Proceedings of the Conference held online on Saturday 2nd March 2024
Contents
Alf Coles
University of Bristol
This report details an on-going study into Romania primary mathematics teaching, conducted in partnership with the British Council. The overall approach is one of “appreciative inquiry”, i.e., looking for what is going well, that could be further developed. An online survey was conducted, answered by over 750 primary teachers, which led to follow-up observations with 41 teachers, in 5 different regions. Observations used the “Teaching for Robust Understanding” (TRU) framework. I detail key outcomes, including a practice of children coming to the board to explain their answers. This latter practice (which I label “chalk talk”) was apparently so ubiquitous that it remained hidden in most observation reports. Teaching practices around formative assessment and getting students reasoning were relatively little seen. One implication for further work is whether “chalk talk” could be a mechanism to develop teaching practices around assessment and student reasoning.
Cosette Crisan1, Bohan Liu1, Zhongtian Ji2 and Kan Guo2
1 UCL Institute of Education, 2 Beijing Normal University
Joint reflections on teaching among Mathematics Teacher Educators (MTE), School-based Mentors (SM), and Student-Teachers (ST) are crucial to the development of STs’ professional knowledge. The MTE-SM-ST triad is a long-standing structure in place to support the development of STs during their school placements in their teacher education programmes. However, few studies have examined the content and forms of MTE-SM-ST conversations in any school subject, mathematics in particular. While research in mathematics education suggests that learning within and as a result of working in such a triad is complex, there remains a gap in understanding the opportunities that such interactions create for promoting subject-specific professional learning of all involved in a triad. This paper presents how the use of a data mining software to analyse the data collected from post-lesson discussions of two such triads (one from UK and one from China) facilitated an understanding of interactions within MTE-SM-ST triads.
The Numbers Count Intervention: Do the Benefits Persist through Key Stage 2?
Ann Dowker
Department of Experimental Psychology, University of Oxford
Starting in 2008, Edge Hill University developed a new intensive mathematics intervention, termed Numbers Count, for Year 2 pupils considered to be in the lowest 5% for mathematics attainment. Children receive half an hour of individualised, or very small-group intervention per day. Children, who received this intervention, performed much better than controls on Key Stage 1 assessments and on standardised tests. In the present study, 6359 children who underwent Numbers Count intervention in 2010-2011 or in 2011-2012 were followed up at the end of Key Stage 2, using information from the National Pupil Database. The children were compared with a group, whose Key Stage 1 results had placed them in the bottom 5% in mathematics. Their performance on Key Stage 2 tests was significantly better than that of the other initially low attainers. This suggests persistent effects of the programme.
Designing digital tasks within rational questioning to build thinking mathematics classroom
Selen Galiç1, Şenol Dost1, Selin Urhan1, Zsolt Lavicza2
1 Hacettepe University, 2 Johannes Kepler Universität Linz
In this study, we introduce a sequence of dynamic algebra tasks from a design-based study in lower secondary schools to build thinking mathematics classrooms within rational questioning. We designed several rational questioning-based dynamic tasks in a GeoGebra Book considering the algebra standards and analysed them based on the Dynamic Geometry Task Analysis Framework within the context of mathematical depth and technological action. These tasks were prepared for the comprehension of the linear equations, representing and generalising linearity with tables, graphs, verbal expressions, and equations, and exploring the rate of change. It is believed that this dynamic curriculum material promotes the use of the dynamic nature of GeoGebra in mathematics education, encourages teachers to ask rational questions, enhances students to think, and supports building thinking mathematics classrooms with high-quality mathematical and technological aspects supported by rationality.
Manish Malik1, Rehan Shah2, Georgina Zimbittas1 and Soumya Manna1.
1 Canterbury Christ Church University, 2 Queen Mary University of London
This work focuses on the re-imagination of the process of creating multiple choice questions by augmenting the skills academic bring, with Generative Artificial Intelligence (GenAI) tools such as ChatGPT. Multiple choice questions can help students practise and internalise concepts and help staff in making classrooms interactive and knowing where their students are in their learning journey and provide remedial support. However, the design process can be challenging, time consuming and rely on the knowledge and experience of staff, in particular their knowledge of any relevant cognitive conflicts or common misconceptions students harbour in a topic. This paper presents some initial results from a study on the integration of GenAI in the design of multiple-choice questions in mathematics within STEM disciplines. The paper shares some pedagogically inspired prompts used with GenAI to co-produce outputs. The paper concludes with recommendations for future research and ethical considerations, particularly concerning copyright issues.
