These abstracts are of papers published in the Proceedings of the Day Conference held at University of Reading, Reading, 7 November 2015. The full research papers are available at http://www.bsrlm.org.uk/publications.html.
The aim of this study is to explore a prospective upper secondary mathematics teacher’s professional identity and how it reveals itself in the 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. The prospective teacher’s reflective writing about ‘what kind of a mathematics teacher he wants to become’ is analysed through content analysis. Among the emerging themes, three were specified for a further analysis: strong content knowledge, technology integration and use of daily life examples. These three aspects of our prospective teacher’s professional identity are explored in the school context using descriptive analysis of data from interviews, observations and reports. It was found that three characteristics of mathematics teacher identity were actualised in practice.
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 US but the cause remains debated. 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 with 30 girls of grades 9 and 10 in three rural secondary schools in Bangladesh. The thematic analysis of these data explores these girls’ attitudes towards mathematics, perceived usefulness of studying higher mathematics, their school experiences, career aspirations, and parents’ professions.
This paper is based on a case from the pilot of my PhD research project with a group of secondary students. It is shown that visual representations can work as a basis for reasoning about addition of fractions for low achieving students. Parallels are drawn to previous research regarding students' informal knowledge for multiplication of fractions.
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.
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, but teachers and teacher trainees need to be able to solve problems themselves in order to do so. This small case study focused 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, and problem-solving skills were analysed, by pre- and post-investigations, using Schoenfeld’s timeline as an analytic tool. Problem-solving can be taught subject to certain factors, for example, knowledge of heuristics and subject knowledge. The teacher trainees’ problem-solving skills changed from a novice-like approach to an expert-like approach. This was useful in small group situations depending on whether the students worked co-operatively or collaboratively.
Maths Hubs, funded by government and coordinated by the National Centre for Excellence in Teaching Mathematics (NCETM) in England, were set up in 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. This paper reports on work undertaken by a team at one university working with one of the North West Maths Hubs. Two primary teachers working in university partnership schools undertook short classroom-based research projects around themes of teaching for conceptual understanding, and use of concrete apparatus. The teachers were supported by two university ITE tutors with interests in teaching for ‘mastery’ and in teachers’ professional development. The teachers reported developments in their own thinking and practice. Also, the community of practice within the university primary mathematics partnership has been enriched though a focus on active practitioner research.
Over the last 10 years, Subject Knowledge Enhancement (SKE) programmes have become an established part of the Initial Teacher Education (ITE) landscape in England. The programme provides, 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. More recently, SKE programmes have become more diverse in terms of mode of delivery with a growth in popularity of online provision. This paper presents an analysis of feedback and evaluations from students on face-to-face mathematics SKE programmes at several institutions through consideration of Ball, Thames & Phelps’ domains of mathematical knowledge for teaching. Evaluations are considered in terms of the outcomes and benefits, including subject knowledge, of these programmes.
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.
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). This study identified four case-study schools which had recently introduced FM with the support of FMSP, and asked what the wider effects of its introduction were. Semi-structured interviews and lesson observations were used to explore teachers’ accounts. Common themes were ‘master discourses’ of introduction, effects on individual teachers and departments, and development of pedagogy. Additionally, we identified differential impacts of department leadership and of the department as a professional community.
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. I also observed the children counting in class and reviewed their class teacher’s planning and assessment of counting to triangulate the data gathered in the task-based interviews. I interviewed the parents of the children involved at the beginning of the study to establish relevant contextual information.
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, at the same time as she participated in a discussion group about a new approach to teach fractions. It was possible to observe changes in her practice. I will argue that these changes were the result of her operating in her 'innovation zone'; acting with confidence even though she was incorporating new elements into her practice. There is evidence to suggest that specific features in the discussion group fostered these changes. The features can be seen as elements to be included in professional development initiatives aiming to change teachers’ practices.
This paper presents a preliminary analysis of data from a doctoral pilot study that explored how mathematics 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. From a Vygotskian perspective, we are socialised 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. Case study data was collected during lunchtime sessions from seven Year 6 children and one teacher over a five day period. Children completed various mathematics challenges on five interactive video games and activities based upon the Year 6 national curriculum. Multiple data collection methods were used: interviews, direct observations and documents. There is some evidence in the data to show the existence of higher order thinking skills.
In this paper we discuss an interview undertaken by one of the authors with a group of three Year 8 students and their teacher as part of the design research work of the Increasing Competence and Confidence in Algebra and Multiplicative Structures (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. The students were asked to make near and far generalisations, which they tended to do by adopting a scalar (or recursive) approach, either in a step-by-step manner or by chunking. From the interviewer’s point of view, the scalar and function perspectives are intimately linked, and on occasions during the interview it was easy to believe that this was true for the students too. However, a closer examination suggests that for these students at least, the connection is still tenuous.
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. Reasoning and labelling questions were presented in the three situations in the pre- and post-test. During teaching, each intervention group learned about fractions in only one of the three situations. Children who were taught in the quotient situation made significant progress in the reasoning and naming fractions, but did not transfer this learning to the other situations. Children taught in the part-whole or in the operator situations only learned how to label fractions, showing no progress on reasoning items. However, they used the labels in both part-whole and operator items. Thus these situations affect differently children’s understanding of fractions.
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 Post-Graduate Certificate in Education (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. Given that lesson observations and subsequent feedback sessions provide an opportunity for mentors and trainees to discuss the teaching and learning of mathematics, the written documents suggest that talk about mathematical content may be limited. This paper may be helpful for others interested in changing their documentation of mathematics lessons in support of the development of primary mathematics specialists.
In contrast to the 2007 secondary curriculum, the new English mathematics curriculum alludes only to Roman numerals in the primary programme of study. Despite the statement "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. The increased expectations for lower and middle attainers in the new curriculum challenge teachers to make more mathematics accessible and memorable to more learners. The history of mathematics can provide an engaging way to do this. There are also opportunities in post-16 mathematics. We use quadratic equations to illustrate some of the ways that history of mathematics can enrich teaching of this topic.
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.
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 MI 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'.
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. Participants report distinct demands in preparation but also that they develop insights into the complexities of teaching and learning, and gain from rehearsing complex activities. Development of A level teaching relies on key messages and informal teacher conversations, often more focused on managerial aspects than mathematics pedagogy.
This research 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. The areas in which it was most commonly used were problems involving fractions, 2-step money problems and division. It was found that children valued the model more in areas of mathematics that were difficult and new to them, and where they felt less confident.
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, 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. Unexpected events from her lesson are described and related to the concept of contingency as outlined in the special issue and the question is asked: is a well-rehearsed response repertoire necessary for teaching for ‘mastery’?
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 south-west 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. Six months later, when given free choice every child chose the standard method and they got the questions correct. Nine higher achieving students were taught chunking successfully but not taught the standard method. Six months later, given a free choice, they were still using the chunking method successfully. With the current focus on fluency and mastery, I am interested in whether there is a need for pupils to learn ‘why’ before ‘how’ (conceptual or procedural) or vice versa.