Content
Lonneke Boels
HU University of Applied Sciences Utrecht
Although numerous studies have examined how students interpret individual graph types, research remains fragmented, lacking a coherent instructional theory on how to develop students’ understanding of distribution. This paper addresses: How can students be supported in moving from case-based to distributional reasoning when interpreting statistical graphs? In response, a local instruction theory is proposed that articulates a progression of graph types—from case-value plots through dotplots to histograms and boxplots—aimed at bridging the conceptual gap between case-based and aggregated representations. This proposal is informed by eye-tracking and statistics education research showing that many students struggle to understand data aggregation in histograms and boxplots. The paper outlines implications for teaching materials aiming to foster distributional thinking across school levels.
Nicola Bretscher1, Jill Adler2,1, Piers Saunders1, Suman Ghosh1
1University College London, 2University of Witwatersrand
We explore how university tutors use a framework for teaching mathematics when providing feedback to pre-service teachers after observing them teach a lesson in school. A framework for teaching mathematics was introduced into university-taught sessions of our initial teacher education programme for secondary mathematics. The purpose of introducing such a framework was to make more transparent elements of mathematics teaching which the tutor team believe, based on our understanding of mathematics education research, are central to improving the quality of pre-service teachers’ instructional practices. Drawing on notions of situated abstraction and transparency, we analyse two telling cases, selected to illuminate when and how tutors use elements of the framework in providing lesson observation feedback. We discuss our initial findings and implications.
Stephen Butterfield
Birmingham City University
Foetal Alcohol Spectrum Disorders (FASD) is a disability caused by alcohol consumption during pregnancy. Neuroscience shows that the teratogenic effects of alcohol on the brain in utero significantly affect the parietal lobe, which is the brain’s centre for numeracy and mathematical calculation. Although there has been some progress in educating children with FASD, very little appears to have been conducted in the UK on access to the maths curriculum for pupils with FASD, especially at KS3 and KS4. FASD is not a condition recorded at birth, so the actual number of affected pupils remains unknown. Studies suggest it could impact around 3% of the school population. It is one of several complex needs and falls within the Special Educational Needs and Disabilities (SEND) spectrum. Although the condition is neurologically based, my focus remains on teaching and learning. My research will aim to identify effective approaches used by teachers.
Dédé de Haan1,2, Gerrit Roorda3,2, Siebrich de Vries2,3, Paul Drijvers1
1Utrecht University, 2NHLStenden University of Applied Sciences, 3University of Groningen
Measuring Mathematical Knowledge for Teaching (MKT) through open-response items proves challenging, with studies reporting variability in reliability and unclear subdomain boundaries. We illustrate this through the development of a 19-item test assessing three MKT subdomains – Specialized Content Knowledge (SCK), Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT) – for Dutch pre-service teachers. Despite careful validation, the instrument demonstrated low internal consistency across subdomains (standardized a=.36-.42). Examining two KCT items revealed two construct-dependent challenges. One item achieved high inter-rater reliability (ICC=.890) yet confounded SCK/KCT constructs, as indicated by qualitative analysis. The other item showed lower inter-rater reliability (ICC=.524); resolving this through strict conceptual scoring criteria revealed pre-service teachers predominantly provide procedural explanations, causing restricted variance and contributing to low internal consistency across the KCT subdomain. These findings suggest that achieving both theoretical purity and internal consistency may be difficult when participants demonstrate predominantly procedural knowledge.
