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British Society for Research into Learning Mathematics

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BSRLM Proceedings: Vol 41 No 2 held online on Friday 4th June and Saturday 5th June 2021

Proceedings of the New Researchers Day Conference held online on Friday 4th June 2021 and the Day Conference held online on Saturday 5th June 2021.

Contents

01 ‘It’s been worth the effort’: Primary school teachers learning to teach mathematics remotely during the pandemic.

Ellen Barrow1, Jennie Golding2, Grace Grima1

1Pearson UK, 2UCL Institute of Education 

We draw on Spring 2021 findings from a 2019-2022 study of impact and use of a ‘mastery’-oriented primary (ages 4-11) mathematics resource, ‘Power Maths’, in England. The study follows 40 classes of primary children and their teachers, in 20 schools, over two years. Our findings span the return into school from the early 2021 lockdown period, comparing and contrasting teachers’ approaches across the two pandemic-related lockdown periods, the first in March-June 2020. Most teachers developed a significantly wider range of, and confidence in, remote learning practices. They came to expect more, and active, new learning, rather than aiming just to consolidate prior knowledge. Many developed active selection of the most appropriate topics for home learning, substantially increased ‘live’ teaching, and found ways to more proactively monitor work. Despite this, some challenges persisted: providing effective formative assessment and insecure knowledge of parental support and of gaps in children’s learning.

 

02 Exploring the identity negotiation of early career mathematics teachers: A pilot study

Amy Birkhead

Sheffield Hallam University

Becoming a mathematics teacher is a period of intense identity negotiation. This study aims to understand how secondary mathematics teachers negotiate their identities during their first two years of teaching by exploring the internal forces that shape their understanding of being a mathematics teacher while navigating the social and cultural conditions of schools. Three early career teachers participated in a pilot study, which employed exploratory interviews supplemented with written personal reflections, and the collection of artefacts. In this paper I will look at the design of these data collection methods, and their potential to help develop a narrative inquiry. Such methods provide opportunities to collect extended narratives which explore teachers’ histories, beliefs about mathematics, and the context in which they work.

 

03 Adult students’ perceptions of constructivist learning, control-value appraisals, and achievement emotions in further education mathematics 

Rachel I. Brougham, Laura J. Nicholson, Linda K. Kaye, Gordon Laing

Edge Hill University   

The current research aimed to explore the links between students’ perceptions of cognitive constructivist principles in learning and their achievement emotions in mathematics. The relationships between perceptions of four constructivist-informed classroom practices, students’ appraisals of control and value, enjoyment and anxiety were investigated using a quantitative questionnaire-based study with a sample of adult students (N=103) of level 2 mathematics in further education. Multiple regression analyses revealed that perceptions of investigation learning related positively with control appraisals, value appraisals, and enjoyment, and negatively with anxiety. Perceived involvement in learning was negatively, and cooperative learning positively, related to anxiety. Implications for practice are discussed, with our conclusion advocating the use of active learning in mathematics.

 

04 “It’s not worth trying to understand the problem, it doesn’t help”: An examination of children’s approaches to solving word problems

Laura Clarke

University of Winchester

The research focused on strategies 29 10 and 11 year old children applied when solving a selection of word problems. In nearly all cases children relied upon superficial, procedural strategies to identify key words and numbers that triggered inefficient and inappropriate strategies such as guess and check.  Children showed remarkable resilience when applying their strategies and were confident in them even when they were unable to solve a problem.  Simple interventions such as asking the children to read the problem aloud, asking prompt questions and drawing bar diagrams were decisive in helping children to understand the problem, select an appropriate strategy and reach a successful solution.

 

05 Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology 

Alison Clark-Wilson, Nicola Bretscher, Cosette Crisan, Eirini Geraniou, Ebert Gono, Andrew Neate and Chris Shore

UCL Institute of Education, University College London 

This working group (WG), which met for the second time in June 2021, was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted as a result of the COVID-19 pandemic. Following a brief introduction to the aims for the WG, we offer three further case studies of teachers’ practices and an emerging synthesis of the cases according to three pedagogic activities that are proving to be particularly challenging.

 

06 Exploring mathematics anxiety amongst pupils at a pupil referral unit  

Alison Flack

UCL Institute of Education, University College London

This research explored the prevalence, origins and expression of mathematics anxiety amongst students at a pupil referral unit (PRU). Eleven students were screened for mathematics anxiety using a questionnaire designed for this purpose. Five students scored highly for mathematics anxiety and the three highest scoring students were selected for interview about their experiences in mathematics classes both in the mainstream and PRU settings. Five themes emerged from thematic analysis: teacher input; negative lessons; subject matter; lack of personal empowerment; and the testing nature of mathematics lessons.

