Mathematics

This chapter discusses mathematics. It is part of a collection which examines educational practice and professional thinking from pre-school and primary, through secondary, further and higher education; and locates Scottish education within its social, cultural and political context

On structures in hypergraphs of models of a theory

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types of models of a theory, are given

Signalizers in groups of Lie type

We classify all CG(t)-signalizers, where G is a finite group of Lie type and t is an automorphism of G of prime order s > 3. Our results extend existing work by Korchagina ([Ko], [Ko2])

'They don't use their brains what a pity': school mathematics through the eyes of the older generation

The paper considers issues in the teaching of mathematics from the viewpoint of a group of people aged 75 and over. Drawing on written accounts of their use of and attitude to mathematics, extracts are identified in which they reflect on their own experiences of learning mathematics at school or give their views on more recent mathematics education. Common themes are mental arithmetic and the use of calculators. Most respondents report positive assessments of their own mathematics education and reservations about more recent systems. Some accounts display inaccurate views of current practices in mathematics teaching and possible reasons for this are considered

“Not Like a Big Gap, Something We Could Handle”: Facilitating Shifts in Paradigm in the Supervision of Mathematics Graduates upon Entry into Mathematics Education

Mathematics is the discipline that a significant majority of most incoming researchers in mathematics education have prior qualifications and experience in. Upon entry into the field of mathematics education research, these newcomers–often students on a postgraduate programme in mathematics education–need a broadened understanding on how to read, converse, write and conduct research in the largely unfamiliar territory of mathematics education. The intervention into the practices of post-graduate teaching and supervision in the field of mathematics education that I describe here aims at fostering this broadened understanding and thus facilitating newcomers’ participation in the practices of the mathematics education research community. Here I outline the theoretical underpinnings of the intervention and exemplify one of its parts (an Activity Set designed to facilitate incoming students’ engagement with the mathematics education research literature). I supplement the discussion of the intervention with comments sampled from student interview and student written evaluation data as well as observations of the activities’ implementation. The main themes touched upon include: learning how to identify appropriate mathematics education literature; reading increasingly more complex writings in mathematics education; coping with the complexity of literate mathematics education discourse; working towards a contextualised understanding of literate mathematics education discourse. I conclude with indicating the directions that the intervention, and its evaluation, is currently taking and a brief discussion of broader implications, theoretical as well as concerning the supervision and teaching of post-graduate students in mathematics education

Categories without structures

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.Comment: 28 page

A nodes model for creativity in mathematics education

This paper sets outs a proposition for a model of understanding creativity in the mathematics classroom. It aims to show that creativity in mathematics can be conceptualised as the mental processes involved in ‘meaning making’ in the mathematics classroom. It is currently primarily a conceptual exploration, with only preliminary empirical investigation, however it is hoped that this is to be addressed in the coming academic year. The paper comes from more formal conceptual development of an informal discussion about what creativity in mathematics actually is between the author and a number of researchers at University of Durham. A variety of ideas were put forward, and while there was little consensus on what creativity in mathematics is, there was agreement on what creativity in mathematics is not – creativity in mathematics is not about making classroom mathematics ‘shiny’. While colourful displays and beautifully drawn graphs were useful in themselves, this did not, the group concluded, constitute creativity in mathematics. Similarly, while setting project work could be considered creativity in mathematics it wasn’t necessarily. It was agreed that there was something more fundamental about what creativity in mathematics may be. This nodes model takes one of the ideas discussed and is an attempt to describe what this ‘more fundamental’ aspect may be

Conceptions, language, culture and mathematics and the New Zealand curriculum.

In this paper we explore two conceptions of mathematics that are evident in literature. Mathematics as a static body of knowledge is one conception, and another is of mathematics being an endeavour that is constructive and creative. With the release of The New Zealand Curriculum (Ministry of Education, 2007), we formalised our ongoing debates about these conceptions by constructing and using metaphors to explore and refine our ideas. In some parts of the curriculum document, there is juxtaposition with a conception of mathematics being social, constructive and creative. However, other aspects of the document appear to reflect the conception of mathematics as a body of knowledge. We express a concern that this latter conception of mathematics may become privileged over other possibilities. We therefore explore what constructive, creative mathematics might look like in a classroom

Which qualities did aspiring teachers value in their ‘best’ mathematics teachers?

When aspiring mathematics teachers were asked to describe one of their own mathematics teachers who had made an impact on them it was found that personal attributes such as empathy, caring and commitment to their students were mentioned most often. This study uses Gossman’s categories of ‘teacher as teacher’ and ‘teacher as person’ to analyse the descriptions of best teachers given by people who were being interviewed for the Post Graduate Certificate in Education in Secondary Mathematics at our Institution. The aim of this study is to add to the growing body of literature which indicates the value of teachers’ personal attributes and how important these can be for student motivation and confidence in mathematics. These attributes are hardly mentioned in lists of teacher competencies compiled as part of Government standards for teachers. We expected that aspiring mathematics teachers, since they are most likely to have been successful at mathematics themselves, would feel positively about mathematics and their mathematics teachers. However a surprising finding from the data was that even successful students occasionally experienced disaffection