These abstracts are of research papers presented at the Day Conference on 7th March 2026 (online).
Content
01 Learning across phases: A collaborative approach to teaching fractions in Initial Teacher Education
Rosa Archer and Natalie Jayson
The University of Manchester
We report on how a collaborative event supported the development of pre-service teachers’ subject and pedagogical knowledge. The event brought together two cohorts: those training to teach pupils aged 11–18 (secondary) and those training to teach ages 5–11 (primary). They engaged in a joint pedagogical discussion focused on fractions. The aim was for secondary pre-service teachers to deepen their understanding of how younger pupils learn through exposure to practical, activity-based approaches. While secondary trainees contributed strong mathematical subject knowledge, primary trainees acted as experts in the effective use of practical activities, strengthening their own subject knowledge and confidence through collaboration with mathematics specialists. Data were collected via an online questionnaire. Findings suggest that the most significant gains arose from observing and reflecting on the trajectory of children’s mathematical development. Both cohorts reported positively on the value of collaborative learning.
02 Designing for invariance: A tool-fading geometric construction task supporting conceptual reasoning for beginning teachers.
Peter Kwamina Awortwe
University of Nottingham
Dynamic geometry environments (DGEs) enable learners to explore geometric relationships through construction and manipulation, particularly by identifying invariant properties under dragging. However, learners may rely on visual and technological affordances without developing deep conceptual understanding. This paper examines the design and implementation of a tool-fading geometric construction task for beginning teachers working collaboratively in a DGE. The task invites participants to construct and explore a configuration in which an angle bisector emerges as an invariant under dragging. The task design integrates pedagogical principles (scaffolding, collaboration, guided reflection, instrumental orchestration) with epistemic principles (invariance, structural generativity, and intentional tool fading). Through guided exploration and dialogic interaction, participants generate and test conjectures about invariant relationships. In a subsequent tool-fading phase, they reconstruct the angle bisector using only a straightedge, prompting a shift from tool-mediated exploration to structurally grounded reasoning. Analysis of on-screen video recordings, dialogue, and written reflections shows that dragging supports conjecture generation, while tool fading encourages justification and reconstruction, leading to deeper conceptual understanding. The study highlights how carefully sequenced task design can support transitions from exploratory interaction to conceptual reasoning in technology-enhanced geometry learning, with implications for teacher education and professional knowledge development.
03 Mathematical reasoning in problem-solving: Analysis of undergraduate mathematics students’ approaches to a problem
Irene Biza and Tim Rowland
School of Education and Lifelong Learning, University of East Anglia
The work presented in this paper was inspired by a flowerbed problem and Rowland’s (2009) reflection on how systematic exploration of particular cases led to the identification of common features, and the formulation of conjectures about the properties of all valid solutions. A similar problem was used with final-year undergraduate mathematics students enrolled in a mathematics education module led by Biza. Students were asked to solve the problem and reflect on their problem-solving approaches as part of a summative assessment. In this paper, we draw on literature on mathematical reasoning and Rowland’s reflections to discuss two students’ approaches to the problem. Preliminary analysis indicates points of interest in relation to students’ use (or non-use) of explorations, variations in their reasoning approaches (with attention to deductive/inductive reasoning), coherence (or lack of) in their reasoning, and variations in what students perceive to be a solution to the flowerbed problem.
04 Worked examples in open and commercial textbooks: Differences in learning opportunities
Serban Boghina, Francis Duah, and Boza Tasić
Toronto Metropolitan University
This study compares worked examples in open educational resources (OER) and commercial calculus textbooks, examining the learning opportunities they afford in terms of the level of cognitive demand, representation, type of response expected, and methods of solution validation. Examples from both resource types were systematically coded using a structured analytic framework, and chi-square tests of independence were conducted to examine associations between textbook type and each analytic category. Results reveal a statistically significant association between the levels of cognitive demand and textbook types. OER textbooks were more likely to include examples at higher levels of cognitive demand than commercial textbooks. Commercial textbooks present more procedurally oriented tasks than OER textbooks. Differences were also observed in representational diversity and the explicit validation of solutions. These findings contribute to ongoing debates about the pedagogical quality of open versus commercial textbooks, suggesting that textbook choice shapes students’ opportunities for mathematical engagement, with implications for task design and selection, as well as instructional decision-making.
05 Evaluating peer-assisted learning using simulated data: A propensity Score study
Juan David Cobo, Francis Duah, Boza Tasić.