Prompt Refinement in Calculus: Using Generative AI to Create Isomorphic Related Rates Problems
Barry J. Griffiths1, Heather A. Edwards1, Zhongzhou Chen1, Katiuscia C.B. Teixeira2
1University of Central Florida, 2Oklahoma State University
In this article, we explore the possibility of integrating generative artificial intelligence (AI) technology into calculus instruction, specifically focusing on the automated creation of isomorphic related rates problems in a way that can be used in asynchronous testing for large classes. Our approach leverages large language models (LLMs) to construct diverse, pedagogically relevant problems, tailored to the demands of institutions where a common test, or a small number of test versions, is no longer feasible. By entering and reiterating the desired parameters, generative AI is used to create an arbitrary number of both generic and isomorphic questions, complete with solutions. With the more general goal being to use AI technology to aid teachers in generating problems that cater to individuals with different learning trajectories, this preliminary study demonstrates the feasibility of using LLMs to create a flexible testing scheme that offers a scalable solution to the challenge of providing large numbers of students with varied and engaging problems.
Holly Heshmati1, Yuqian (Linda) Wang2, Patrick Barmby3 and Wenping Zhang4
1University of Warwick, 2University of Durham, 3No More Marking, 4Zhejiang International Studies University
This study investigates secondary pre-service teachers’ Mathematical Knowledge for Teaching (MKT) in the context of Teaching for Mastery (TfM). Participants (50 PGCE Secondary Mathematics trainees) were asked to describe their understanding of TfM through mind-maps and reflective open-ended questions. Data were analysed using the MKT framework and evaluated via comparative judgement. Analysis of 229 coded instances revealed strong Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), alongside notable improvement in Knowledge of Content and Students (KCS). Questionnaire responses indicated that engaging in comparative judgement supported trainees in moving beyond procedural interpretations of mastery, fostering deeper understanding of curriculum coherence, variation, and structure. The findings demonstrate that the MKT framework provides a robust lens for interpreting teacher knowledge, while comparative judgement functions as assessment-as-learning, supporting the conceptual development and refinement of emerging professional knowledge among novice mathematics teachers.
Chang Jiang
University of Cambridge
This feminist poststructuralist inquiry explores how gendered discourses within Chinese Lesson Study (CLS) shape female mathematics teachers’ subjectivities, as the latter confront contradictory demands: proving mathematical competence in a masculinized discipline while performing feminine deference to predominantly male Teaching Research Staff (TRS). The study addresses three questions: What are female mathematics teachers’ experiences of CLS? How do gendered discourses and power relations shape their subjectivities? What spaces for resistance exist? Using feminist poststructuralist discourse analysis (FPDA), I examine how teachers position themselves within competing discourses and trace moments where they reproduce, negotiate, or resist available subject positions. Data include two semi-structured interviews with 12–16 female teachers across China and written reflections after CLS sessions. The research contributes to understanding how collaborative teacher development may unintentionally reproduce gender inequalities, with implications for creating more equitable professional development approaches in mathematics education in China.
Emily Macmillan
University of Oxford
This paper describes an intervention designed to influence student teachers’ pedagogical choices when teaching negative number arithmetic. Secondary mathematics student teachers were asked to script imaginary classroom conversations before and after discussing a range of contrasting representations for negative numbers. The scripts showed variation in the critical evaluation of the representations and the connections student teachers made to the underlying mathematical structures within, and beyond, negative number arithmetic. I describe here three of the representations explored in the intervention and examine their role in developing understanding of curriculum-wide structures.
Using TIMSS items to develop mathematics with meaning – but whose meaning matters?
Rachel Marks and Jennie Golding
UCL Institute of Education
We report on an exploration of how we might repurpose TIMSS assessment items for classroom use to promote meaningful mathematical engagement. During this work, we uncovered a tension between pupils’ and teachers’ beliefs about the purposes of mathematics learning, leading to some unexpected outcomes. Working with Year 5 and Year 9 teachers and pupils in England, we selected and adapted TIMSS tasks for integration into regular lessons and collated data from classroom observations, pupil dialogue, and teacher interviews. Thematic analysis, identifying patterns in engagement and value orientations, indicated that pupils often approached tasks through procedural lenses, prioritising correctness and assessment-related practices, whereas teachers sought to foster reasoning and process-focused learning. This misalignment of priorities sometimes led to counterproductive engagement, highlighting tensions between policy-driven assessment cultures and aspirations for mathematics with meaning.
