Proceedings of the Day Conference held online on Saturday 6th November 2021.
Nicola Bretscher, Eirini Geraniou, Alison Clark-Wilson and Cosette Crisan
UCL Institute of Education, University College London
This working group (WG) met for the third and final time in November to work on the six case studies that were presented during the March 2021 and June 2021 meetings. We recap an overview of the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted and point to findings from recent research on how mathematics education adapted during the pandemic. We connect the WG case studies to these findings to draw conclusions with respect to how practitioners responded to teaching mathematics online and the evolution of their related practices. Drawing on contributions from WG members, we then suggest ways in which teachers’ practices developed during the pandemic will impact evolving pedagogies in mathematics education.
Jennie Golding1, Mark J. Hill2, 3, Irene Custodio2 and Grace Grima2
1University College London Institute of Education, 2Pearson UK, 3University of Kent
Concerns around discrepancies in mathematics participation by gender are longstanding in many jurisdictions. Normatively, those are a question of social justice: if girls are being disproportionately excluded for conscious or unconscious reasons at any level of the curriculum ‘system’, those should be addressed. Economically, disincentives for girls’ engagement might also impinge on both personal and national thriving. While more girls than boys took pre-university STEM ‘A Levels’ in recent years in England, Wales and Northern Ireland, issues remain specifically with mathematics. This paper draws on the 2020 PISA Field Trial data to outline some areas of concern as perceived by 15-year-olds in England, Wales, and Northern Ireland in early 2020. We first identify key issues recognised in previous literature, and then locate those within the 2020 dataset. By exposing the continuation and extent of these challenges in mathematics, the paper has potential also to identify opportunities to address them.
Owen Hooper, Elena Nardi
University of East Anglia
We report findings from a small-scale investigation into how university mathematics teaching (UMT) adapted to the challenges presented by the move to an online learning environment during the COVID-19 pandemic. Six interviews were conducted with lecturers in a UK university and then analysed through a commognitive lens. Two themes emerged from the analysis: the “faceless audience”; and, “coping without the chalk and blackboard“. Amongst the innovative and productive UMT routines that emerged in the midst of the pandemic emergency and at quite short notice, were, for example, the use of multiple-choice questions and emoticons as a barometer for student engagement and understanding (replacing previous reliance on facial expressions and nods of heads). We conclude with reflections – and a call for further research – on whether these urgently devised and implemented innovations are here to stay or whether old UMT habits will prove too hard to die, and return.
Rosalyn Hyde1, Rosa Archer2 and Sally Bamber3
1University of Southampton, 2University of Manchester, 3University of Chester.
This study reports on the perceptions and understanding of beginning teachers regarding mastery approaches to teaching mathematics to 11–16-year-olds. It draws on qualitative data from six semi-structured interviews using vignettes designed to interrogate teachers’ understanding of the features of mastery learning within their practice. The data were transcribed and analysed thematically, drawing on the literature in the field. Whilst capturing the full complexity of beginning teachers’ perceptions and understanding is beyond the scope of this study, the data provides insight into these teachers’ experiences at a time when mastery learning discourse is prominent in England. The study found that beginning teachers had different interpretations of the principles of mastery learning. It also found tensions between beginning teachers’ beliefs, practice, professional knowledge and sense of agency in their developing classroom roles. Some beginning teachers found it challenging to talk about pedagogy and had continuing misconceptions about teaching and mastery approaches.
Darren Macey and Lucy Rycroft-Smith
University of Cambridge
Engaging in research, in particular choosing methodologies, is a deeply personal act that reveals truths about the world of the researcher even as the researcher seeks to reveal new truths about the world. These choices are not neutral; and neither are they merely practical, but rooted in our alignments, our identities, and our research communities. Just as they can locate us as servants to a hegemonic paradigm or as subverters of norms, they can locate us at the core of communities, or on the boundaries of them. In this paper we explore some of the possible models which may support researcher dialogue around the ways in which we (may be seen to) position ourselves and our research and the potential implications of those choices.