 

07 The views of STEM specialisation among academics 

Vesife Hatisaru

University of Tasmania 

In this paper, an analysis of responses to the D-STEM task (Draw a STEM Learning Environment), provided by fifteen university educators at an Australian university, was used to illustrate the views of STEM specialisation among STEM educators. Participants relatively exhibited either knower-code view (foregrounding dispositions of STEM knowers) or knowledge-code view (foregrounding STEM disciplinary knowledge), while élite-code view (foregrounding both) was observed less. The LCT approach (Legitimation Code Theory) has been found promising in developing a language by which what counts as STEM specialisation can be explicitly communicated.

 

08 Listening to Claire: Analysing one student’s story told in the context of resitting mathematics in a post-16 college

Rachel Helme

University of Bristol

For students who are labelled as low prior attaining, having the opportunity to tell self-positioning stories about their own identity work can enable a researcher to reflect on the teaching and learning of mathematics through the students’ lived experience. This article demonstrates the creation of a poetic structure as a device for listening to student voice as part of a project in the context of resitting mathematics in a post-16 college. A rubric was developed for the creative process, adding consistency both within and across different poems formed during the analysis. The rubric enabled me to focus on the voices identified rather than the potential unpredictability found in the creative process.

 

09 Connecting music and mathematics: Exploring the professional development of primary school teachers in the English context

Caroline Hilton and Jo Saunders

UCL Institute of Education, University College London

Building upon previous research, a small-scale qualitative study was established to work with generalist class teachers in primary schools in London, UK. The research explored how music and mathematics may be co-taught so as to support ongoing professional development. Early findings suggest that the co-teaching of music and mathematics supported: i) a meaningful context for exploration and mastery within both subject domains; ii) extended dialogues within both subject domains; iii) collaborative dialogues between teachers focused on problem solving and learning in preference to previous foci around content and repetition; and iv) a need for the further examination of the impact of teacher identity on issues including planning, craft and professional knowledge and the notion of an ‘expert’.

 

10 Anti-racist and decolonial practice in teacher education  

Manjinder Kaur Jagdev

York St. John University 

PGCE mathematics students work in groups to create lesson plans and resources about the historical and cross-cultural roots of mathematics, with written reflections on celebrating diversity. Last years’ lesson activities included: ‘The Game Ayo’, ‘Yoruba Number System’, ‘Towers of Hanoi’, ‘Crop Circles’ and ‘Tangrams, Sudoku and Kenken’. The students reflected on the implications on their classroom teaching with pupils, relating to unconscious bias and decolonisation of the national curriculum. At the summer BSRLM workshop 2021, ideas were shared from colleagues and students at York St. John university and for classroom teaching. BSRLM colleagues contributed to the Padlet for initial teacher education. Collaborative curriculum development practice with teachers in schools is envisaged. This will involve planning and teaching mathematics topics, interviews, lesson observations and conversations. Learning about contributions to mathematics from people from around the world, can help pupil engagement and interest, whilst addressing diversity, inclusion and social justice issues.

 

11 Breaking down the barriers to offering Level 3 Core Maths: Findings from interviews with large A level providers 

Stephen Lee1, Jo Deko2, Iram Hussain2

1Mathematics in Education and Industry, 2Tribal

Almost 12,000 students in over 600 schools/colleges now study Level 3 Core Maths. The uptake has grown steadily since its inception in 2016, but there continues to be barriers for some institutions to offering the post-16 qualification. As part of the work of the Advanced Mathematics Support Programme, a small-scale study was conducted into ‘large A level providers’ who didn’t offer Core Maths. 66 large A level providers were in scope of the study, and this paper reports on feedback received from 20 interviews and 10 survey responses. Findings show that a major barrier within this type of institution is that many students are already taking alternate level 3 mathematics qualifications, i.e. A level Mathematics. Other hurdles are connected to this, such as timetabling and teacher shortages. Two additional concerns centered on the funding associated with the qualifications, as well as a lack of university recognition for Core Maths.

 

12 Secondary students engaging in a live online enrichment programme 

Sofya Lyakhova1, Andrew Neate1, Samantha Durbin2 and Rachel Dorris2

1Swansea University, 2The Royal Institution of Great Britain 

The study reports on a series of Royal Institution (RI) Mathematics Masterclasses that took place in Wales in Spring 2021. The RI Masterclasses are a popular example of a mathematics enrichment activity and would usually take place in a traditional face-to-face environment, such as a university lecture theatre or school classroom. However, the 2021 series took place online due to Covid-19 restrictions. Through feedback collected after each session we investigate how the design of the online classes influenced students’ engagement with mathematics.

