Proceedings of the Day Conference held at Liverpool Hope University, Saturday 11th November 2017
Contents
01 Pre-service primary teachers’ approaches to mathematical generalisation
Julie Alderton1, Gina Donaldson2, Gwen Ineson3, Tim Rowland1, Chronoula Voutsina4, Kirsty Wilson5
1University of Cambridge, UK, 2Canterbury Christchurch University, UK, 3Brunel University London, UK, 4University of Southampton, UK, 5University of Birmingham, UK
In our teaching with primary pre-service teachers (PSTs), each of us includes generalising tasks in the context of mathematical reasoning. We set out to explore the value of such activity from the perspective of PSTs and their approaches to generalisation. In this paper, we focus on one PST’s mathematical reasoning when working on the ‘flower beds’ problem. We consider what motivates shifts in attention, we reflect on the significance of students’ prior experience, and of student collaboration in our teaching sessions.
02 One teacher’s awareness in a mathematics classroom: towards an observation methodology
Julian Brown
University of Bristol, School of Education
Starting from the position that it is desirable for students of mathematics to develop awareness of mathematics and acknowledging that it is not possible for a teacher to access students’ awareness directly, attention shifts to the ways in which teachers use their pedagogical and subject knowledge to educate awareness. Drawing on in-class observation, review of video-record and teacher interview, I report an attempt to mark instances of teacher awareness of student awareness and to trace associated decision-making relating to student attention within a mathematics lesson. I consider differences in what is noticed by observer and teacher and how this might relate to teachers’ on-going development.
03 Reflections on trying to import cultural practices from one country to another
Laurinda Brown
University of Bristol, School of Education
Revisiting interviews with mathematics teachers’ first lessons with a new group from about 25 years ago that have not, formally, been written up, I ask the question: “How possible or desirable is it to try to import the culture and practices of one country’s mathematics teaching and learning to another?” After sharing the outcomes of the original interviews, I will compare and contrast teaching and learning mathematics in Hungary and the UK, drawing from a 25-year experience of an exchange link of prospective teachers. No matter what new initiatives are suggested by governments, the culture, values and beliefs of the teachers will tend to influence what becomes the experience of learners in the classroom.
Julia Croft1 and Sam Fisher2
1University of Bedfordshire, 2Redborner Upper School and Community College
In 20152016, the Teacher Subject Specialism Training (TSST) programme was launched to attract teachers who have previously qualified to teach other subjects. In this case study, the perceptions of participating teachers, departments and tutors regarding the development of sufficient subject specific knowledge and pedagogy are explored. A model is proposed of plural transitions to and through “complex identit[ies]” (Leach & Moon, 2000, 397) as perceptions of competence are disrupted and reconstructed. Viewing the findings from a socio-constructivist perspective, the roles of tutor and coach in this identity formation are reconsidered, building on the work of Shulman (1986) and Korthagen (2004).
Adam Haunch
Liverpool Hope University
We examined the emotional affect of a small cohort of nine postgraduate students enrolled on a subject knowledge enhancement (SKE) course on a teacher training programme in the northwest of England as they undertook a series of three substantial mathematical investigations. We noted a relationship between creative attempts at the problems and an increase in anxiety in the students. The results from the study appear to show that some students undergo substantial emotional changes, both positive and negative over the course of an investigation, despite the maturity of the cohort of students. This suggests that some additional thought should be given to the emotional wellbeing of students when planning intensive, investigative, mathematics lessons.
06 Learning to respond: The use of verbal metacommunication as a mathematics teacher educator
Tracy Helliwell
University of Bristol
Both as a teacher of mathematics and a new mathematics teacher educator, I have been struck by the importance of verbal metacommunication as a way of responding in discussions about teaching. Having worked on my verbal metacommunication in the classroom for many years as a teacher of mathematics, my attention has now turned to working on verbal metacommunication as a mathematics teacher educator. In this paper, I present an existing framework for some data from discussions with a collaborative group of mathematics teachers that I am working with in a facilitative role. Initial findings suggest the need for the development of a framework more fit for purpose as a facilitator of discussions with groups of teachers.
