Subject Resources – Primary Mathematics

• The National Centre for Excellence in the Teaching of Mathematics
• Association of Teachers of Mathematics
• Mathematical Association
• National Association of Mathematics Advisers
• The Association of Mathematics Education Teachers

• White Rose Maths

Resources and schemes of work from White Rose Maths are popular in primary schools all over the country. It may be worthwhile asking if trainee teachers are using White Rose Maths at their placement schools. If so, critically exploring their resources could be beneficial.

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• Third Space Learning

Third Space Learning is a mathematics intervention programme used by an increasing number of primary and secondary schools. However, their website also contains a series of excellent blogs written for teachers by teachers. Encouraging trainee teachers to read these blog posts is a simple, free way of ensuring they stay up-to-date with evidence-informed approaches in mathematics. I cannot recommend this website enough.

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• Cambridge Maths Espresso

Every two months Cambridge Mathematics produces an espresso, a “small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind.” Each espresso is one double-sided A4 page which synthesises the latest research on a chosen debate within mathematics. Their succinct writing and excellent use of infographics make these 'espressos’ suitable for trainee teachers.

Education Endowment Foundation (EEF) Guidance Reports

The EEF has produced two superb guidance reports on the teaching of mathematics. Each report comes with at least five recommendations as well as a summary poster. The recommendations (e.g., dedicate time for children to learn and integrate mathematics throughout the day) can also provoke  useful discussion amongst trainee teachers.

• Improving Mathematics in the Early Years and Key Stage 1 (2020) 
• Improving Mathematics in Key Stages 2 and 3 (2017)

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Literature and Research on Maths Anxiety

There is a growing body of research that recognises not only the existence of maths anxiety, but its prevalence amongst children, the general public and even primary teachers. This is a discussion that cannot be avoided and lends itself nicely to developing critically reflective teachers.

Jackson, E. (2008) ‘Mathematics Anxiety in Student Teachers’, Practitioner Research in Higher Education, 2 (1), pp. 36-42.

• This research considers the mathematics experiences of trainee primary teachers in their training year.
• Recommendations for ITE providers are not given but this paper gives a clear overview of the issues trainee teachers may be having.

Wicks, K. (2021) Tackling Anxiety in Primary Mathematics Teachers. Critical Publishing: St Albans

• This book is a useful starting point to consider how to approach the issue of maths anxiety with teachers of primary mathematics.
• It also encourages those in ITE to critically reflect on their own pedagogical approaches to primary mathematics.

Carey, E. et al (2019) Understanding Mathematics Anxiety: investigating the experiences of UK primary and secondary school students, Nuffield Foundation. 

• Another short, useful report that investigates children’s experiences of maths when they were at school.
• Again, potentially useful as a reflective discussion to approach the issue of maths anxiety.

Cambridge Mathematics (2017) ‘Maths anxiety’ Espresso, (6). 

• A wonderful ‘espresso’ which synthesises the available research as well as providing clear steps for all teachers of mathematics.

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A ‘Mastery’ Approach to Teaching Mathematics

National Association of Mathematics Advisers (2015) Five Myths of Mastery in Mathematics. 

• An important reading that explores the myths of a mastery approach and highlights how poorly the term is understood.
• Particularly useful to explore with trainee teachers after they have had some experience observing maths lessons in their placement schools.

Cambridge Mathematics (2017) ‘Mastery in mathematics’ Espresso, (16)

• A concise summary of the research, and even history, which underpins a mastery approach.

McCourt, M. (2019) Teaching for Mastery. John Catt Educational: Woodbridge

• This book is a useful dive into the theory and history of teaching for mastery.
• Probably not suitable for trainee teachers but it’s a fascinating read for any primary maths teacher or teacher educator.

NRICH (2019) Creating a Low Threshold High Ceiling Classroom. 

• ‘Low threshold high ceiling’ approaches to mathematics are often seen as a key feature of a mastery approach.
• This article from NRICH explores the theoretical links as well as giving some concrete examples.

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Instrumental v. Relational Understanding in Mathematics

Skemp, R. (1976) ‘Relational understanding and instrumental understanding.’ Mathematics Teaching, (77) pp. 20-26. 

• A must-read article for all primary trainee teachers.
• It is short, accessible and will provoke initial discussions around the difference between understanding something conceptually and understanding something procedurally.
• A useful article to read before trainee teachers reflect on their own experiences of being taught mathematics when they were at school.

Fitzmaurice, O. (2014) ‘‘Ours is not to reason why, just invert and multiply’: an insight into Irish prospective secondary teachers' conceptual understanding of the division of fractions’, Irish Educational Studies, 33 (4), pp. 467–488. 

• A fascinating article for all maths teacher educators.
• The article uses the division of fractions as a lens through which to explore limitations of maths ITE programmes.
• It gives clear implications for maths teacher educators, with clear parallels to Skemp’s earlier work on relational / instrumental understanding.

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Social Justice and Racial Justice in Mathematics

Wright, P. (2016) ‘Social justice in the mathematics classroom’, London Review of Education, 14 (2), pp. 104-118. 

• This research paper explores how traditional approaches to teaching mathematics can perpetuate inequities and injustices in society.

NRICH (2015) Mastering Mathematics and the New Curriculum

• This article is a summary of a conference address.
• It explores how a mastery approach to mathematics is, ultimately, a social justice issue as we aim to shift from talking about ‘able’ children to ‘enabling’ children.