 

13 A further education student teacher’s mathematical and pedagogical knowledge seen in the teaching of circumference and area of the circle

Natheaniel Machino

University of East Anglia

Students get confused about the concepts of area and circumference of circles as teaching emphasizes memorizing formulas rather than understanding concepts. In this paper, I report findings of the analysis of an episode of a lesson on ‘Area and circumference of the circle’ taught online by a student teacher to a Further Education class. The analysis employed the Knowledge Quartet – a framework for the analysis of mathematics teaching, with a focus on teacher knowledge. Findings show the student teacher’s Foundation is strong in some areas and less strong in other areas. Transformation and Connection were observed to be not strong but some good examples of recognition of conceptual appropriateness were observed. No sign of contingency was observed as students either did not contribute or their contributions were directed to the teacher only making it difficult to observe whether any teacher action was a result of the students’ contributions.

 

14 Why do we learn? A public engagement project for Egyptian schools

Mariam Makramalla

New Giza University

Commissioned by the Public Engagement division at Cambridge University, this project aims to trigger cross-generational public debate about the purpose and value of schooling, utilizing the arts as an awareness raising filter and as a platform for self expression. In this paper, I outline the rationale and relevance of the project, the role of the arts as a mediator between mathematics teachers and society as well as some preliminary findings in relation to partnership negotiations between societal stakeholders, schools and art institutes. The paper concludes with a discussion about implications of the project along with opportunities for upcoming public engagement.

 

15 The capacities of pre-service teachers to effectively teach mathematical problem-solving

Emma M. Owens and Brien C. Nolan

CASTel, School of Mathematical Sciences, Dublin City University

The project addresses the development of capacities for teaching problem-solving among pre-service, post-primary (12-19 years old) mathematics teachers (PSMTs). A key concern is what these capacities are and this study incorporates the questions of what mathematical and pedagogical knowledge and skills teachers need, and what attitudes underpin effective teaching of mathematical problem-solving. This study was conducted in an Irish university setting with three cohorts of participants undertaking concurrent initial teacher education programmes. The participants had previously received formal instruction in a university module that focused on the ‘Rubric Writing’ approach to problem-solving. The project investigates the PSMTs’ beliefs regarding problem-solving, understanding of a mathematical problem, problem-solving proficiency, and ability to pose mathematical problems. We report on the mixed-methods approach we took to addressing these questions, and provide an overview discussion on our findings. We will also discuss how these findings will influence our taught modules on problem-solving and problem-solving instruction.

 

16 ‘Hard to focus, difficult to learn’: Covid19 impacts on teaching, learning and progression for A Levels in mathematics

Ben Redmond1, Jennie Golding2, Grace Grima1

1Pearson, 2UCL Institute of Education

We explore year 13 (age 17-18) student accounts of how Covid19 has impacted their learning for pre-university mathematics qualifications in England. Findings derive from the final year of a four-year study (2017/18 to 2020/21) exploring enactment and impact of reformed mathematics ‘A Levels’, and efficacy of associated Pearson resources and assessments. Research tools were adapted to focus on impacts of Covid19. In this cohort’s first year of A level (2019/20), teaching and learning was severely disrupted. Teachers anticipated significant, wide-ranging learning gaps as students progressed to year 13. Using data from Autumn 2020 and Spring 2021 we analyse student accounts of how continued disruptions to teaching and learning have impacted them. Variable access to teachers, barriers to collaborative work, and challenges of remote or reduced contact working have resulted in reduced depth and breadth of learning. Additionally, many students reported negative impacts on mathematical confidence and wider mental health.

 

17 Can GeoGebra’s augmented reality tool provide a looking glass into a mathematical wonderland?

Katherine Riding

UCL Institute of Education, University College London

GeoGebra has been well researched within the mathematics education community; however, the majority of this literature does not examine the recent edition to the GeoGebra family, GeoGebra 3D Calculator with Augmented Reality (GeoGebra 3D/AR). This master’s study sought to examine how primary school students (age 7 to 12 years old) used ‘AR manipulatives’ to model familiar household objects. Due to the pandemic, the study was conducted over two ‘virtual workshops’ which propelled a second technological tool/environment to the fore; teaching, learning and researching within the ‘Zoom classroom’. Participants’ interactions were analysed qualitatively through Bruner’s enactive-iconic-symbolic framework. All young participants identified real-life objects (enactive mode), constructed virtual objects in GeoGebra 3D/AR (iconic and symbolic modes) then ‘augmented’ these AR manipulatives alongside real-life artefacts (all modes). Furthermore, the virtual workshops revealed how student-centred orchestrations such as ‘spot-and-show’ and ‘sherpa-at-work’ were extremely challenging to replicate in a remote setting.