07 Orchestrating institutionalisation in card-matching lessons: The use of ‘big cards’
Marie Joubert1 and Ingrid Mostert2
1University of Swansea, 2University of Johannesburg
This paper reports on one aspect of the FaSMEd project in South Africa. In the project, teachers trialled lessons, at the heart of which small cards were used in activities involving matching or classifying mathematical objects. To address the difficulty of bringing such lessons to a close, as an experiment, big versions of the small cards were provided for the teachers. The findings suggest that teachers use the cards in a variety of ways, some of which appear to be more effective than others; it appears that teachers need more support in thinking through the decisions that need to be made in planning effective discussions when finishing a lesson.
08 The experience of Mathematics Anxiety in primary schools: A case study
Heidi Kirkland
University of Leicester
Mathematics Anxiety, defined as ‘feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of ordinary and academic situations’ (Richardson and Suinn, 1972, p.551) has been sparsely researched within primary schools in the UK. Research needs to identify the individual experiences of children with Mathematics Anxiety in a qualitative manner in order to move our understanding forward. A case study method was used, focusing upon a 9 year old pupil. Findings suggest that her experience of Mathematics Anxiety involved self-comparison to peers and family, avoidance, a lack of self-belief and confidence, as well as consistent worry, embarrassment and uncertainty.
09 Enlarging a tangram: do the pieces still fit? An account of an interview and its use in the design of a lesson on multiplicative reasoning
Dietmar Küchemann
In this paper I report on an interview with three Year 8 (Grade 7) pupils in which they each attempt to enlarge one piece from a simple tangram drawn on squared paper. I go on to discuss how the interview informed the design of an ICCAMS lesson on multiplicative reasoning.
10 Universities as a driver of A level uptake: The case of Maths and Further Maths
Stephen Lee1, Chris Saker2, Claire Baldwin1
1Mathematics in Education and Industry, 2Essex University
We are at a crossroads. New, harder, GCSE Mathematics qualifications were taken for the first time in Summer 2017 and that cohort of students are now studying the all new linear (rather than modular) Mathematics A levels. There is already suggestion from teachers that numbers starting Mathematics and Further Mathematics A levels may have reduced. This paper reports on analyses of data on A Level entry numbers, UCAS data showing mathematics A level students’ course choices, and degree course entry requirements. We discuss the important role universities can play in helping to maintain entry numbers to A level Mathematics and Further Mathematics.
11 Re-analysis of observations of lessons of students in Chile working on mathematical tasks
Paola Ramirez
University of Bristol
This paper presents a re-analysis of the behaviour of Grade 8 students (aged 13–14 years) in Chile within mathematics lessons where they are engaged in their usual mathematics tasks and in a mathematics modelling task for the first time. Observations and re-analysis of the teacher’s and students’ behaviours from an enactivist perspective showed that patterns emerged, such as interval of waiting, in the interaction between the teacher and students.
12 Commognitive analysis of a teacher’s mathematical discourse on the derivative
Innocent Tasara
School of Education, University of Leeds
Research on the teaching of the derivative (and limit) is still not as extensive as the research on students’ learning of calculus. This paper introduces the commognitive theory and reports on a commognitive analysis of a teacher’s discourse on tangents, gradient and differentiation with a Year 12 class in England. Mathematical discourse is characterised by four commognitive constructs: word use, visual mediators, endorsed narratives and routines. These constructs provide discursive foci for analysing mathematical discourse. Data sets include two face-to-face interviews with the teacher and an observation of an introductory lesson on differential calculus.
13 Report from the Critical Mathematics Education Working Group meeting
Pete Wright
UCL Institute of Education
This BSRLM working group met for the third time with the aim of discussing ways of promoting research that brings about positive social change through mathematics education. The meeting began with a presentation and discussion, led by Peter Gates, around recent developments in the field of CME and possible directions for future research. This was followed by a discussion, led by Hilary Povey, of the possible foci for future meetings of the working group.