Discourses of mathematical reasoning: analysis of three reform frameworks
Candia Morgan1, Ewa Bergqvist2, Jill Adler3, Magnus Österholm2
1Institute of Education, University College London, 2Umeå University, 3University of Witwatersrand
Curricula in many countries include mathematical reasoning as an aim, a competence or proficiency that students should acquire. This inclusion has been supported by wide dissemination of frameworks advocating reform that have arisen from the research community. We present the first part of a project aiming to investigate how ideas about reasoning originating in these frameworks are recontextualised in curricula, textbooks and classrooms. We analyse discourses about reasoning in three such frameworks, identifying how each characterises the nature of mathematical reasoning and the ways students are expected to relate to it. We also examine the extent to which reasoning is construed as a goal of mathematics education or as a means to achieving other goals. In this paper, we explain the methods used for analysing reasoning discourse and identify key findings from the analysis.
Lucy Rycroft Smith & Darren Macey
University of Cambridge
Writing mathematical questions, tasks or activities – along with criteria for ‘correctly’ answering them – is specialised and important work which has been previously done by teachers and designers with expertise and experience in their use. In this study, we asked three different large language models (Copilot, Claude, and ChatGPT3.5) to design questions to assess students’ understanding in the topic of the area of a rectangle, using ten prompts with nuanced differences. We found variety in the length, mathematical correctness, and ways to surface student understanding across the three models, suggesting that not all large language models give the same kinds of response when question generating, and teachers and designers may wish to experiment with different LLMs when considering which might be best for their needs. We suggest that future research can build on this study by exploring more dialogic co-design between LLMs and human agents.
The big picture: designing infographics in mathematics education
Lucy Rycroft-Smith & Fran Watson
University of Cambridge
As designers of Cambridge Mathematics’ Espressos, we reviewed the literature around infographic design and considered ways in which infographics might be useful to teachers, especially as part of a process of knowledge brokering. Here, we outline different conceptions of infographic design and use, concluding with our own design principles placed in context of the work of others. We use our experiences to offer a possible set of criteria to determine an effective infographic for communicating educational research.
Rehan Shah1, Manish Malik2
1 Queen Mary University of London,2 Canterbury Christ Church University
A systematic approach was undertaken to locate and analyse empirical research examining the use of ‘threshold concepts’ in mathematics teaching within STEM higher education disciplines. The primary research question, designed using the PICO framework, aims at investigating how the teaching of these concepts as ‘threshold concepts’ compares with teaching them more traditionally in relation to student understanding, performance and experience. A search was conducted across multiple databases following the design of search clauses and well-defined inclusion and exclusion criteria. Publications were selected for inclusion by screening and appraising results obtained from databases and keywords refined through a scoping study. This work-in-progress paper systematically documents and draws insights from the key demographic characteristics (publication year, source, context and methods) of the shortlisted studies.
Sinéad Vaughan
University College London
This study is based on my PhD, developed in response to the 2017 A level Mathematics specification, which for the first time included clear statements concerning use of technology. However, little is known about enactment, teachers’ knowledge of technology use is frequently limited, and there is a lack of professional development. Hence, taking a design-based research approach, I aim to address these issues by evolving design principles for creating educative curriculum materials – i.e., materials designed to promote student and teacher learning. Drawing on the Mathematical Pedagogical Technology Knowledge framework, I constructed a theoretical framework to produce the first iteration of my materials and conducted a pilot project.
Primary school teachers tackling social justice issues through teaching mathematics
Pete Wright1, Caroline Hilton2 and Joel Kelly3
1University of Dundee, 2IOE, UCL’s Faculty of Education & Society, 3The Blue School, CofE
In this paper we present further findings from the Primary Maths & Social Justice research project. The aim of the project was to explore how primary school teachers can tackle social justice issues through teaching mathematics. We employed a participatory action research methodology, which is a collaborative approach that recognises the essential contributions of both academic researchers (with their previous experience of research) and teacher researchers (with their in-depth knowledge of learners) to the research process. We established a research team that held a series of meetings in which we planned, taught and evaluated a series of research lessons. We carried out a thematic analysis of the data collected from these meetings and follow-up interviews. We discuss here three themes that emerged from this analysis: students’ increasing levels of ‘socio-mathematical agency’; teachers’ reflections on enacting change through collaboration; and the impact on teachers’ practice of their developing relationships with mathematics.