Proceedings of the Day Conference held at Reading University on 7th Nov 2015
Hatice Akkoç and Hande Gülbagci-Dede
Marmara University, Turkey
The aim of this study is to explore a prospective upper secondary mathematics teacher’s professional identity and how it reveals itself in
school context. Data was collected in the last year of a teacher preparation program during field experience courses in a state university in Istanbul,
Turkey. Data collection instruments are unstructured interviews, observations of lessons and post-lesson reports.
02 Bangladeshi rural secondary school girls’ participation in higher mathematics optional course: What are the influences?
K. M. Nabiul Alam
UCL Institute of Education, University of London
Previous research has shown that women are still underrepresented in the Science, Technology, Engineering and Mathematics (STEM) field compared to men in many countries, including those from the European Union and the United States but the cause remains debated (Halpern et al., 2007). The negative effect of gender stereotypes relating to women’s perceived lower ability in domains such as mathematics and reasoning is considered to be the one possible explanation for this underrepresentation. This paper reports on a pilot study based on three Focus Group Discussions (FGDs) with 30 girls of grades 9 and 10 of three rural secondary schools in Bangladesh.
University of Nottingham
This paper is based on a case from the pilot of my PhD research project with a group a secondary students. I will argue that visual representations can work as a basis for reasoning about addition of fractions for low achieving students, similarly to what was shown by Nancy Mack regarding informal knowledge for multiplication of fractions.
University of Brighton
This paper reports on the findings from a small-scale intervention study that explored developing perseverance in mathematical reasoning in children aged 10-11. The interventions provided children with representations that could be used in a provisional way and included opportunities and time to generalise and to form convincing arguments. This enabled the study group to persevere in their mathematical reasoning, from making trials and testing conjectures to forming generalisations and convincing arguments. The children reported pride in their understanding. A tentative framework describing these interactions is proposed.
05 Research into teaching problem solving to primary teacher trainees using Schoenfeld’s (1985) timeline
University of Wales, Trinity Saint David
Problem solving is at the forefront of Mathematics Education. PISA results show that pupils in Wales have poor problem solving skills.
Problem solving skills need to be taught in schools. Teachers and teacher trainees need to be able to solve problems themselves in order to teach problem solving. This small case study focussed on how problem solving can be taught to undergraduate teacher trainees and what impact it had on their own problem solving. A problem solving course was designed and evaluated. Problem solving skills were analysed, by pre and post investigations, using Schoenfeld’s (1985) timeline. Problem solving can be taught subject to certain factors e.g. knowledge of heuristics, subject
knowledge The teacher trainees’ problem solving skills changed from a novice like approach to an expert like approach with respect to Schoenfeld’s (1985) timelines. This was useful in small group situations depending on whether the students worked co-operatively or collaboratively.
Lynn Duckworth1, Steve Lawley2 and Mahnaz Siddiqui3 and Mary Stevenson3
1Childwall CE Primary School; 2St Silas CE Primary School; 3Liverpool Hope University
Maths Hubs, funded by government and coordinated by the National Centre for Excellence in Teaching Mathematics (NCETM), were set up in England 2014 to act as regional focal points for the development of excellent practice in mathematics teaching and learning (www.mathshubs.org.uk). Hubs support local ‘work groups’: activities initiated by practitioners.
07 The importance of subject knowledge for mathematics teaching: An analysis of feedback from Subject Knowledge Enhancement Courses
Ruth Edwards1, Rosalyn Hyde1, Mary O’Connor2 and Jacqueline Oldham3
1University of Southampton, 2University of Birmingham, 3St Mary’s University, Twickenham
Over the last ten years, Subject Knowledge Enhancement (SKE) programmes have become an established part of the Initial Teacher Education (ITE) landscape in England, providing the opportunity for those who do not have sufficient degree level mathematics for direct entry to Post Graduate ITE programmes the opportunity to develop their mathematics knowledge prior to undertaking teacher preparation.
University of Reading
Drawing on my doctoral research, this paper explores some of the qualitative tools used to gain a small group of girls’ perspectives on mathematics and how they make sense of their mathematical identities. It introduces a range of approaches including scrapbooking, digital photography, drawings, concept-mapping and metaphor elicitation used within a small-scale interpretive study, along with presenting some
findings and implications for practice.
09 Wider school effects of introducing a higher level mathematics course with flexible support: initial findings from case studies
Jennie Golding and Cathy Smith
UCL Institute of Education
In England entrance to mathematics-intensive courses at high status universities now usually requires achievement of a ‘Further Mathematics’ (FM) qualification as well as Mathematics A-level. Introduction in the small proportion of schools/colleges where teaching for FM is not routinely available is supported by the Further Mathematics Support Programme (FMSP).
The University of Birmingham
This study explores how a child’s competence in counting develops during the Nursery year in a state-funded primary school in central London where all of the children speak English as an additional language. For this doctoral research project I tracked the developmental journey of seven children in the Nursery setting. I carried out task-based interviews with the children over the year and evaluated their counting skills and their ability to spot counting mistakes made by a puppet when counting in a real-life context.
Rita Santos Guimaraes
University of Nottingham
The aim of my PhD research project is to investigate interventions that foster equity in teachers’ practices and also to understand why specific actions in the classroom promote more equitable learning environments. This paper is focused on what I have learnt from lesson observations and from an interview with a mathematics teacher, while she experienced a discussion group about a new approach to teach fractions. It was possible to observe changes in her practice.