Toronto Metropolitan University
Peer-assisted learning (PAL) is a widely used support strategy in post-secondary education, aimed at enhancing student success in challenging courses such as undergraduate mathematics. PAL involves collaborative learning facilitated by trained peers. Despite its popularity, observational studies evaluating PAL in mathematics education often lack rigour due to selection bias, unbalanced covariates, and unbalanced treatment assignments, hindering valid causal inference. This paper explores the use of Propensity Score Analysis (PSA) to estimate causal effects in observational studies. PSA balances covariates across treatment groups and reduces selection bias, enabling more reliable treatment effect estimates. We examine the effectiveness of PSA in evaluating PAL research using a simulated dataset based on an observational study of a post-secondary mathematics course, with the goal of estimating the impact of PAL participation on student grade performance and comparing PSA methods.
06 Mathematics anxiety, attitudes and performance in Hong Kong primary school children
Ann Dowker1 and Winifred Mark2
1University of Oxford, 2Hong Kong University
The study investigated mathematics performance and attitudes among first- and third-grade pupils in a Chinese-medium and an English-medium school in Hong Kong. The participants included 47 children in the Chinese-medium school (22 first-graders, 25 third-graders) and 43 children in an English-medium school (27 first-graders, 16 third-graders. They were given the Mathematics Attitude and Anxiety Questionnaire and the British Abilities Scales Basic Number Skills (BNS) test. The attitude questionnaire contains four scales: Self-rating, Liking for maths, Anxiety and Unhappiness at failure. Third-graders scored higher than first-graders on the BNS arithmetic test. They showed more Unhappiness at Failure (but no other attitude differences. Chinese-medium school pupils scored higher than English-medium school pupils on BNS. They showed more Anxiety and a lower Self-rating, but greater Liking for maths than the English-medium school pupils did. There were no School/ Grade interactions. All attitude variables correlated with one another, but none with BNS.
07 Do explicit learning outcomes help or hinder: Evidence from a small-scale experimental study in calculus.
Francis Duah
Toronto Metropolitan University
Sharing learning outcomes prior to instruction is commonly justified through constructive alignment and theories of self-regulated learning. Constructive alignment proposes that clearly articulated outcomes align teaching and assessment, while self-regulation research suggests that explicit goals support planning and monitoring. However, experimental evidence of their impact on undergraduate mathematics appears limited. This study reports a small-scale randomised experiment examining whether learning outcome prompts influence achievement on a calculus topic (sequences). Twenty-two participants were randomly assigned to a treatment group (n =12), who received notes with learning outcome prompts and were instructed to use them to guide their reading and understanding, or to a control group (n = 10), who received identical notes without outcomes and were instructed to read for understanding. Participants completed a 12-item quiz and a brief background survey. An independent-samples t-test showed that the treatment group (M = 9.33, SD = 3.42) scored lower than the control group (M = 11.60, SD = 4.55), though the difference was not statistically significant, t(20) = 1.34, p = .197. The effect size was moderate (d = 0.57). Given the small sample, the study was likely underpowered. Follow-up interviews with six students suggested that learning outcomes functioned as navigational tools. The findings complicate assumptions about learning outcome-sharing and raise questions about how students interpret and enact stated goals in university mathematics.
08 Sustainability in mathematical modelling competitions: An analysis of competition tasks
Arya Fu
Shanghai Experimental Foreign Language School
This study examines how sustainability is represented and made mathematically actionable in secondary-level modelling competition task statements. Using qualitative document analysis, we analysed 48 publicly available tasks (2020-2025) from two contexts: HiMCM (n=12) and SJMMA (n=36). Tasks were coded in three stages for sustainability salience, structural positioning, and dominant mathematical framing. Sustainability was salient in most HiMCM tasks, but in a minority of SJMMA tasks. When salient, sustainability was predominantly positioned as a driver in both competitions, while SJMMA showed a broader spread of non-driver roles. Framing patterns indicate different emphases: prediction-oriented framings occur more frequently in HiMCM, whereas decision/evaluation framings are more prevalent in SJMMA.