Marks, R. (2013) ‘“The Blue Table Means You Don't Have a Clue”: the persistence of fixed-ability thinking and practices in primary mathematics in English schools.' FORUM, 55(1) pp. 31-44. 

• A useful article to critically explore ability grouping in primary schools.
• Links to social justice can be made, as well as using this article to encourage trainee teachers to critically reflect on their own experiences at school and their experiences on their placements.

Cambridge Mathematics (2020) ‘Racial equity in mathematics education’ Espresso, (33)

• This espresso explores how the discipline of mathematics is not necessarily ‘gender-neutral, colour-blind, and culture-free'
• It also explores how mathematics classrooms can be highly racialised spaces and gives suggestions as to how teachers can resist dominant deficit narratives.

Cambridge Mathematics (2019) ‘EAL students in mathematics classrooms’ Espresso, (26)

• This espresso explores the difficulties that EAL students may face in mathematics classrooms, as well as concrete strategies that teachers could take.

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Cognitive Science in Mathematics

Willingham, D. T. (2009) ‘Is it true that some people just can’t do math?’ American Educator, Winter 2009-2010 pp. 14-19, 39.

• This journal article, written by renowned cognitive scientist Daniel Willingham, argues that the vast majority of people are capable of learning mathematics to a good level.

Sealy, C. (2020) Cognitive Load Theory in the Primary Classroom. 

• This is a series of six blog posts which were inspired by Craig Barton’s ‘How I Wish I’d Taught Maths’ podcasts.
• Sealy offers a primary perspective on what Cognitive Load Theory looks like for primary teachers. All points will tie in nicely to wider pedagogical approaches in cognitive science, such as Rosenshine’s (2012) Principles of Instruction.

Cambridge Mathematics (2017) ‘Working memory for mathematics learning’ Espresso, (10)

• Another useful synthesis of the research available on working memory, including how differences in mathematics outcomes can often be explained by differences in working memory capacity.

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The Early Years Foundation Stage (EYFS)

Haylock, D. and Cockburn, A. (2017) Understanding Mathematics for Young Children. SAGE: London

• A useful starting point for primary trainee teachers. This book may be beneficial as pre-course reading.

Williams, H. J. (2020) ‘Mathematics in the Early Years: What matters?’ Impact, special issue: cognition and learning (8, Spring 2020) pp. 32-35.

• Brilliant article from the Chartered College’s Impact magazine. Raises some fascinating questions for trainee primary teachers or those new to EYFS.
• The section on how numbers differ to quantities is articulated brilliantly. Crucial reading for all primary trainee teachers.

Carpenter, S. (2021) Early Learning Goals: Subitising Numbers. 

• With the new EYFS framework focusing heavily on subitising, this article explores what subitising is, why it’s so important, and common errors that adults often make.

Cambridge Mathematics (2021) ‘The number line’ Espresso, (35) 

• This espresso explores all that is pedagogically brilliant about number lines, including the crucial differences between number lines and number tracks and why this is so important for Early Years practitioners.

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Fluency, Number Bonds and Multiplication Tables

Joint ATM & MA Primary Group (2021) The Teaching and Learning of Multiplication Bonds: a Position Statement. 

• A useful three-page statement which argues how mathematics is still a subject focused on thinking, and not memorising.

Cambridge Mathematics (2017) ‘Learning and assessing times tables’ Espresso, (1) 

• This espresso synthesis the research on learning multiplication tables.
• It also includes a useful infographic which may prompt reflective discussions around trainee teachers’ own experiences of learning times tables.

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The Teaching of Problem Solving

Foster, C. (2019) The fundamental problem with teaching problem solving.

• Fascinating three-page article on the teaching of problem solving.
• Foster shines a light on, what he argues, is poor teaching practice.
• Useful as a discussion point with trainee teachers after they have had some experience of teaching or observing maths on their placements.

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Misconceptions and Variation Theory

Hansen, A. (2020) Children's Errors in Mathematics. (5th edition). London: Learning Matters.

• This book is useful for trainee teachers to understand the importance of pre-empting and anticipating common misconceptions.
• This book works well alongside introducing Variation Theory, particularly the concept of examples and non-examples.

Almond, N. (2021) What is Variation Theory?

• A useful, concise introduction to Variation Theory, focusing on conceptual variation and procedural variation.

Clear links can be made to the importance of pre-empting misconceptions and a mastery approach to teaching mathematics.

Times Tables in 10 Minutes

• Jill Mansergh, from Bath Spa University, teaches a group of trainee teachers how to use a counting stick to learn the 17 times tables.
• Poses some interesting questions regarding how fluency can be developed in the maths classroom

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Five Principles of Extraordinary Math[s] Teaching: 

• TED Talk from Dan Finkel. It is both interesting and relevant to anyone involved in primary education.

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• The Ofsted Subject Report (2021) on mathematics can be found by clicking here.

It is important to also recognise that Ofsted’s latest ITE framework highlights the importance of a “critical introduction to key educational […] debates within the trainees’ specialist subject(s) and/or phase(s)”. In order to promote further debate, analysis and thinking, responses to the Ofsted Subject Report have been considered below:

• Art Curriculum Plus
• Third Space Learning