Evidence-based maths pedagogy for primary and secondary teachers. Covers mastery approaches, concrete-pictorial-abstract, mathematical reasoning, and the research behind effective mathematics teaching strategies.
Here's the article:Maths pedagogy is constantly evolving, and as educators, staying abreast of evidence-based approaches is crucial for fostering a deep understanding and appreciation of mathematics in our students. According to Hattie (2009), the effect size of teacher clarity on student achievement is d = 0.75, highlighting the significant impact of how we present and explain mathematical concepts. This article explores several effective pedagogical strategies grounded in research, offering practical applications for teachers in the classroom. For further guidance, see our article on science pedagogy.
Conceptual understanding is the cornerstone of effective maths education. It moves beyond simply memorising procedures to grasping the underlying principles and connections within mathematical concepts (Skemp, 1976). When students understand the 'why' behind a mathematical rule, they are better equipped to apply it in novel situations and build a stronger foundation for future learning.
In the classroom, this translates to a shift from teacher-led demonstrations of algorithms to student-centred explorations of mathematical ideas. For example, when teaching fractions, instead of immediately introducing the rule for adding fractions with different denominators, use concrete manipulatives like fraction bars or Cuisenaire rods to allow students to visually explore the concept of finding a common denominator.
Cognitive Load Theory (CLT) posits that our working memory has limited capacity, and learning is optimised when we minimise extraneous cognitive load (unnecessary information) and maximise germane cognitive load (effortful thinking related to the learning material) (Sweller, 1988). By understanding how students process information, teachers can design lessons that are both engaging and effective.
A practical application of CLT involves simplifying problem presentations. Avoid cluttered worksheets or overly complex instructions. Break down complex problems into smaller, manageable steps and provide clear, concise explanations. Use worked examples strategically, focusing on one specific skill or concept at a time, and gradually increasing the level of difficulty. The EEF's Metacognition and Self-Regulated Learning guidance report advocates for teaching students strategies to manage their own cognitive load (EEF, 2018).
Spaced practice involves distributing learning over time, rather than cramming information into a single session. Retrieval practice, on the other hand, is the act of actively recalling information from memory (Brown, Roediger III, & McDaniel, 2014). Combining these two strategies is a powerful way to enhance long-term retention.
Implement regular, low-stakes quizzes or mini-tests that require students to retrieve previously learned information. Integrate spaced repetition software or flashcard apps into your lessons to help students review key concepts at increasing intervals. For example, after teaching a unit on multiplication, revisit it briefly in subsequent lessons through quick recall activities or problem-solving tasks. This helps to solidify understanding and prevent forgetting.
Encouraging students to talk about maths is a vital component of effective pedagogy. Mathematical discourse involves students explaining their reasoning, justifying their solutions, and challenging each other's ideas (NCTM, 2014). This fosters deeper understanding, promotes critical thinking, and develops communication skills.
Create a classroom environment where students feel safe to share their thinking, even if it's incorrect. Use sentence starters to guide discussions, such as "I agree with… because…" or "I disagree with… because…". Pose open-ended questions that require students to elaborate on their reasoning. For instance, instead of asking "What is the answer?", ask "How did you arrive at your answer?" or "Can you explain your strategy?".
Feedback is a crucial element of the learning process. Effective feedback is specific, actionable, and focuses on the process rather than just the answer (Hattie & Timperley, 2007). It provides students with clear guidance on how to improve their understanding and skills.
Provide feedback that is timely and directly related to the learning objective. Instead of simply marking answers as correct or incorrect, provide specific comments on the student's reasoning and problem-solving strategies. Use sentence starters like "You're on the right track because…" or "Consider using… to solve this problem." Encourage self-reflection by asking students to identify their own strengths and areas for improvement. The EEF's guidance report on feedback emphasises that effective feedback should be focused on the task, the process, or self-regulation (EEF, 2021).