 

18 Deep questions of evidence and agency: How might we find ways to resolve tensions between teacher agency and the use of research evidence in mathematics education professional development?

Lucy Rycroft-Smith & Darren Macey

University of Cambridge

We reviewed the literature around evidence-informed practice, teacher agency, and professional development for mathematics teachers, using a conceptual saturation approach to identify tensions around the contested nature of evidence and possible rights and responsibilities of ‘evidence-informed’ professional development. We found that narrow definitions of evidence and its ‘implementation’ may be used to create a powerful orthodoxy around research in practice, reducing teacher agency and resisting alternative discourse.  We propose accepting a wide definition of ‘evidence-informed practice’ in order to reduce tensions between research use and devaluing other types of knowledge, and conclude with the need for good quality mathematics education professional development to provide teachers with metaevidential insulation and critical resistance by attending to the nature of evidence as well as merely interpreting it.

 

19 Role of reading comprehension and maths computation in word problems solving: A comparison of Arabic EAL and English-native adults learning maths in England

Usama Saad

Loughborough University

To investigate the role of reading comprehension and maths computation abilities in successful word problem solving, 40 adult participants (Arabic and English native speakers who have previously studied maths in England) have been recruited. They have been tested on three subtests (WRAT V for text comprehension & maths computation, and PISA for word problems) to measure their skills in reading comprehension, maths computation and word problems. The results suggested that reading comprehension and maths computation were significant predictors for Arabic-native speakers’ performance in the word problems subtest, but maths computation was the only significant predictor for English-native speakers. These results raise questions about the suitability of word-problems-curricula for assessing the maths abilities of different populations.

 

20 Using prompt videos to improve problem-solving skills

Andrew Stewart-Brown

Independent researcher

The article describes the development of a resource to support candidates for the United Kingdom Mathematics Trust’s (UKMT) Challenges. It describes how the Challenges were introduced in a school and how they work. The data provided by the UKMT in its Yearbooks and the pedagogical value of the Challenges as a means of encouraging problem-solving are considered. The interventions undertaken to support candidates over the years, which culminated in the development of the prompt videos, are discussed. Academic research on prerequisites for teaching and learning problem-solving is addressed and leads to a description of how prompt videos address students’ difficulties. The program of research and work for the next year is outlined.

 

21 Exploring the relationship between preschoolers’ pattern awareness and mathematical understanding

Ziyan Wang

UCL Institute of Education, University College London

This study analyses data from Thouless and Gifford’s pattern project to address two research questions: (1) Whether preschoolers’ pattern awareness and mathematical understanding influence each other? And in what ways? (2) Whether the improvement of preschoolers’ pattern awareness advances their mathematical understanding? I conducted ordinal logit regression and paired t-tests to analyse the data. The results indicated that there is a correlation between children’s pattern awareness and mathematical understanding. Preschoolers’ mathematical understanding has limited influence on their pattern awareness, whereas their pattern awareness has a noticeable impact on their mathematical understanding. The findings also suggest that the improvement of pattern awareness leads to the advancement of mathematical understanding, and that pattern awareness was improved by training. However, the practice of pattern awareness should be targeted and provide children with enough experience. Meanwhile, not all aspects of pattern awareness led to progress in mathematical understanding.

 

22 How to make practice more perfect? How to make practice more productive?

Sze Man Yeung and Taro Fujita

Graduate School of Education, University of Exeter

Although practice is regarded as a crucial component for promoting procedural fluency, it is always stereotyped as mechanically repeating steps and being over-simplified to ‘More practice makes perfect’. This phenomenon might result from the incomplete understanding of conceptual and procedural knowledge. Therefore, it is necessary to reposition the role of procedural learning by introducing deep procedural learning. Deep procedural knowledge refers to the cognitive understanding of the computational processes and flexible use of computational strategies. Purposely designed productive practices, which aim at developing higher-order thinking when practising essential procedural skills, are expected to prompt the deep procedural learning. To evaluate the progress of procedural learning by using productive practice, theoretical framework about the relationship between deep procedural learning and mathematical thinking is introduced in this paper.

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