Abate L Kenna
Manchester Institute of Education, University of Manchester
This paper presents a preliminary analysis of data from a doctoral pilot study that explored how maths game based learning can be used in a small group setting to support children’s development of higher order thinking skills. This research is situated in a sociocultural theory of learning. We are socialized and enculturated in our development from childhood to adulthood and share and learn aspects of our received view with key figures in our lives, for example, parents, teachers and peers (Vygotsky, 1930).
13 A look at two algebra tasks involving sequential data, that seem to prompt a scalar rather than function approach to the underlying linear relation
Dietmar Küchemann and Jeremy Hodgen
University of Nottingham
In this paper we discuss an interview undertaken by one of the authors (DEK) with a group of three Year 8 students and their teacher as part of the design research work of the ICCAMS project. The interview involved two tasks in which pairs of values connected by a linear relationship were presented sequentially, either in a table or as coordinate points on a Cartesian grid.
University of Minho, Portugal
This study investigates the effects of a teaching intervention on children’s reasoning and naming of fractions in quotient, part-whole and operator situations. A pre-test, intervention and post-test design was used with 37 six- to seven-year-olds from primary schools in Braga, Portugal. The children had not been taught about fractions in school.
15 Investigations into interpreting and constructing lesson observations of PGCE primary mathematics specialists’ lessons
University of Bristol, Graduate School of Education and Bath Spa University
I am researching the discussions that primary mathematics specialist trainees have, about the teaching and learning of mathematics, with their school-based training mentors in their PGCE year. I see developing greater awareness of these conversations as important with the move towards PGCE courses that are predominantly school based. In studying lesson observation documents my findings indicate that greater attention is given to the general running of the lesson than the mathematical content.
Leo Rogers and Sue Pope
British Society for the History of Mathematics (BSHM); Manchester Metropolitan University
In contrast to the 2007 secondary curriculum, the new English mathematics curriculum alludes only to Roman Numerals in the primaryprogramme of study. Despite the words: ‘Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems.’ in the Purpose of Study section there is no further mention of historical or cultural roots of mathematics in the aims, or in the programmes of study.
17 Cambridge Mathematics Education Project: developing a framework for students ‘deep’ understanding in Key Stage 5 mathematics
Tatiana Rostovtseva and Sharon Walker
University of Cambridge
This paper outlines the focus and activities of the Cambridge Mathematics Education Project’s (CMEP) evaluation process. In particular, it summarises the essential features of the case study research currently underway in Key Stage 5 classrooms across England. The case study research aims to evaluate the implementation of CMEP resources in classrooms, as well as investigate the types of learning environments and experiences the resources help to promote.
18 An analysis of the essential difficulties with mathematical induction: in the case of prospective teachers
Yusuke Shinnoa and Taro Fujitab
aOsaka Kyoiku University/ University of Exeter; bUniversity of Exeter
Although proof by mathematical induction (MI) is one of the important methods of mathematical proof, gaps and difficulties have been reported in mathematics education research so far. This study provides an analysis of the essential difficulties with mathematical induction that are experienced by prospective mathematics teachers. We take the notion of “mathematical theorem” proposed by an Italian research group, and use this to describe in more detail the structural understanding of MI from a theoretical standpoint. Data are collected by a set of questions based on the idea of “proof script” method. The results suggest that the difficulties of MI are concerned with prospective teachers’ understanding of logical relations which we call “sub-theorem” or “meta-theorem”.
Cathy Smith and Jennie Golding
UCL Institute of Education
Teachers in England typically begin their substantive posts with little experience of teaching advanced mathematics. This project investigates the question ‘How, and with what effects, are early career teachers inducted into teaching A-level mathematics?’ through five longitudinal case studies. Data has been collected over two years from lesson observations and interviews with teachers and department heads. Early thematic analysis suggests that A-level teaching in early career is viewed as an incentive over core teaching, a contrast that offers motivation and relief through its change of work conditions.
20 Using the Singapore Bar Model to support the interpretation and understanding of word problems in Key Stage 2
Ruth Spencer and Helen Fielding
Nottingham Trent University
The research project was conducted in a large junior school where children, normally confident with calculation, experience difficulties with the interpretation of word problems. The Singapore Bar model was chosen to provide a clear visual representation in order to support all children identifying the underlying structure of word problems, and would hopefully narrow the gap between the genders.
Manchester Metropolitan University
Inspired by the 2015 special issue of Research in Mathematics Education – ‘Mathematics teaching: tales of the unexpected’ – this paper relates ideas about contingency to the demands on primary school teachers in England to deliver a new ‘mastery’ National Curriculum. Drawing on an observation of and interview with one newly qualified teacher, Mandy, this paper explores how her ability to enact a ‘mastery approach’ is stifled by both her commitment to the established school routine for lesson planning and her lack of experience.
University of Bristol
In this small-scale study, I focus on the mathematical area of division (particularly the chunking and standard algorithms).The study takes place in a larger than average-sized, state-funded primary school in the southwest of England where the percentage of free school meals is lower than the national average. For one group of 17 low achieving students, having been taught chunking and getting confused, the standard method for short division was taught successfully.