09 Understanding Anupad: Preliminary Findings from the Analysis of a Mathematics Diagnostic Assessment Tool in India
Nayanatara Gautham, Jioo Nimkar
Quality Education Support Trust (Quest)
Persistent gaps in foundational numeracy remain a significant challenge in Indian classrooms, with many students progressing through grades without mastering basic mathematical concepts. As a result, learning levels often vary widely within the same classroom, making grade-level assessments insufficient for informing instruction. Diagnostic assessments can help teachers identify students’ conceptual understanding and learning gaps to support targeted instruction. This paper presents preliminary findings from the standardisation process and analysis of Anupad, a mathematics diagnostic assessment developed as part of a level-based learning programme implemented by the Quality Education Support Trust (QUEST) in Maharashtra, India. Data from 2,323 students in Grades 6-8 across 27 project sites were analysed. Results indicated high internal consistency (Cronbach’s α = 0.88) and strong content validity. Factor analysis examining the underlying structure of the data identified a two-factor model representing procedural and conceptual understanding, accounting for 32% of the variance. These findings provide preliminary evidence supporting the reliability of the assessment.
10 Integrating Multi-duo Artefacts to Develop Spatial Skills and Geometrical Reasoning
Liying Huang and Taro Fujita
University of Exeter
Geometrical reasoning and spatial skills are essential for students’ success in geometry and for their future lives. The study adopts a design-based research approach with three phases of classroom observation. Participants were students in grades 7 to 10 from three schools in China. This paper presents findings on how combining any two of three artefacts, namely tangible objects, Virtual Reality, and GeoGebra 3D, into what we call multi-duo artefacts, creates a highly integrated learning environment. The results show that geometrical reasoning supports spatial skills by helping learners externalise their skills. In turn, spatial skills provide epistemic feedback that enriches geometrical understanding. Overall, these findings suggest that this integrated learning environment catalyses students’ development of a deep understanding of geometry.
11 Balancing complexity and usefulness in developing and working with a teaching framework
Jenni Ingram1 and Kirstin Erath2
1OUTER, Department of Education, University of Oxford, UK, 2Martin-Luther-Universität Halle-Wittenberg, Germany
There is a plethora of frameworks addressing various aspects of teaching, for the purposes of both analysing and developing teaching. In our work with teachers across seven countries on three continents, we frequently found that teachers’ descriptions of their practices did not neatly fit into single frameworks but rather connected and combined different aspects of multiple frameworks in varied productive ways. Consequently, we worked on developing a framework that attempted to capture this variety and the relationship between different frameworks within our focus on language and communication in mathematics classrooms. Teachers found this framework familiar and reported resonances with how they thought about their practices, but not useful in developing or analysing their practice. In this proceeding, we analyse why a framework that captured teachers’ accounts failed to support analysis or development of teaching, identifying tensions between complexity and usability.
12 Seeing, saying and reasoning: Observing mathematics teachers’ spatial reasoning
Emily Macmillan, Jenni Ingram and Corinne Angier
University of Oxford
Spatial reasoning, the ability to visualise, manipulate, interpret and solve problems using images, is not only key for success in mathematics and other STEM subjects, but also essential for everyday life. Spatial reasoning has been shown to be teachable, and improved spatial reasoning skills have been linked to improved performance in mathematics. Yet little research has been conducted into teachers’ spatial reasoning. We are investigating mathematics teachers’ articulations of their spatial imagery and reasoning as they describe and attempt to explain a dynamic image with a peer. We discuss preliminary findings of this study, focusing on moments of dissonance, when the participants’ reasoning changed direction or where they disagreed with each other.
13 What are the ‘orderings’ of mathematics education research? How might we need to contain/constrain them in arguing for a mathematics education for solidarity and hope?
Hilary Povey
Sheffield Hallam University
Given the current socio-political-ecological context, I am concerned to problematise how (mathematics) education research is ‘ordered’ – what taken-for-granted and mostly unnoticed assumptions underpin our practices, the language we use, the artefacts we employ, the textual conventions we are required to adopt, the generally hidden practices of reviewing and how the products of research are and should be valued – what ‘counts’. I discuss why these ‘orderings’ matter and why we should all be concerned to work for a mathematics education for solidarity and hope, whatever our field. Throughout, I ask questions rather than suggest answers, and I argue that this continuous interrogation of the self and the community is a necessary practice.
