**BSRLM Proceedings: Vol 40 No 2 held online on Friday 3rd July 2020**

Proceedings of the New Researcher Day Conference held online on Friday 3rd July 2020

## Contents

Aehee Ahn

*University of Bristol*

This research is aimed at finding a novel way of investigating students’ understanding of mathematics. Mathematics as a language of conceptual tools is full of representations, and students re-interpret the representations to understand mathematical concepts. A metaphor is an important aspect of learning mathematics, with regards to it beings a powerful linguistic approach for creating and extending meanings of a concept. In this research, I carry out script writing tasks with 6th grade Korean primary students. In these tasks, a prompt that includes a mathematical situation is provided, and students are asked to write a script in a dialogue format for the prompts, similar to writing a scenario for a role-play. I describe their scenarios and examine a concept of a fraction in the students’ writings.

Jessica Barnecutt

*UCL Institute of Education, London *

My thesis explores perceptions of students leading their own learning during Project Based Learning (PBL) in the secondary mathematics classroom in the UK. In this paper I describe the contributions of two theoretical lenses, activity theory and complexity thinking, to my interpretation of teacher embrace of facilitating student led learning. I consider the role of a theoretical lens for interpretation, and outline how I view the two lenses as being complementary aids to help me gain understanding of an empirical phenomenon whose complexity may have been more difficult to grasp with only one lens. I describe each theory and detail their specific influence on my interpretation.

**03 GCSE Mathematics resit students’ narratives of their relationship with mathematics**

Despoina Boli

*UCL Institute of Education *

A number of recent studies have focused on the widespread disengagement that Further Education (FE) GCSE Mathematics students in England often show and have introduced approaches to improving attainment. However, few of these evidence students’ prior experiences to any extent. I report on a study which gives FE students the opportunity to explore their experiences with mathematics through their previous schooling and provides the researcher the ground to understand the factors that shaped their current engagement with the subject. Seven GCSE Mathematics resit students were interviewed using a narrative approach. Using semi-structured prompt questions, students were able to reach back to their previous experiences with mathematics and tell their stories. Early data analysis shows that key factors in shaping students’ engagement with mathematics were a) their relationship with the teacher, b) teenage class distraction, and c) the ability to transfer mathematical function from classroom to examination.

**04 Pre-service mathematics teachers’ understanding of geometric concepts through writing jokes**

Büşra Çaylan Ergene^{1}, Şerife Sevinç^{2}, Özkan Ergene^{1}

^{1}*Sakarya University, *^{2}*Middle East Technical University*

This study aimed to understand how geometric concepts were integrated into jokes and which contexts were preferred in the jokes. For this purpose, pre-service teachers were asked to write jokes related to geometry at the end of a Geometry course and 41 written documents were included in the data set. The data were analyzed through content analysis in a qualitative data analysis software called MAXQDA (VERBI Software, 2019). The geometric concepts used by the pre-service teachers included polygon, line, angle, circle, point, ray, line segment, plane, diagonal, edge and disc. The most frequently used geometric concept was polygon. Among the polygons, pre-service teachers mostly used the triangle and addressed various aspects of a triangle such as triangle types, properties of triangles, auxiliary elements and concepts related to the triangle. For the contexts, the pre-service teachers mostly preferred personification, assigning human qualities and attributes to geometric concepts in the jokes.

**05 Teaching students to write and read mathematics**

Jos Gunns, Rachael Carey, Andrew Donald and Lee Butler

*University of Bristol*

Students typically come to university without knowing how to write mathematics. Rather than treat it as a problem that individual members of staff have to deal with by themselves, we created half a module designed to explicitly teach students how they are expected to express mathematical concepts, ideas and proofs. By introducing this topic right at the start of students’ university experience, we succeeded in created an improvement that lasted into students’ second year. We also discovered along the way that students don’t know how to read mathematics, and so we expanded our remit into ‘study skills’, rather than focusing purely on writing well.

