Proceedings of the Conference held on Saturday 4th November 2023 at University of Bristol
Sunita Babbar, Gwen Ineson
Brunel University London
This small-scale study of secondary maths PGCE student teachers used a range of calculation problems to explore their preferred method for solving problems for themselves, and for supporting pupils. Data gathered included written jottings of their calculations, identified strategies used in the classroom, and follow-up interviews to explore their approaches. Analysis used the I and S-Rationale framework (Herheim, 2023) to explore how they came to decisions about their proposed teaching approach in their classrooms. Results show that although they could identify a range of approaches to support long division and multiplication of decimals, a narrow procedural approach dominated responses to a division of fractions problem, both for themselves and for their teaching. Further time and space is needed to explore what might be possible for student teachers on a one-year postgraduate programme, to build their confidence and understanding, to encourage their pupils to have an S-Rationale approach to learning.
Fay Baldry, Farhat Syyeda & Ben Harvey-Ashenhurst
University of Leicester
This paper is a part of a Knowledge Exchange project with a Maths Hub within the Midlands region of England. Maths Hubs are major providers of professional development (PD) for teachers of mathematics having been funded by the government for ten years. The aim of the project was to develop an understanding about how the impact of Maths Hub activities could be evaluated. We focused on NCETM Maths Mastery due to the pivotal role it plays in the hub activities. The theoretical framework developed for this study draws on the PD models of Guskey (2002) and Desimone (2009). Following a qualitative research design, data was collected through semi-structured interviews. Our initial findings show that knowledge and understanding about Maths Mastery vary considerably, even among those with long standing and substantial involvement with the Maths Hub. Moreover, assessing PD to identify concrete links with outcomes, as the providers sought, is problematic.
Alf Coles1 and Christof Weber2
1School of Education, University of Bristol, United Kingdom, 2University of Teacher Education Lucerne, Switzerland
In this article we share some ideas about how socio-ecological thinking intersects with algorithmic thinking, in mathematics education. Socio-ecological approaches to mathematics education have, at their centre, a radical idea that there is no separation between nature and culture, or body and mind, or information and matter. Such approaches provoke questions about how our research concerns might alter if we take seriously the precarious nature of the sustainability of life on the planet. We illustrate such a re-working of research concerns by considering algorithmic thinking. Algorithmic thinking, as we understand it, involves not only performing and designing, but also analysing and comparing algorithms. One way its research and teaching might alter, in light of questions of sustainability, is to include reflective knowing of algorithms.
Jenni Ingram and Gabriel Lee
University of Oxford
Both teachers and students encounter linguistic challenges in mathematics classrooms. Many of these challenges are also mathematical in nature and are often topic-specific. In this paper, we examine these challenges as they arise when teachers and students interact around a widely used task focusing on the truth-values of algebraic equations. The data arises from a collaborative project between teachers and researchers focused on developing materials to support language-responsive mathematics teaching. These materials focus on offering guidance on using widely used or known tasks in language-responsive ways. Videos from the lessons in which the teachers implemented these materials were analysed. In these lessons, the challenges encountered arose when the students and teachers were discussing the relationship between the examples generated and the conclusions drawn from these examples.
University of Bristol
I observed anecdotal evidence that the modality chosen by teachers presenting examples seemed to impact student participation and accuracy in example-problem pair work, where students are expected to copy an example and then complete a similar ‘my turn’ problem. This research was designed to systematically review student books and identify any trends in their work when I modelled examples using a PowerPoint, whiteboard and visualiser. The data suggest participation is consistent across the three modalities, but accuracy varies. The visualizer seems to ensure the most accuracy across multiple metrics. I explored the context of the trends using a reflective journal.
One part of my PhD research explored how Black and Wiliam’s five key strategies for effective formative assessment can apply digital game-based learning (DGBL) in mathematics education through primary school teachers’ views. 10 primary school teachers in England participated in interviews. Results of a thematic analysis indicated that teachers believe that different student characteristics and game types significantly influence the potential of DGBL as an effective formative assessment tool for mathematics education. Furthermore, teachers emphasized that the games that are widely used in mathematics education are far from fulfilling the five key strategies that Black and Wiliam’s framework suggests.
University of Bristol, Gordano School
Teaching students with low confidence and motivation in mathematics can be challenging. I teach mathematics in a secondary school where students are grouped based on a wider range of prior attainment than has previously been the case. Some of my students report that they “cannot do maths” and I believe they have not yet experienced enough joy in their mathematics classrooms. One way to consider my teaching practice in relation to these challenges has been through a focus on task design and by exploring the elements of mathematical tasks that can help support students’ confidence and motivation. In this study, students were asked to evaluate two mathematics tasks based on a theoretical framework of design elements. It was found that students’ confidence is increased when the structure of the task is familiar, and that classroom culture needs to be carefully considered to support confidence and motivation.
Institute of Education, University College London
This study aims to find a set of principles for designing examples, which can serve as theoretical guidance or practical tools in mathematics education to assist educators in creating teaching materials and helping teachers organise their lessons. I use variation theory as the theoretical basis to explain learning, choose multiplication as the context topic in mathematics education, and apply design research to generate a set of design principles, then develop a set of examples based on them. I collected data through interventions with groups of three students and analysed their responses to each example I designed. So far, I have proposed a set of initial design principles (iteration 0), tested and improved those examples (iteration 1 and iteration 2). This study is currently working on iteration 3.