Proceedings of the Day Conference held at University of Brighton, Saturday 12th November 2016
01 Prospective mathematics teachers’ views on pedagogical affordances of dynamic geometry systems for understanding geometry theorems
Marmara University, Turkey
This paper explores prospective mathematics teachers’ views on pedagogical affordances of using technology for understanding geometry at upper secondary level. The study was situated within a four-year teacher preparation program in Turkey. Participants are eleven prospective mathematics teachers who worked in groups of twos and threes. Each group was asked to select and investigate two Geometry theorems one of which was an extra-curricular theorem. They prepared a report which reflected on pedagogical affordances of investigating geometry theorems and their proofs in Geogebra environment, finding different themes for affordances of extra-curricular theorems.
Christian Bokhove, University of Southampton
Edward Redhead, University of Southampton
Prior research indicates that spatial skills, such as Mental Rotation Skills (MRS), are a strong predictor for mathematics achievement. Other studies have shown that MRS can be instilled through training and that they are a good predictor of another spatial skill: route learning and wayfinding skills. This paper explores these assumptions and reports an experiment with 43 undergraduate psychology students from a university in the south of England. Participants were randomly assigned to two conditions. Both groups were given pre- and post-tests on wayfinding in a maze. Results indicated that the intervention group decreased the length of time needed to complete the task, but that the results were not significant.
Alison Borthwick & Micky Harcourt-Heath
For 10 years we have collected year 5 children’s calculation question responses. We examine the range of strategies used and the success of each strategy. This paper continues this research with a sixth data set. Like the previous research we have collated the proportions of children who are successful and explore the strategies employed. This study also includes examination of responses from a small group of children from the same class to consider how successful they are across the four calculation strategies.
04 Working Group report: Building and sustaining active research collaborations with teachers of mathematics
Alison Clark-Wilson and Gill Adams
UCL Institute of Education and Sheffield Hallam University
The BSRLM working group met for the third time to explore collaborations between teacher and researchers in the processes of doing, reflecting upon and engaging with the findings, of mathematics education research. Following a brief presentation of the main findings from the recent ICME Survey on ‘Teachers working and learning through collaboration’ the group divided to address two discussion topics. The first concerned the opportunities for researchers to collaborate with teachers and schools as active participants in research studies.
05 Exploring prospective mathematics teachers’ professional identities through communities of practice framework: Post-lesson reflection report technique
Hande Gülbağcı-Dede and Hatice Akkoç
Marmara University, Turkey
The aim of this study is to investigate prospective mathematics teachers’ professional identities by analysing their post-lesson reflection reports. The study was conducted in a teacher preparation program in a state university in Istanbul, Turkey. Participants of the study are 21 upper secondary prospective teachers who taught a total of 45 lessons in two partnership schools. Data source of this study is 33 post-lesson reflection reports. They were analysed using content and descriptive analysis. Three constructs of communities of practice framework were explanatory for revealing approaches: engagement, imagination and alignment.
Jenni Ingram and Nick Andrews
University of Oxford
There are three common algebraic methods for solving quadratic equations in UK classrooms: factorising; completing the square; and using the quadratic formula. However research shows that internationally students tend to choose to use the quadratic formula, even when the quadratic equation is given in factorised form. As teacher educators, we were interested in the methods used by teachers. In this paper we explore the decisions student teachers make when solving quadratic equations using three tasks.
Dietmar Küchemann and Jeremy Hodgen
University of Nottingham
The rectangular array is widely regarded as a key model for developing an understanding of multiplication. It can provide insight into the structure of multiplication and make visible its commutative and distributive properties. Also, as the array evolves into the area model, it can aid the shift from multiplication with whole numbers to multiplication with rationals. However, research literature on primary school children suggest that getting to grips with the structure of the array is far from trivial. Our work with secondary school students suggest that we tend to underestimate these difficulties and move on from the array too quickly.
08 Learning calculus: Derivative as a difference quotient, a limit and as a function, some historical origins and pedagogical considerations
Leo Rogers1 and Sue Pope2
1British Society for the History of Mathematics (BSHM); 2Manchester Metropolitan University
Calculus is at the heart of advanced school mathematics. This branch of mathematics has a rich and fascinating history that can enrich learning and humanise what is too often perceived as a set of routines for completing exam questions with little appreciation of how these techniques have developed over time and the sophisticated mathematical concepts underpinning them. We draw on notions of threshold concepts and troublesome knowledge to consider the pedagogical implications.
Suja Sivadasan*, Helen Thouless#, Pablo Mayorga* and Sue Gifford*
* School of Education, University of Roehampton, London
Across schools in the United Kingdom, it is common for teachers to identify children as having significant difficulties with mathematics. The authors’ experiences in schools suggest that, despite interventions, these children continue to have significant mathematical difficulties. Currently there is little research and a lack of agreement across literature as to the characteristics of children who have significant mathematical difficulties, and the aspects of mathematics that those children find difficult. In this paper, the authors provide a preliminary review of the literature in this field and propose a study in UK primary schools to address the gaps identified.