Whose Mathematics? Whose Curriculum?
Tom Macintyre, Morwenna Griffiths with Sheila Hamilton
Introduction
Our research is a small-scale, exploratory investigation of some possible factors related to patterns of inclusion and exclusion in maths education. Varying levels of uptake may be related to what is taught, as well as how it is taught or assessed, all within the wider societal view or perception of the subject and its place in the lives of individuals. It can be difficult to separate the what and the how but this study aims to do this by placing a firm emphasis on the curriculum, as a means of evaluating the what. The aim is to determine what effect if any the curriculum has on peoples’ relationships with mathematics and how such relationships influence theirparticipation and achievement in the subject.
In Scotland there is one leading body that advises on the ‘curriculum’ both in terms of curricular coverage across a range of subjects and also within each subject discipline there are guidelines for practitioners to manage the Teaching and Learning of subjects. Curricular documents emanate from the Scottish Executive Education Department through the agency of Learning & Teaching Scotland (LTS). Curricular Guidelines on mathematical development or Subject Arrangements are available at all stages: Curricular Framework 3-5, Mathematics 5-14, Standard Grade Arrangements, National Qualification Arrangements. Each of these documents provides advise on pedagogy (the how) as well as detailed coverage of the desired content, often referred to as the Curriculum. These are recognised and accepted by practitioners as guidelines. As such they differ from the requirements of a National Curriculum as found in other parts of the UK.
Research questions:
We are interested in the relationship between perceptions of the mathematics curriculum and perceptions of identity. Naturally, we are interested in patterns of inclusion and exclusion in maths education as they relate to broad political categories such as gender, race, social class, etc. It is likely that other self-identifications e.g. as being – or aspiring to be - cool, nerdy, logical, expressive, creative, clever are also related to inclusion and exclusion. We want to focus on the secondary school where curriculum choices and attainments appear to be more powerfully correlated with such categories.
Does the mathematics curriculum in the middle years of secondary school tend to exclude pupils because of their identifications related to gender, race, class, logic, expressiveness, creativity, etc.?
We are uncertain how any perceived special difficulty of maths relates to these identifications. So this question will be kept in mind during the investigation, but itdoes not form a full research question at this stage.
For this small-scale study into how participation and achievement might be affected by curricular choices or structures it was decided to focus on the frameworks that related to the end of compulsory education: currently Standard Grade (SG). The SG Arrangements for Mathematics, as published on provide a statement of the curricular coverage for each level of study, along with detailed content lists for each of Foundation, General and Credit levels.
We look at such issues using two main sub-questions:
(1) Through different subject areas in the secondary school curriculum. Each subject area has its own stereotypes and identifications often related to political categories. Within Scottish education each subject area has responsibility for relating its curriculum to literacy and numeracy, as laid down in theStandards for Initial Teacher Education (SITE) and for Full Registration (SFR). So all teachers will have an influence on pupils’ perceptions of mathematics.
1.1How do a range of curriculum specialists in secondary teacher education perceive mathematics and mathematicians.
1.2How do they see the contributions of their subject to numeracy and to the mathematics curriculum in the broader sense?
(2) Through the curriculum content and the examples chosen to contextualise it:
Are learners able to see self or their interests represented within the text book?
Literature.
There is very little as far as we can see, actually on the curriculum. There is more on pedagogy, a division we constantly kept to the fore to ensure the focus of this project rested on the curriculum and how its presentation might affect participation and achievement. Sociological researchers (Ensor & Galant, 2002; Dowling, 1998) have expressed concern over the potentially negative impact on individuals that an agenda of integration and relevance might promote. Dowling argues that the rhetoric of integration and relevance assumes that every day experiences of all learners are the same – yet different social groups will have varying expectations. Within mathematics education there has been a gradual shift towards a utilitarian agenda, favouring functional or public mathematics, or numeracy as a subset of mathematics, at the expense of abstract or esoteric mathematics that might bring more acceptable challenges and applications for those not wishing to be restricted to a utilitarian agenda in their study of the subject (Dowling, 1998; Davis, 2001; Roper et al, 2005). Textbooks can be viewed as providing the ‘framing’ of the curriculum, as categorised by Bernstein. Through school textbooks the curriculum is exemplified for practitioners, a number of whom will rely on the textbook as the definitive document in preference to a curricular framework or programme of study (Apple, 1986; Hasan, 2000). Surprisingly little attention has been paid to this aspect of textbooks with only a few studies offering any analysis in terms of identity, participation and achievement (Dowling, 1998; Haggarty & Pepin, 2002).