Students learn in different ways, and using a variety of representations is essential for catering to diverse learning styles. The concrete-pictorial-abstract (CPA) approach, also known as the concrete-representational-abstract (CRA) approach, involves introducing concepts using concrete manipulatives, then transitioning to pictorial representations, and finally moving to abstract symbols (Bruner, 1966).
When introducing a new concept, start with concrete materials like base-ten blocks, counters, or fraction bars. Then, move to pictorial representations such as drawings, diagrams, or number lines. Finally, introduce abstract symbols like equations and formulas. For example, when teaching addition, students could first use counters to physically combine groups, then draw pictures to represent the addition, and finally write the corresponding equation. This multi-sensory approach helps students develop a deeper understanding of the concept.
Metacognition refers to the ability to think about one's own thinking. It involves awareness of one's own cognitive processes, such as planning, monitoring, and evaluating (Flavell, 1979). By teaching students metacognitive strategies, we can empower them to become more effective and independent learners.
Encourage students to reflect on their learning process by asking questions like "What strategies did you use to solve this problem?" or "What was challenging about this task, and how did you overcome it?". Teach students specific metacognitive strategies, such as self-questioning, summarising, and planning. Provide opportunities for students to practice these strategies in a variety of contexts. The EEF's Metacognition and Self-Regulated Learning guidance report offers practical strategies for developing students' metacognitive skills (EEF, 2018).
While the pedagogical approaches discussed above are supported by research, it's important to acknowledge their limitations. One common critique is the difficulty of implementing these strategies consistently in a classroom setting, especially with limited resources and time constraints. Furthermore, some research findings may not be universally applicable across all contexts or student populations. The effectiveness of any pedagogical approach depends on a variety of factors, including the teacher's expertise, the students' prior knowledge, and the specific learning environment.
It is also crucial to remember that research in education is often complex and nuanced. Over-reliance on effect sizes or simplistic interpretations of research findings can lead to misguided practices. Teachers should critically evaluate research evidence and adapt strategies to suit the unique needs of their students. Continuously reflecting on one's own practice and seeking feedback from colleagues are essential for professional growth.
Evidence-based maths pedagogy is not a static set of rules, but rather a dynamic process of continuous learning and improvement. By embracing research-informed strategies and adapting them to their own unique contexts, teachers can create engaging and effective learning environments that foster a deep understanding and appreciation of mathematics in all students.
Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick: The science of successful learning. Belknap Press.
Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.
Education Endowment Foundation (EEF). (2018). Metacognition and self-regulated learning: Guidance report. EEF.
Education Endowment Foundation (EEF). (2021). Effective professional development. EEF.
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285.
These peer-reviewed studies provide the research foundation for the strategies discussed in this article:
Cognitive, Motivational, and Pedagogical Factors Influencing Effective Teaching and Learning in Math Education View study ↗
Gopal Bc (2025)
This action research explores how specific teaching methods can improve the learning of trigonometry for education students. The study aims to address common student difficulties such as confusion and lack of engagement, ultimately improving their performance. This research is valuable for teachers looking for practical ways to make trigonometry more accessible and engaging for their students, potentially leading to better understanding and results.
Innovative Strategies in Math Education: The Impact of PBL and TaRL on Concept Mastery and Classroom Dynamics View study ↗
6 citations
Sriyanti Mustafa et al. (2024)
This study investigates the combined effects of Problem-Based Learning (PBL) and Teaching at the Right Level (TaRL) on mathematics learning, focusing not only on academic results but also on classroom interactions and student engagement. It highlights how these methods impact the dynamics between students and teachers, as well as student participation. Teachers can use this research to understand how PBL and TaRL can create a more interactive and effective learning environment, going beyond just improving test scores.
Innovative Mathematics Pedagogy: Evidence-Based Strategies for Enhancing Student Learning View study ↗
W. C. Tang (2025)
This review examines modern trends in maths education, focusing on student-centred approaches, technology integration, and addressing maths anxiety. It highlights the importance of active learning, personalised technology use, and psychological strategies in the classroom. This is important for teachers who want to move away from traditional methods and create a more engaging and supportive learning environment that caters to individual student needs and reduces anxiety.