University College London
Through semi-structured interviews with 19 deaf and hearing teachers and other school staff, I explored the narratives formed and developed around identity and education in the mathematics classroom. Using inductive content analysis I found that classroom talk was an activity that all participants considered to be important for teaching and learning, but that led to particular challenges for deaf people. Mathematical discussion has the potential to be an inclusive practice where pupils and staff can contribute to understanding in the classroom, or one where some participants are excluded. Some challenges were common to both deaf pupils and staff, and other experiences were particular to the participants’ role in school. Holding the two possibilities of inclusivity and exclusivity in tension, participants found their own ways of making mathematical talk useful and inclusive for themselves and their pupils.
University of Bristol, UK
A prototype app was developed that uses AI to recognise placements of Cuisenaire rods on a table via a webcam and generates pre-programmed utterances, such as the lengths of the rods. A theoretical framework is proposed which brings together Wittgenstein’s concept of a language-game, consisting of language and its interwoven actions, with Froebel’s Kindergarten pedagogy of children creating ‘worlds’ by interweaving block play and story-telling. In this framework Froebelian ‘worlding’ can be understood as enacting language-games around block play, and the rules of a language-game, or ‘worlding’, around mathematical block placements can be endorsed by the app’s utterances. This framework was used to design an experiment carried out with primary school children. I reflect on the results, focusing on a video-clip of a 6- year-old’s interactions with the app, and tentatively identify evidence of a mathematical ‘re- worlding’, transforming rods from counters into lengths.
University of Bristol
Images of mathematics held by students and teachers are complex, with varying attributable characteristics. Affective factors such as beliefs and attitudes have been found to be significant in influencing outcomes. This case study examines the images of mathematics held by three adolescents and their teacher in a Steiner school in the UK. The Steiner-Waldorf curriculum approaches mathematics through cognitive, emotional, physical, and spiritual aspects. The findings indicate that a quality of relationship to mathematics, involving imagination, as expressed in the curriculum, is common to a teacher and students.
Mariam Siddiqa Rashid
Over the past few decades, learners’ perceived apprehensions in resit Mathematics lessons at Further Education (FE) college gained much attention in the England. Resit Mathematics learners are those who did not achieve Mathematics at school leaving age. Moreover, research in Mathematics education globally revealed different aspects of Mathematics-related apprehensions, especially in younger generations. However, there has not been much work done on understanding resit Mathematics learners’ apprehensions and their learning needs to improve the situation. This paper explored learners’ beliefs about Mathematics using Implicit Theories. Resit Mathematics learners’ experiences were explored to understand their learning needs at FE college. I used Focus Group Interviews with Mathematics learners from different vocational areas at FE college. These interviews helped them recall their Mathematics experiences and encouraged them to compare and share in the discussion. Initial data analysis identified that most of the resit Mathematics learners’ experiences were mainly negative at secondary school.
The Maria Grzegorzewska University
There are wonderful moments in our lives that we would like to remember for as long as possible, and those that we do not like to get back to. There are those that make us aware of something important and those that potentially do not matter much. Scientific research shows us that these somehow important events are significant for the development of mathematical aptitude. Both the experiences that crystallize giftedness and the experiences that paralyze them, play a huge role in the entire course of human life. What to do to identify them best and use their full potential? I will try to answer this question in the text below.
University of Cambridge
Problem-based learning (PBL) is an important form of student-centred pedagogy that departs from the conventional form of teacher-centred pedagogy often reported in Chinese classrooms, and so there is a need to understand how Chinese teachers perceive PBL. This study used a case study methodology and in-depth focus group discussions with 6 teachers from three Chinese secondary schools to investigate Chinese teachers’ views on the implementation of PBL in Chinese mathematics classrooms. The findings indicated that PBL was relatively accepted by the participants, who believed that PBL could improve students’ problem-solving skills and interest in mathematics. However, participants considered that exclusively using PBL would not be ideal, and they advocated combining PBL with conventional teaching (CT) for the best learning outcomes. Implications for research and practice are discussed in light of these findings.