Proceedings of the Day Conference held at the Leeds University on 11 Jun 2011
Stephen Broughton, Paul Hernandez-Martinez, Carol Robinson
Mathematics Education Centre, Loughborough University
First-year mathematics undergraduates were asked about their experiences of using computer-aided assessment (CAA) in their mathematics modules. It forms a small component of their summative scores in some modules. The aims of these focus groups were to establish how students use CAA systems and how they respond to its feedback. This paper discusses why these should be of interest, how students responded, and the implications on future work.
University of Manchester
Bertrand Russell famously talked of mathematics as possessing an ‘austere beauty’. It would seem though that the capacity to appreciate the aesthetic aspects of our field is not necessarily the preserve of the mathematical elite. Indeed, a number of educators believe that such considerations have, in conjunction with various cognitive factors, the potential to play a significant role with respect to the student learning of mathematics in the classroom. We consider here the notion of the mathematical aesthetic within this context, drawing on the work of a number of key thinkers in this area. Our preliminary explorations focus on a number of lesson observations, and the intention at this stage is merely to ascertain whether or not aesthetic considerations are playing any part in students’ mathematical development in the classroom. We provide a brief discussion of our findings thus far, highlighting potential issues and dichotomies that would appear to arise as a consequence of the current climate of test-score-driven schooling.
03 The use of conversation analysis in identifying creative approaches to mathematical problem solving
University of Wales, Newport
Techniques of conversation analysis have been used in an effort to better understand the thought processes of adults engaged in a range of mathematical tasks. Participants were asked to provide a commentary during problem solving, in a non-judgmental environment with minimum intervention from the researcher. Interesting outcomes from the work are: an inability to link arithmetic and algebra in problem solving, a lack of specialised mathematical vocabulary, misuse of standard algorithms which have been learned in a superficial manner without full understanding, and a preference for justification by concrete example rather than through abstract reasoning. Distinct differences in approach to problem solving are observed between participants with different preferred learning styles.
Paul Hernandez-Martinez, Loughborough University
Julian Williams, University of Manchester
Valerie Farnsworth, University of Leeds
Our Transmaths projects aimed to understand how different practices in mathematics during the transition to higher education impact on students’ dispositions and identity and influence their future success in mathematically demanding subjects. In this paper, we discuss three examples of university transition support mechanisms and how these seem to be helping students, in particular, those who are considered mathematically weak, to make a successful transition into university. We discuss implications for pedagogy, curriculum and institutions.
05 The development of Taiwanese students’ understanding of fractions: A problem-based learning approach
University of Cambridge, UK
Problem-based learning (PBL) was first implemented in medical education at the McMaster University in Canada in the late 1960s. Now, we are seeing an explosion in the use of PBL in its various adaptations across many levels and subject areas. This paper outlines some preliminary findings from a one-year PBL teaching intervention on students’ understanding of fractions in a Taiwanese fifth-grade mathematics classroom. The purpose of the study is twofold. Firstly, it seeks to investigate the process of implementing PBL in the context of a Taiwanese elementary school. In doing so, it aims to help others to gain some usable insight by showing them this intervention as it really was. Secondly, it aims to understand what impacts a series of PBL intervention has on the students’ understanding of fractions and to add to the knowledge base on the teaching and learning of fractions.
Dr Ray Huntley
University of Gloucestershire
This paper reports on the findings of a doctoral study exploring primary trainee teachers’ choices of mathematical examples and the relationship between this and their mathematical subject knowledge. Through a combination of interview analyses and lesson plans gathered from the final school placement of one cohort of Bachelor of Education trainees, some approaches appear to be commonly held by trainees about the nature and purpose of examples in the planning and teaching process. This paper presents the research design and summarises the outcomes from the data.
Jenni Ingram, Mary Briggs, Keith Richards and Peter Johnston-Wilder
University of Warwick
The nature of mathematics, the nature of beliefs about mathematics and what it means to learn mathematics have long been discussion points in mathematics education (Thompson 1984; Boaler, Wiliam and Zevenbergen 2000). The research discussed in this paper focuses on what is said in the classroom during whole class teaching episodes. Using transcripts from two secondary mathematics teachers, we examine how the learning of mathematics is discursively constructed by the teacher and his/her pupils. This conversation analytic approach uses only the content of the interaction to describe the nature of mathematical activity in that interaction. We cannot directly access the beliefs of teachers and pupils, but an examination of how they talk about mathematics reveals how the learning of mathematics and classroom mathematics can be jointly constructed by a teacher and his/her class in quite different ways.
Department of Education and Professional Studies, King’s College London
‘Ability’ is a powerful ideology in UK education, underscoring common practices such as setting. These have well-documented impacts on pupils’ attainment and attitude in mathematics, particularly at the secondary school level. Less well understood are the impacts in primary mathematics. Further, there are a number of consequential practices of an ability ideology which may inhibit pupils’ learning. This paper uses data from one UK primary school drawn from my wider doctoral study to elucidate three such consequential practices. It examines why these issues arise and the impacts on pupils. The paper suggests that external pressures may bring practices previously seen in secondary mathematics into primary schools, where the environment intensifies the impacts on pupils.
Goldsmiths, University of London
In this paper I raise questions about the role of progress within mathematics education. I look at how progress defines a linear and teleological relationship between the past, present and future. This idea then sets the parameters within which researchers, policymakers and practitioners work in mathematics education, constraining the questions that we ask, the answers that we give and the actions that we take in the present. I suggest some alternatives to the progressive narrative of past-present-future as perhaps the only way not to answer ‘yes’ to the question: does mathematics/education make things better?
Department of Education and Professional Studies, King’s College London
i-Pads in front of the children in networked classrooms have the potential to transform learning. In mathematics particularly, interaction by screen-touch using fingers or stylus seems preferable to keyboard and mouse. Their portability and reliability, so that children can take them home, and their potentially low price, are other attractions. It is proposed that to maximize their potential to improve learning, the Tablets should be configured so that they emulate workbooks -combining textbook, exercise book, test-paper and progress record -and be embedded in a school-wide managed learning environment that combines effective learning management support for class teachers with safe-keeping of students work and records.
11 The English assessment regime: how consistency and standards stifle innovation and improved validity for the assessment of mathematics
Liverpool Hope University
This paper describes the national assessment regime for mathematics in England for 5 to 16-year-olds which is the basis of school accountability. Most of these assessments comprise timed written tests or exams that are designed to assess the statutory national curriculum programmes of study. For pre-16 learners, the assessments are developed nationally, and teacher assessment is reported alongside test outcomes. There is considerable evidence that teachers are over-reliant on the tests and adjust their assessment to match that of test outcomes. At age 16 independent commercial organisations (awarding organisations) develop public examinations (GCSEs) in a regulated marketplace. There is fierce competition between awarding organisations to gain and maintain market share. The regulatory system for the development of tests and exams and maintenance of standards is rigorous but restricts innovation and improvements in validity.
University College Plymouth, St Mark and St John
This is the first part of a project to explore the factors influencing life-long engagement in mathematical activity. In preparation for the first phase, involving semi-structured interviews, I propose a draft version of a construct for ‘disposition’ with four components; beliefs / values / identities; affect / emotion; behavioural intent / motivation; needs. I discuss this in the following brief account, which also draws upon the discussion from the conference session which highlighted the need for clarity and specificity in the use of terms such as ‘attitude’, ‘disposition’ and ‘motivation’.