Proceedings of the Day Conference held at the University of Edinburgh on 16 Nov 2013
Hatice Akkoç, Sibel Yeşildere-İmre and Mehmet Ali Balkanlıoğlu
Department of Secondary Science and Mathematics Education, Atatürk Faculty of Education, Marmara University, Turkey; Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylül University, Turkey; Department of Sociology, Faculty of Arts and Sciences, Marmara University, Turkey.
This paper focuses on the notion of identity and how it is formed through stories. Many researchers equate identity with the construction of stories. This exploratory case study examines professional identity by interpreting stories which come out of an interview with a prospective mathematics teacher. A semi-structured interview was conducted during a school placement. The interview data was analysed using Kegan’s (1982; 1994) constructive-developmental theory. Findings will be discussed in the light of usefulness of the theory in exploring identity through storytelling.
02 “It’s not a sausage factory!” Primary teaching assistants’ experiences on a short intensive block of study on mathematics
Open University, Faculty of Education and Language Studies
This paper reports on an initial study, which aimed to evaluate the learning experiences of teaching assistants studying a four-week block on mathematics as part of an Open University module, Subject knowledge and professional practice in primary schools. This paper focuses on the design of the evaluation and summarises some of the key findings to date and how they will inform the main study to follow. Findings from the initial study suggest that the impact of such a course of study on pupils’ learning and behaviour may be more extensive than TAs recognise.
03 An alternative destination for post-16 mathematics: views from the perspective of vocational students
University of Nottingham
The English government has recently raised the school leaving age to 18 and introduced a requirement for 16-year olds who have not achieved a grade C in the national certificate (GCSE) for mathematics to repeat this examination. These are significant changes affecting the place of mathematics in post-16 education. The current lack of an alternative qualification to GCSE implies an acceptance that a single mathematics curriculum is a suitable preparation for students of all abilities, despite their widely differing destinations. In this paper, case studies of vocational student groups in Further Education will be used to explore students’ views of the relative merits of a GCSE mathematics course compared to one leading towards a functional mathematics qualification, in the context of their experiences in school and college. The evidence suggests that these students respond more positively to a curriculum that is related to their expected use of mathematics in the future rather than to the repetition of a subject they associate with school. The reasons for these views may provide a useful contribution to the discussion about an alternative curriculum.
Makbule Gozde Didis, Ayhan Kursat Erbas, Bulent Cetinkaya, Erdinc Cakiroglu
Faculty of Education, Middle East Technical University
Teachers’ understanding and interpretation of students’ mathematical thinking is among the important components of knowledge for teaching as often stressed by the mathematics education community. Thus, teachers should acquire and enhance their knowledge and skills for understanding and interpreting students’ thinking even before they begin their professions. In teacher preparation programs, using documentation of instructional practices such as students’ written works and video records of classroom lessons would provide prospective teachers with opportunities for in-depth exploration of students’ thinking. Thus, the purpose of this study was to investigate to what extent prospective secondary mathematics teachers enhanced their interpretation of students’ thinking when they first worked on non-routine tasks themselves as students and then examined actual solutions produced by high school students. Twenty-five prospective mathematics teachers were the participants of the study. The data sources consisted of individual reflection papers, focus group interviews and notes of prospective teachers while working on students’ work and field notes. The results showed that as a result of investigation of students’ thinking manifested in the students’ written works and video cases, prospective teachers started to question and tried to examine the details of students’ thinking and to understand students’ ways of thinking in depth.
Umeå University, Sweden; University of Oxford, UK
Three students Dan, Levi and Thor, attempt a group task containing worksheets A and B. While worksheet A asks students to calculate and compare surface area to volume ratio of a sphere for six successive units, worksheet B asks them to consider the metabolism of living cells and the bearing the ratio has on their functioning and size. While Levi and Thor own the group task, follow its instructions and deliberate on its questions, Dan declares his intention of observing Levi and Thor and takes a free ride. Based on students’ inscriptions and transcript of audio-recordings, I show how Levi and Thor work through calculations required in worksheet A with ease, even coming up with conjectures. In attempting worksheet B they are able to correlate better metabolism in cells with a smaller radius, yet question if that model is indeed borne out in reality. Three constructs from cultural-historical activity theory and/or CHAT namely leading activity, germ cell of activity and learning activity are utilised to shed light on attempts by Dan, Levi and Thor at their group task.