Here's the article:Maths pedagogy is constantly evolving, and as educators, staying abreast of evidence-based approaches is crucial for fostering a deep understanding and appreciation of mathematics in our students. According to Hattie (2009), the effect size of teacher clarity on student achievement is d = 0.75, highlighting the significant impact of how we present and explain mathematical concepts. This article explores several effective pedagogical strategies grounded in research, offering practical applications for teachers in the classroom. For further guidance, see our article on science pedagogy.
Conceptual understanding is the cornerstone of effective maths education. It moves beyond simply memorising procedures to grasping the underlying principles and connections within mathematical concepts (Skemp, 1976). When students understand the 'why' behind a mathematical rule, they are better equipped to apply it in novel situations and build a stronger foundation for future learning.
In the classroom, this translates to a shift from teacher-led demonstrations of algorithms to student-centred explorations of mathematical ideas. For example, when teaching fractions, instead of immediately introducing the rule for adding fractions with different denominators, use concrete manipulatives like fraction bars or Cuisenaire rods to allow students to visually explore the concept of finding a common denominator.
Cognitive Load Theory (CLT) posits that our working memory has limited capacity, and learning is optimised when we minimise extraneous cognitive load (unnecessary information) and maximise germane cognitive load (effortful thinking related to the learning material) (Sweller, 1988). By understanding how students process information, teachers can design lessons that are both engaging and effective.
A practical application of CLT involves simplifying problem presentations. Avoid cluttered worksheets or overly complex instructions. Break down complex problems into smaller, manageable steps and provide clear, concise explanations. Use worked examples strategically, focusing on one specific skill or concept at a time, and gradually increasing the level of difficulty. The EEF's Metacognition and Self-Regulated Learning guidance report advocates for teaching students strategies to manage their own cognitive load (EEF, 2018).
Spaced practice involves distributing learning over time, rather than cramming information into a single session. Retrieval practice, on the other hand, is the act of actively recalling information from memory (Brown, Roediger III, & McDaniel, 2014). Combining these two strategies is a powerful way to enhance long-term retention.
Implement regular, low-stakes quizzes or mini-tests that require students to retrieve previously learned information. Integrate spaced repetition software or flashcard apps into your lessons to help students review key concepts at increasing intervals. For example, after teaching a unit on multiplication, revisit it briefly in subsequent lessons through quick recall activities or problem-solving tasks. This helps to solidify understanding and prevent forgetting.
Encouraging students to talk about maths is a vital component of effective pedagogy. Mathematical discourse involves students explaining their reasoning, justifying their solutions, and challenging each other's ideas (NCTM, 2014). This fosters deeper understanding, promotes critical thinking, and develops communication skills.
Create a classroom environment where students feel safe to share their thinking, even if it's incorrect. Use sentence starters to guide discussions, such as "I agree with… because…" or "I disagree with… because…". Pose open-ended questions that require students to elaborate on their reasoning. For instance, instead of asking "What is the answer?", ask "How did you arrive at your answer?" or "Can you explain your strategy?".
Feedback is a crucial element of the learning process. Effective feedback is specific, actionable, and focuses on the process rather than just the answer (Hattie & Timperley, 2007). It provides students with clear guidance on how to improve their understanding and skills.
Provide feedback that is timely and directly related to the learning objective. Instead of simply marking answers as correct or incorrect, provide specific comments on the student's reasoning and problem-solving strategies. Use sentence starters like "You're on the right track because…" or "Consider using… to solve this problem." Encourage self-reflection by asking students to identify their own strengths and areas for improvement. The EEF's guidance report on feedback emphasises that effective feedback should be focused on the task, the process, or self-regulation (EEF, 2021).
Students learn in different ways, and using a variety of representations is essential for catering to diverse learning styles. The concrete-pictorial-abstract (CPA) approach, also known as the concrete-representational-abstract (CRA) approach, involves introducing concepts using concrete manipulatives, then transitioning to pictorial representations, and finally moving to abstract symbols (Bruner, 1966).
