These summaries are of research papers presented at the Day Conference on November 2024, University of Southampton. Full papers are available at http://www.bsrlm.org.uk/publications/proceedings-of-day-conference.
Contents
Key topics and concepts of school algebra
Mela Aziza1 and Chris Sangwin2
1Universitas Islam Negeri Fatmawati Sukarno Bengkulu, 1,2University of Edinburgh
This study aimed to identify key topics and concepts of school algebra across diverse grade levels and ages. Reviewing school algebra was done as a preliminary stage before identifying key algebraic concepts at the transition to higher education. A comprehensive literature review was conducted on four mathematics curricula (Scotland, Indonesia, the United States, and the International Baccalaureate). Although the four mathematics curricula revealed a few differences in grade and age of students in learning algebra topics, students were taught common key algebra topics and concepts at school. The curricula highlighted five key topics of algebraic schools: (1) variables, (2) algebraic expressions, (3) equations, (4) inequalities, and (5) functions and graphs. These five key topics covered some key concepts.
Holly Heshmati,1 Yuqian (Linda) Wang2 and Patrick Barmby3
1University of Warwick, 2University of Durham, 3No More Marking Ltd.
Teaching for Mastery (TfM) has been developing for over a decade in England. As a result, there is the need to assess teacher trainees’ understanding of concept. We therefore report a preliminary study that tested an alternative approach, called comparative judgement, as a formative assessment method to identify teacher trainees’ views of essential aspects of TfM. Twenty-seven teacher trainees from two research-intensive university PGCE Secondary Maths courses drew a mind-map to show their understanding by the end of the course. Their work was then assessed by 14 Maths course leads in teacher training programmes. We report two main findings. First, the perceived best piece and the least one of trainees’ understanding reveal the range of their current understanding. Second, the comparative judgement approach to assessing pre-service teachers’ work seemed to be a reliable method to utilise. The results can facilitate mentors to support noticing and implementing of mastery approaches further.
Number, algebra, symbols and notation: What is the pedagogic challenge?
Dave Hewitt
Loughborough University
In this paper I present some activities which attempt to bring the reader’s attention to the complex relationship we have with symbols and mathematical notation. The purpose of this is to highlight that developing meaning for symbols and notation is not straight-forward. I continue the paper by offering examples from research, and from my personal experiences with students, of times when it was the notation, rather than the underlying mathematics of the situation, which presented difficulties for those students. I finish by raising the issue of whether there might be a specific focus on teaching notation per se, and that this is a different pedagogic challenge to teaching algebra.
Liying Huang, Taro Fujita
University of Exeter
Spatial reasoning is considered a basic mathematical skill. Given the importance of spatial reasoning skills, this study aims to contribute to the successful development of students’ spatial reasoning skills through a combination of digital and tangible objects. This study aims to describe and analyse the spatial skills in geometry teaching and learning with the multi-duo of artefact framework in this paper. To achieve this goal, we used duo of digital and tangible tools (Virtual Reality, GeoGebra and traditional tangible artefacts) for design-based research. We analysed data from our pilot study of experimental learning activities in spatial geometry carried out by Chinese students in grades 7-10. We identified moments of development in the use of spatial skills as students engaged in 3D geometry problems using VR, GeoGebra and tangible artefacts. The analysis also showed that students effectively ustilised their spatial reasoning skills through the use of multiple duo artefacts.
Genevieve Tatters
University of Bristol, School of Education
A challenge for mathematical teachers is to identify ways of thinking mathematically that are characteristic of understanding but also to support children in reasoning and exploring mathematics in their own ways, allowing them to experience ‘wow’ moments and the enjoyment that mathematics can bring. Encouraging children to make connections with prior knowledge can help children embed number concepts and become more confident and proficient at mathematics in later primary years. The present research proposes a teaching and learning framework encouraging children to make connections to develop greater understanding and reasoning skills using open-ended activities. This paper reports on a pilot empirical study focused on a growing awareness of the relationship between focused talk and teacher questioning, children’s own graphics and concrete representations. The outcomes of the pilot study indicated the importance of focused teacher questioning to elicit the development of reasoning skills through children’s collaborative talk.
Ruth Trundley1, Andy Parkinson2, Alison Borthwick3, Stefanie Burke1, Andy Tynemouth1, Helen Edginton1, Felicity Smith4 and Emily Farran4
1Devon Education Services, 2Government of Jersey, 3University of Nottingham, 4Univeristy of Surrey
We report initial findings from a study across England and Jersey on whether pupils make more use of their understanding of multiplication having experienced the multiplication tables check (England) than pupils who have not experienced the check (Jersey). The study involved a short set of questions designed to test multiplicative reasoning by comparing linked abstract and contextual questions. The two similarly sized samples were analysed, using chi-squared analyses, which showed a lack of evidence to any meaningful statistical difference between jurisdictions. However, key questions on pupils’ automaticity with multiplication bonds were raised. Furthermore, an attitudes survey investigated the thinking of pupils and teachers on the impact of learning multiplication table facts. The survey highlighted differences in perception of what it means to be good at maths and what are useful learning resources that led to paradoxical opinions of fluency.
Jingyun Zhang
University of Cambridge
Drawing on participatory research with 10 kindergarten children and 11 primary school children in a disadvantaged county in Yunnan Province, Mainland China, the study examines how Chinese children’s maths subjectivities are produced during the transition from kindergarten to primary school. Applying Foucault’s concept of technology of the self, I discuss how children navigate the metonymic and metaphorical axes within fluid maths discourses through the technologies of meaning-making, meaning-forgetting, and meaning-reinserting.