14 Designing a teacher-controlled AI Chatbot for conceptual learning of fractions in primary school
Eirini Rachmanidi and Christina Misailidou
National Kapodistrian University of Athens
FractionsCoach is a teacher-controlled conversational agent designed to support primary pupils’ conceptual understanding of fractions, with a particular focus on fraction comparison. Grounded in research on whole-number bias and the importance of magnitude reasoning, the tool aims to scaffold students’ transitions between representations and support the development of mathematical justification. The system operates through an adaptive learning pathway structured into phases (same denominator, same numerator, and mixed comparisons), with progression informed by learners’ performance. A key design feature is the use of graduated formative feedback, moving from visual and conceptual support to brief targeted explanations, while deliberately avoiding direct answer provision. As a result, the design of this tool highlights the potential of constrained, teacher-controlled AI to enhance conceptual learning in primary school mathematics.
15 Analysing nursery rhymes and songs for use in mathematics learning in the early years
Lucy Rycroft-Smith
University of Cambridge
A research and design project is being undertaken which explores the idea of using songs and nursery rhymes for mathematics teaching for young children (aged 2-4). As part of the project, a scoping literature review and a draft taxonomy were completed and are presented here. There is surprisingly little research on the use of songs and rhymes in mathematics learning, despite widespread reports of practitioners using them often, and evidence suggests that repeated weak claims and grey literature may currently be taking the place of more robust, connected and reliable findings. A draft taxonomy of different ways that songs and rhymes might be useful is proposed, including features such as pattern and structure. A call is made for further research focusing on ways in which songs and rhymes could support mathematics learning, including the use of gesture and movement, and a library curating these is suggested.
16 In-service teachers’ beliefs about the nature of mathematics between rural and urban contexts: A beginning step towards critical mathematics education in Indonesia
Hana Sofiyana
University College London- Institute of Education
This study examines differences in Indonesian in-service teachers’ beliefs about the nature of mathematics across rural and urban contexts. Despite growing interest in teachers’ beliefs, limited research has explored how these vary across socio-geographical settings in Indonesia. A survey design was employed with 200 purposively selected teachers (100 rural, 100 urban). The data were analysed using independent t-tests and Rasch models. Results indicate that rural teachers are significantly more likely than urban teachers to endorse absolutist views of mathematics, while no significant differences were found in fallibilist beliefs. However, teachers’ beliefs did not fit a strict absolutist–fallibilist dichotomy. Instead, many demonstrated hybrid and contextually mediated belief systems, often holding dual orientations. Many viewed mathematics as both fixed and dynamic while remaining hesitant toward sociocultural interpretations. These findings challenge rigid classifications and emphasise the socially situated nature of teachers’ beliefs. The shared presence of fallibilist tendencies across contexts suggests potential for advancing Critical Mathematics Education (CME) in Indonesia. These findings emphasise the necessity of context-sensitive professional development that supports teachers in integrating mathematical reasoning with social and cultural relevance.
17 Accounting for absence: Secondary schools, Piaget and manipulatives.
Annie Worley
University of Exeter
Manipulatives are valuable tools for enhancing mathematical understanding. Taking the view that mathematics is for all, this study aims to explain why manipulatives are not commonly used to teach mathematics in secondary schools and to shed light on non-constructive biases that affect their use. Six secondary school mathematics trainee teachers were interviewed at key points of their training to determine the formative beliefs they brought to the process, and how lectures and placements affected their approach to manipulatives. A critical examination of Piaget’s theory of cognitive development was used to show how abstract thinking is prioritised in teaching, discouraging the use of manipulatives when teaching higher-level mathematical concepts. The need for planned experience during placement and a greater understanding of how manipulatives can be used were identified as ways to promote their use.
18 Implementing mathematical literacy across contexts: A comparative analysis of Indonesia, South Africa, and China
Zhu, Rongxin
The University of Edinburgh
Mathematical literacy has emerged globally as an educational goal, yet its implementation varies widely, shaped by differing curriculum structures, assessment regimes, and underlying cultural perceptions. This paper presents a comparative analysis of how mathematical literacy is conceptualised and enacted in three contrasting education systems: Indonesia, South Africa, and China. Drawing on a qualitative synthesis of curriculum policy documents, assessment frameworks, and research literature, the analysis focuses on three dimensions of implementation: the role of assessment in shaping classroom practice, the positioning of mathematical literacy in relation to disciplinary mathematics, and the implications for teachers’ pedagogical practices and professional identity. The paper argues that mathematical literacy cannot be understood as a uniform construct; rather, it represents a family of practices shaped by local educational priorities and reform trajectories, with implications for curriculum design, teacher education, and comparative mathematics education research.