and learning processes in general and history education in particular.

Data availability

The data of this study is the primary source, which is the roster of students' results and education policies. The student results/ marks analyzed for this study are from two Sebeta town public secondary schools: Sebeta secondary school and Burka Sebeta secondary school and Ethiopian education policies. So, the data are available from the corresponding author upon reasonable request from anyone.

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Corresponding Author of the article: Fekede Sileshi Fufa. Abera Husen (PhD, Assistant Professor). Ketebo Abdiyo (PhD, Associate Professor). Authors’ contribution statements 1. Initially, Fekede Sileshi convinced Abera Husen and Ketebo Abdiyo as the study should be conducted. 2. Then, Abera Husen devised the study's theory. 3. Fekede Sileshi and Ketebo Abdiyo verified the analytical methods of the study. 4. Abera Husen encouraged Fekede Sileshi to investigate the study. 5. Ketebo Abdiyo supervised the overall findings of this work.

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Fufa, F.S., Tulu, A.H. & Ensene, K.A. Exploring the significant problems confronting secondary schools history education: a baseline study. Discov Educ 3 , 52 (2024). https://doi.org/10.1007/s44217-024-00132-8

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Received : 05 August 2023

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DOI : https://doi.org/10.1007/s44217-024-00132-8

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