See, Hear! Exploring pattern understanding in music and mathematics
Sarah McCarthy1 , Adam Ockelford1, Sue Gifford1, Helen Thouless2 and Sharon Kirk3
1University of Roehampton, 2St. Mary’s University, 3West Hill School
This co-designed exploratory study sought to test a theoretical taxonomy of visuo-spatial pattern understanding, mapped from the Sounds of Intent framework of musical development. Researchers developed classroom-appropriate pattern games that progressed in complexity. The games were played using objects or sounds or both together. Participants (N = 20) in a primary special school in England completed up to five sessions with a researcher or practitioner. Children’s engagement and progress were videoed, then analysed using an adapted musical assessment. Findings indicated that children recognised patterns across musical and spatial domains, with the strongest benefits arising when games combined sounds and visuo-spatial elements. Early evidence suggests that the taxonomy and games are a useful tool for practitioners seeking to support children’s understanding in mathematics and music. Future, larger-scale experimental work is needed to evidence the effectiveness of integrated pattern making in improving children’s mathematical and musical understanding.
Sam Parkes
University of Reading
Whilst evaluation of primary mathematics teaching is a well-embedded element of school improvement practice, the perceptions and experiences of those involved are poorly represented and under-researched both empirically and theoretically. This study offers new empirical data on current evaluation processes in primary mathematics. It also offers a new theorisation of the evaluation of primary mathematics teaching through its use of a conceptual framework focusing on professional development, professional knowledge, and professional identity. Key findings highlighted inconsistencies of perception and experience in relation to effective mathematics teaching, knowledge of primary mathematics and evaluation processes, and clarity of purpose and ownership of evaluations. These variations support the conclusion that there is a need for fairer, more coherent, and more useful evaluation processes of primary mathematics teaching and a new model for the provision of these based on mutual engagement, joint enterprise and a shared repertoire of tools is proposed.
Eleni Pepona
The Perse School Cambridge
Statistics and probability have a distinct literacy that students often find challenging to get to grips with. The type and level of rigorousness of language that is required in written communication is a hybrid of mathematical notation and natural language narrative. As such, students transitioning into A-level (pre-university) study of these topics often struggle to appreciate the need for and adapt their communication style accordingly. In this action research project, I investigated developing students’ literacy through literacy-focused instruction in studying an undergraduate textbook. An analysis and comparison of the class’s end of year assessment results to a baseline assessment task showed promising development in their literacy in this topic.
Giving meaning and comparing %: the case of the Mary & John task
Jérôme Proulx
Université du Québec à Montréal, Canada
This Research Report (RR) presents preliminary findings on a study about students’ ways of making sense of % through their engagements with tasks. Grade-8 students’ strategies for solving one comparison task are looked into, a modified version of Hart’s (1981) Mary & John task, as a way to investigate the meaning students give to the role of the referent-unit. Using the statistic vs. function uses of %, these preliminary findings insist on the rich variety of meanings and justifications students offer when comparing %, and how this variety depicts an enlarged view of what is to be considered adequate or not when comparing % situations.
Farhat Syyeda, Fay Baldry, Ben Harvey-Ashenhurst
University of Leicester
This paper forms part of an Action Research (AR) project conducted in the East Midlands region of England, involving women from low-income and under-served communities. The research aimed to explore the challenges women face in returning to education, and to support their engagement in adult learning through carefully crafted interventions such as interactive mathematics workshops. Whilst in the wider study, we collected data through two sets of focus group interviews with 34 participants, here we focus on workshop activities only. Collaborating with a local adult education college and two primary schools, we organised four workshops inviting children and their families to participate in playful mathematics learning using everyday objects such as coins, dry pasta, stationery items etc. The workshops were designed to present mathematics as fun, accessible, and inclusive, with the goal of breaking down barriers to education and promoting awareness of intergenerational and lifelong learning.