Dr Tim Jay, Dr Jo Rose, Dr Ben Simmons
Graduate School of Education, University of Bristol
This project focuses on parents’ funds of knowledge about how they use mathematics in informal, practical ways (for example in the home economy, in their work, and in planning activities), and how these funds of knowledge can be used to support children’s mathematical development. Research suggests that there are close connections between children’s mathematics learning, their economic literacy, and the support that they receive from parents and/or carers. We see this as an opportunity to take an innovative approach to school-home partnerships: developing the means to empower parents to make use of the everyday mathematics that they know and understand to support their children’s learning. In this paper, we report our project to investigate parents’ beliefs and feelings about their own knowledge and understanding of mathematics, and their current perceptions of their role in their children’s mathematics learning. This investigation informs a series of workshops designed to help parents find ways to support their children’s mathematics learning, drawing on parents’ social and cultural funds of knowledge.
07 Extended teacher professional development courses – feedback on the impact of undertaking MEI’s Teaching Advanced Mathematics (TAM) and Teaching Further Mathematics (TFM) courses
Stephen Lee, Sharon Tripconey and Sue de Pomerai
Mathematics in Education and Industry
Mathematics in Education and Industry (MEI) provide extensive opportunities for teachers to undertake professional development. Great value is placed on the feedback from those participating in the courses to establish their impact on the individual and their classroom practice and how they might be improved. In summer 2013 feedback was sought from the participants in the 2012/13 cohorts of two extended professional development courses: Teaching Advanced Mathematics (TAM) and Teaching Further Mathematics (TFM). Two online surveys were designed using two different pieces of online software – a 15-question instrument that considered various elements of the TAM course and a more in-depth multi-sectioned 50-question instrument for TFM. The in-built analysis tools for each piece of software were utilised for initial analysis. In this paper, an outline of the TAM and TFM courses will be given, along with a discussion of the design of the two questionnaires, their administration and reflection on participants’ feedback. Included will be consideration of how a 65% response rate was obtained for the extensive TFM survey, using a small incentive and how this contrasted to a high 85% response rate for the TAM survey, which wasn’t incentivised. Finally, the impact of these extended courses on teachers’ attitudes and developing practice through the feedback provided will be reflected upon.
Faculty of Education, Manchester Metropolitan University
This paper is based on a study carried out with a group of students doing a one-year Post Graduate Certificate of Primary Education course. During this course, the students had use of an iPad, provided by the university. The students used these to collect and analyse video evidence from their taught mathematics sessions. The aim was that this process would nurture students’ capacity to reflect upon teaching and learning in mathematics, in line with Mason’s (2002) ‘discipline of noticing’.
Institute of Education, University of London
From several years of teaching an in-service masters course ‘ Learning geometry for teaching’, a set of teacher self-report data has been accumulated that records incidences of teachers not being able to ‘see’ a theorem or geometrical relationship that they were in the middle of explaining or discussing. This paper uses a neuroscientific understanding of the self-oriented (egocentric) and other-orientated (allocentric) processing pathways in the brain as a theoretical lens to start to understand this phenomenon. It will be argued that ‘ visualisation loss mid explanation’ needs not be due to lack of teacher mathematical knowledge. The related issue of teacher defence against the discomfort of loss of geometrical insight is also raised and the question of whether a consequence of this defence might be avoiding geometrical practice in the classroom is discussed.
10 ‘Understanding mathematics in depth’: an investigation into the conceptions of secondary mathematics teachers on two UK subject knowledge enhancement courses
Liverpool Hope University
This report is of an investigation into conceptions of ‘ government founded understanding mathematics in depth’, as articulated by two specific groups of novice secondary mathematics teachers in England. Most participants in the sample interviewed have compgovernment-funded mathematics subject knowledge enhancement courses, which were devised with the aim of strengthening students’ understanding of fundamental mathematics. Qualitative data was drawn from semi-structured interviews with 21 subjects. The data reveals some key themes common to both groups, and also some clear differences. The data also brings to light some new emergent theory which is relevant in novice teachers’ contexts. To provide background context to this study, quantitative data on pre-service mathematics Postgraduate Certificate in Education (PGCE) students is also presented, and it is shown that at the university in the study, there is no relationship between degree classification on entry to PGCE and effectiveness as a teacher as measured on exit from the course. The data also show that there are no significant differences in subject knowledge and overall performance on exit from PGCE, between students who have previously followed a subject knowledge enhancement course, and those who have followed more traditional degree routes.