University of Stirling
‘Learning for Sustainability’ (LfS) is an entitlement for every child in Scotland and encompasses three strands: sustainable development; global citizenship; and outdoor learning. This study explored how three beginning mathematics teachers are making sense of global citizenship within their developing identities as teachers. A case could be made for both a narrative and a discourse analysis approach and their possible incommensurability is discussed. Interpretive approaches can be criticized for the researcher extracting data and imposing their own meaning which runs contrary to feminist and decolonial aspirations that align with a critical global citizenship education. An attempt has therefore been made to work differently with the transcripts. The students were asked about their view of mathematics and their decision to become a mathematics teacher. The study suggests that a teacher’s conception of mathematics as a discipline may be a ‘way in’ to discussing how they envisage engaging with LfS.
Nancy Barclay, Richard Harvey-Swanston and Rachel Marks
School of Education, University of Brighton
This paper reports findings from a small-scale case study of four primary schools in England who have adopted mastery textbooks/schemes for their mathematics teaching. We focus on the case of Newly Qualified Teachers (NQTs) who bring to their first post recently developed understandings of mathematical learning theory together with limited experience in the classroom. In joining a school undergoing what Mathematics Subject Leaders (MSLs) hope to be transformational change in mathematics teaching practices, they face a unique combination of issues: how to learn to take responsibility for their pupils’ mathematics learning, developing their understanding and practices of mastery, and managing the structure, organisation and recommendations of the textbook/scheme. Our focus was on how these NQTs, supported by their schools, managed these three complex – and sometimes contradictory – aspects, and the role textbooks played in managing their journey through these issues.
University of Bristol
Given that teachers cannot attend to all aspects of the complex environments of mathematics classrooms in an equal way, following the locus of teacher attention might provide insight into teacher awareness of the learning of students. Such insight, in turn, might open spaces in which teachers can explore their practice. This report considers the questions asked by a mathematics teacher in a classroom as a possible mechanism for tracing teacher attention through observable behaviours. Drawing on a framework based on attention, within an enactivist stance, observations made in a series of mathematics lessons with a group of 14- and 15-year-old students are considered. Differences in the classifications of questions made by the teacher and the researcher are used to highlight moments of ambiguity which are, in turn, used to probe the awarenesses of both participants. Methodological implications are discussed, with a view to further data collection and analysis.
East Sussex County Council
An action research project for an M.A. focused on a form of mathematical representation which has recently been promoted by the National Centre for Excellence in the Teaching of Mathematics (NCETM) in many primary schools in England through their Teaching for Mastery programme. This small scale study was carried out in a Year 6 classroom, using observations and semi-structured interviews.
University of Brighton
The development of fluency in arithmetic is a central aim of mathematics teaching and of the primary National Curriculum in England. In the case of multiplication, fluency tends to be associated with the recall of facts and the application of procedures, rather than broader efficiency or flexibility. These proceedings report on a classroom-based collaborative action research study which sought firstly to clarify a shared interpretation of fluency and secondly to enable 8-9 year old children to develop such fluency in mental multiplication. Central to our approach was the aim of extending and connecting conceptual knowledge so that children were able to innovate their own solving procedures rather than only applying known strategies. Our findings indicate that exploration of representations increases flexibility by facilitating greater awareness of possible solution paths, and that evaluation of potential solution paths leads to greater efficiency.
Ysgol Bryn Elian
This research follows on from the research: Exploring teachers’ and students’ responses to the use of a Flipped Classroom teaching approach in mathematics (Oakes, Davies, Joubert & Lyakhova, 2018)
Specifically it focuses on a teacher’s perception of the impact of utilising a Flipped Learning classroom; both using the participation in the above research and drawing on the work of other authors.
The research will dig deeper into the categories of preparation, homework and lessons and ascertain from the teacher perspective whether these areas can become the non-negotiable elements of the course. It will also consider the impact of workload and the assumptions that as teachers we make of students’ understanding of technology and time management.
The primary source of the data analysis is qualitative and the main area to analyse is whether the preparation and trust that is given to students in this type of learning is repaid?
Sue Johnston-Wilder1 and Kate Mackrell2
1University of Warwick, 2University College London Institute of Education
We consider mathematics anxiety to be a result of cultural violence. We explore the possibilities offered by Marshall Rosenberg’s nonviolent (compassionate) communication (NVC), developed as a means of addressing conflict, to contribute to the existing work on mathematical resilience (MR), which seeks to address mathematics anxiety and avoidance. Nonviolent communication assumes that compassion is innate, that human behaviour comes from needs, which are indicated by feelings, and stresses the importance of empathy. This resonates with MR, and in particular validates the Growth Zone Model, an important and successful MR strategy involving the non-judgmental awareness and articulation of feelings and needs and the link between these.