**06 Connecting the real world to mathematical models in elementary schools in Luxemburg**

Ben Haas^{1}, Yves Kreis^{2} and Zsolt Lavicza^{1}

^{1}*Johannes Kepler University Linz, *^{2}*University of Luxemburg*

In the Luxemburgish national curriculum for elementary schools (MENFP, 2011) experimentations and discoveries of mathematics concepts in courses are strongly recommended. Elementary school teachers should engage students in active mathematical modelling approaches, where they can develop processes and content skills through discoveries. Moreover, learned skills should be connected to real-world problems and situations to foster a better understanding of students’ living environments. Nevertheless, this teaching culture in mathematics is unusual in elementary schools and teachers tend to teach based on textbooks. Students mostly learn mathematics by imitation and repetition rather than through modelling mathematics with real-world problems and situations. Thus, to develop new methodologies in teaching mathematics and to meet the requirements of the national curriculum, we designed different technology-enhanced teaching and learning methods to engage students in experimental approaches within and outside classrooms. Moreover, we conducted three studies with digital and physical modelling, augmented reality, and a tutoring system in elementary school mathematics courses. Based on our collected data, we identified settings and tasks likely to support active mathematical modelling approaches.

**07 Mathematical definitions: what works and what doesn’t?**

Dominika Majewska

*Cambridge Mathematics*

The Cambridge Mathematics (CM) team has developed the CM Define It app – a survey tool which collects information about existing definitions of mathematical key words. The tool is aimed at professionals in the mathematics education community, including teachers, academics, researchers, and curriculum and resource developers. Survey respondents are presented with a key word and up to five definitions that address all learners, and which are taken from international sources. They are asked to rate the presented definitions on a five-point rating scale, according to how suitable they are for the learners with whom they work. They may then choose to provide justification for their ratings, including how accessible and accurate the definitions are for the learners they work with. The aim of this survey tool is to inform the CM team of what makes for a ‘successful’ definition of a mathematical term, which may eventually inform the glossary layer in the Cambridge Mathematics Framework (CMF) – a flexible and inter-connected map describing the mathematics learning of 3-19 year-olds. This paper will present the CM Define It app, the theory behind its development and its structure, functionality and aims. It will also describe the changes made to the survey tool based on user feedback following a pilot study.

Nejla Tugcem Sahin

*Mathematics University of Aberdeen*

This study aims to surface dispositions of primary student teachers in relation to mathematics teaching and learning in economically diverse settings. Bourdieu’s concepts of field and habitus are mobilized to explore participants’ dispositions. Ernest’s typological analysis of aims for mathematics education is employed to analyze the data collected. Findings revealed that majority of the participants can be located in the group of technological pragmatists who aim for learners to gain basic mathematical skills. A small number of participants, on the other hand, seem to be located in the category of progressive educators who aim for learners to gain confidence through learning mathematics. This paper argues that a theoretical analysis of student teachers’ dispositions can provide a useful tool to understand how their prospective mathematics teaching dispositions can be shaped.

John Thomas

*University of Warwick*

Mathematics anxiety is an “adverse emotional reaction to math or the prospect of doing math” (Maloney & Beilock, 2012, p.404) that negatively impacts individuals’ experience of and progress in mathematics. There are studies examining the impact of mathematics anxiety on highly academic people (e.g. Beilock & Carr, 2005) but fewer large-scale studies of interventions in schools (Carey et al., 2019). The Growth Zone Model (Lee & Johnston-Wilder, 2017) helps students recognise and overcome negative emotions related to mathematics anxiety. I describe a pilot study into the benefits of introducing the Growth Zone Model to students in years 11 and 13 in a highly academic, selective school. Year 11 students were preparing for higher tier GCSE Mathematics and year 13 students IB Higher Level Mathematics. Time was allocated to discussion of students’ emotional reactions, using the Growth Zone Model and associated tools (Johnston-Wilder et al., 2020) to moderate negative responses to difficult mathematics problems. Data is presented indicating the degree to which mathematics anxiety is an issue for these students and responses to a questionnaire about the efficacy of the Growth Zone Model are analysed. A case study examining one student’s response to the intervention is presented, highlighting the potential for the intervention to make a positive change.

Vivien Townsend

*Manchester Metropolitan University*

This paper reports findings from my recently completed doctoral study into the ways in which three Year 6 teachers approached the task of teaching new fractions content in the 2014 National Curriculum. Their different approaches to teaching led me to explore theoretical tools to understand why they taught as they did. The first of these tools, ‘history-in-person’, enabled me to understand teachers’ identities as both ever-forming and complex, and as informing action. And the second, ‘internally persuasive discourse’, brought insight into how the teachers orchestrated discourses including those of teaching and accountability. Theory led me to a sympathetic and nuanced understanding of my teacher participants and enabled me to realise why teaching like Claire is simply not an option for everyone. I will close by drawing out potential implications for anyone wanting to (in any small way) influence the work of teachers.