Methodological approach
The approach taken is discourse analysis. Our understanding of discourse analysis is strongly influenced by MacLure (2003). She helpfully outlines a wide range of approaches, while favouring one of them. She draws a broad distinction between research focused on discourse, using broadly deconstructive methods – a discursive approach to reality – and research focused on discourse using more linguistic, content analysis. Both approaches take text as the starting point. We lean to the first, but use elements of the second in order to do so. For instance, we have used the method of counting occurrences of kinds of images or names. However we have also used deconstructive techniques such as focusing on oppositions (usually binary), and uncovering the use of metaphor.
The research is framed by a provisional and constructive epistemology. We begin by assuming the curriculum is constructed through the interaction of several discourses. Hence we have chosen more than one, intending that this would lead to open-ended and revisable conclusions. The two sources chosen are (a) mathematics textbooks and (b) the responses of specialists in a range of curriculum areas to questions related to mathematics, mathematicians and identity. We wanted to use the analysis of one source of evidence to interrogate the other in an iterative process. Thus the conclusions are always revisable because of the likelihood that two methods will not be entirely commensurable, and, also because any conclusions will be open to further dialogue with analysis drawn from other sources of curriculum discourse.
Method
Textbooks.
An analysis of text books used to deliver the curriculum was carried out,. The texts are those for General and Credit level of study, by TeeJay Publishers, namely:
General Maths 3G, General Maths 4G and Int-2-Credit Mathematics Books 1 & 2.
Another resource, looked at more briefly, is an older set of textbooks published by Blackie and Chambers. The titles Mathematics in Action 3B and 4B have been widely used by schools but these are now being replaced by practitioners with either an updated version of the same title or replacement with TeeJay series at the equivalent level.
The complexities and abstract nature of some mathematical content may be instrumental in putting some people off. However, those same complexities and abstract concepts may equally engageother people, with the attraction of the discipline being precisely that complexity and abstraction. Efforts have been made at policy level to ‘soften’ the subject with an increasing emphasis on numeracy or functional mathematics as opposed to what other might regard as real or abstract mathematics. With that background agenda, the initial analysis of the text books sought to focus on topic coverage that fell into one of those categories:
Wages & Salaries, Money (Functional mathematics)
Trigonometry (Abstract mathematics)
Within each chapter, evidence of self or interests relevant to the learners was looked for with reference made to the broad categories of inclusion from the literature. (Gender, Class, Race, Sexuality, Cool, Nerdy, Logical, Clever as discussed earlier)
Interviews
Interviews with teacher educators were semi-structured, using the following questions, each of which were probed further.
- Do you think of yourself as somebody who can do maths? (Why? What areas?)
- What do you think people who can do mathematics are like?
- How do you relate your subject to the requirements of teaching numeracy across the curriculum (SITE & SFR)?
The interviews were analysed using the following frames:
- Oppositions and comparisons.
- Metaphors
- Examples of mathematics curriculum mentioned.
- Statements about characteristics of people who can do mathematics
Biographies
Tom Macintyre (SL in School of Education) with a teaching responsibility for mathematics and education components of UG and PG programmes of Initial Teacher Education. Research interests outlined on ECME page at
Morwenna Griffiths is Professor of Classroom Learning at EdinburghUniversity. Her research interests are in social justice, philosophy, and the interaction of educational theory and practice, especially through action-research and self-study. Her recent research has included both philosophical theorising and empirical investigation, related to social justice, public spaces, the nature of practice, feminisation and creativity.
Sheila Hamilton was a researcher at the Scottish Council for Research in Education (The SCRE Centre, University of Glasgow) for many years. She is now an independent consultant. Her research has included equality issues in education and evaluations of educational initiatives in schools. Many of her research reports can be found on the SCRE website.