Ems Lord, Director of NRICH
University of Cambridge
In our increasingly crowded curriculum, nurturing mathematical curiosity could be easily overlooked in the classroom. This paper reports the findings from an ongoing NRICH project addressing the scarcity of curiosity in many of our classrooms. Through the lens of a geometric classroom activity, it explores the extent that primary-aged learners are able and willing to work in a curious manner. This paper draws upon both teacher interviews and focus group discussions with the learners. It reflects on the obstacles towards embedding a culture of curiosity in our schools and suggests possible avenues for further investigation.
Dominic Oakes1, Teri Birch2, Sofya Lyakhova1
1Swansea University, 2Wrexham Glyndŵr University
We have presented previously on ‘Connections: Deepening A-level Mathematics through curriculum design and support. How best to develop and research?’ (BSRLM November 2017) and ‘Bringing a connected curriculum to life’. (BSRLM March 2019) These sessions looked at creating various representations of connections in the WJEC A-level curriculum, culminating in creating a 3D environment using the Unreal Game Engine. Developing the 3D Curriculum is a first step in our research, which aims to investigate firstly whether and how teachers of A-level Mathematics could use the 3D Curriculum to inform their short- and long-term teaching plans and secondly whether students will find it valuable in developing their mathematical understanding.
Dominic Oakes, Marie Joubert, Sofya Lyakhova
In response to teachers’ complaints about an overcrowded curriculum, FMSPW initiated a research project into the Flipped Classroom Approach (FCA) in two phases. We have already reported on teachers’ and students’ experiences of introducing and using the FCA (Phase 1) at previous conferences ( Joubert, Oakes, & Lyakhova, 2019; Oakes, Davies, Joubert, & Lyakhova, 2018). In this second phase of our research we are focusing on the teaching and learning of mathematics, looking at how teachers are using the time gained and teachers’ and students’ perceptions of improved mathematical learning.
University of Warwick
What happened to the 1980s vision where computers would be an integral part of teaching of secondary mathematics? The Cockcroft Committee referred to computers providing opportunities for enhancement of teachers’ existing practice and to work in new ways that had not been possible before (1982, p.117) while pointing out that there was under-use of technology in schools and lack of good quality mathematics software. Her Majesty’s Inspectors (HMI’s) investigated the use of calculators as a replacement for mathematical tables suggesting that their use in examination courses was not widespread, which some interpreted as no calculators to be used during the course. Comments about under-use are still highlighted in numerous reports, including the National Centre for Excellence in Teaching Mathematics (NCETM) 37 years later. What is restricting digital technology use in secondary school mathematics? This article considers some of the reasons for lack of progress towards the vision of the 1980s.
University of Bristol
Based on an enactivist approach, this paper shows what actions of distinction a mathematics teacher with their 23 students (ages 13–14 years old) make when they were doing mathematics in their usual way and also when working with a mathematical modelling task for the first time. The actions of distinction of the teacher are linked with his/her micro historicity, triggering mathematical interactions in their students.
Leo Rogers1 and Sue Pope2
We discuss some strategies and tools that can be used to integrate the History of Mathematics in a meaningful and effective way into the everyday activities of the classroom. We start from fundamental ideas already embedded in the mathematics curriculum and produce material to enrich the mathematical experience of learners and their teachers.
Nejla Tugcem Sahin
University of Aberdeen
This paper is from the pilot phase of a larger PhD study which aims to explore and develop student teachers’ views of social reproduction through mathematics education, within the framework of Bourdieu’s theory of social reproduction and Freire’s critical pedagogy. The pilot study developed workshop activities to explore and improve student teachers’ views on social reproduction promoting practices. Initial analysis of the findings revealed that the participants might, unknowingly, promote social reproduction in their teaching practice. However, some change in their views have been identified in the post-workshop data. These tentative findings suggest that there may be merit in further investigation of the value of engaging student teachers in such activities to better prepare them to support economically disadvantaged learners in school mathematics.
University of Georgia
This paper discusses a methodological tool called research problems as a way of working and communicating across disciplines. The two kinds of research problems considered are inertia problems and blockages. These problems are used in concert with selected philosophical concepts from Deleuze and Guattari and form the starting point of a methodology developed in a PhD dissertation. The choice of philosophical concepts was strategic as its new materialist influence may aid researchers in thinking in new ways beyond the strong influence psychology has had in mathematics education over the past several decades. This methodology is specifically aimed at designing and implementing technological interventions in mathematics education settings. Ultimately, the research problems approach is offered as a basis for a type of inquiry that is experimental, rigorous, and capable of capturing unexpected outcomes.
Helen C. Williams
UCL Institute of Education, London
In recent years, drawing on successful models of mathematics teaching in jurisdictions such as Shanghai and Singapore, mastery teaching in mathematics has become commonplace in England, yet there has been little research into the effectiveness of this method for students in English schools. Moreover, there is no research into its appropriateness for pupils with special educational needs. This paper outlines a case study carried out in one primary special school in outer London and discusses the approach taken by the school which had implemented a mastery teaching approach to mathematics. It examines the features of mastery teaching, the challenges faced by pupils with moderate learning difficulties and the adaptations needed in order to make the programme successful. This school found that adopting a mastery approach had a positive effect on teaching and learning in mathematics.