When introducing a new concept, start with concrete materials like base-ten blocks, counters, or fraction bars. Then, move to pictorial representations such as drawings, diagrams, or number lines. Finally, introduce abstract symbols like equations and formulas. For example, when teaching addition, students could first use counters to physically combine groups, then draw pictures to represent the addition, and finally write the corresponding equation. This multi-sensory approach helps students develop a deeper understanding of the concept.
Metacognition refers to the ability to think about one's own thinking. It involves awareness of one's own cognitive processes, such as planning, monitoring, and evaluating (Flavell, 1979). By teaching students metacognitive strategies, we can empower them to become more effective and independent learners.
Encourage students to reflect on their learning process by asking questions like "What strategies did you use to solve this problem?" or "What was challenging about this task, and how did you overcome it?". Teach students specific metacognitive strategies, such as self-questioning, summarising, and planning. Provide opportunities for students to practice these strategies in a variety of contexts. The EEF's Metacognition and Self-Regulated Learning guidance report offers practical strategies for developing students' metacognitive skills (EEF, 2018).
While the pedagogical approaches discussed above are supported by research, it's important to acknowledge their limitations. One common critique is the difficulty of implementing these strategies consistently in a classroom setting, especially with limited resources and time constraints. Furthermore, some research findings may not be universally applicable across all contexts or student populations. The effectiveness of any pedagogical approach depends on a variety of factors, including the teacher's expertise, the students' prior knowledge, and the specific learning environment.
It is also crucial to remember that research in education is often complex and nuanced. Over-reliance on effect sizes or simplistic interpretations of research findings can lead to misguided practices. Teachers should critically evaluate research evidence and adapt strategies to suit the unique needs of their students. Continuously reflecting on one's own practice and seeking feedback from colleagues are essential for professional growth.
Evidence-based maths pedagogy is not a static set of rules, but rather a dynamic process of continuous learning and improvement. By embracing research-informed strategies and adapting them to their own unique contexts, teachers can create engaging and effective learning environments that foster a deep understanding and appreciation of mathematics in all students.
Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick: The science of successful learning. Belknap Press.
Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.
Education Endowment Foundation (EEF). (2018). Metacognition and self-regulated learning: Guidance report. EEF.
Education Endowment Foundation (EEF). (2021). Effective professional development. EEF.
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285.
These peer-reviewed studies provide the research foundation for the strategies discussed in this article:
Cognitive, Motivational, and Pedagogical Factors Influencing Effective Teaching and Learning in Math Education View study ↗
Gopal Bc (2025)
This action research explores how specific teaching methods can improve the learning of trigonometry for education students. The study aims to address common student difficulties such as confusion and lack of engagement, ultimately improving their performance. This research is valuable for teachers looking for practical ways to make trigonometry more accessible and engaging for their students, potentially leading to better understanding and results.
Innovative Strategies in Math Education: The Impact of PBL and TaRL on Concept Mastery and Classroom Dynamics View study ↗
6 citations
Sriyanti Mustafa et al. (2024)
This study investigates the combined effects of Problem-Based Learning (PBL) and Teaching at the Right Level (TaRL) on mathematics learning, focusing not only on academic results but also on classroom interactions and student engagement. It highlights how these methods impact the dynamics between students and teachers, as well as student participation. Teachers can use this research to understand how PBL and TaRL can create a more interactive and effective learning environment, going beyond just improving test scores.
Innovative Mathematics Pedagogy: Evidence-Based Strategies for Enhancing Student Learning View study ↗
W. C. Tang (2025)
This review examines modern trends in maths education, focusing on student-centred approaches, technology integration, and addressing maths anxiety. It highlights the importance of active learning, personalised technology use, and psychological strategies in the classroom. This is important for teachers who want to move away from traditional methods and create a more engaging and supportive learning environment that caters to individual student needs and reduces anxiety.
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