Research in Mathematics Education Volume 13, Issue 2, 2011
[ISSN 1479-4802 (Print), 1754-0178 (Online)]
Special Issue: Deepening engagement in mathematics in pre-university education
The latest edition of Research in Mathematics Education - the Official journal of the British Society for Research into Learning Mathematics - brings together articles that emanate from the Transmaths research project Keeping open the door to mathematically demanding courses in Further and Higher Education that researched students and mathematics in transition through college. You can find the following papers here.
Introduction to the Special Issue: deepening engagement in mathematics in pre-university education
At a time when many countries wish to improve their capacity in terms of scientifically and technologically educated young people, mathematics has an increasingly important role to play in support of this agenda. International studies tend to lead to headlines about performance and achievement, but widening participation in mathematics requires more than this. Fundamentally, we need students to develop positive dispositions towards mathematics and continued study of the subject. The articles brought together in this special issue explore underlying issues reporting on the work of a research project that focused on two different programmes of mathematical study in the first year of post-compulsory study in England. The wide-ranging work that is reported provides timely insights, through both quantitative and qualitative lenses, as students in transition negotiate their identities as young people in general, and in relation to mathematics in particular.
Wake, G. (2011) Introduction to the Special Issue: deepening engagement in mathematics in pre-university education. Research in Mathematics Education 13:2, pages 109-118.
Students' views on their transition from school to college mathematics: rethinking ‘transition’ as an issue of identity
We examine the transition from school (compulsory education) to college (post-compulsory/pre-university) of students who are continuing their mathematical education. Previous work on transition between institutions suggests that transitional problems can be critical, and students often regard mathematics as ‘difficult’ during transitional periods. However, our analysis of students' interviews showed a more positive discourse, one of reported challenge, growth and achievement; transition was not seen as an obstacle but as an opportunity to develop a new identity. Particularly in relation to mathematics, this was reflected in a need for a better understanding of the subject, and for being more responsible for their learning. Thus, we propose to re-think transition as a question of identity in which persons see themselves developing due to the distinct social and academic demands that the new institution poses. Conceptualising transition in this way could have important practical implications for the way that institutions support students' transition.
Hernandez-Martinez, P., Williams, J., Black, L., Davis, P., Pampaka, M. and Wake, G. 2011a. Students’ views on their transition from school to college mathematics: Rethinking ‘transition’ as an issue of identity. Research in Mathematics Education 13:2, pages 119–30.
Teachers telling tales: the narrative mediation of professional identity
This paper draws on the biographical narratives of two mathematics teachers who describe themselves as ‘traditional’ and ‘connectionist’ teachers respectively. Holland et al.'s amalgam of Bourdieu, Vygotsky and Bakhtin, including ‘figured worlds’, ‘positionality’, ‘self-authoring’, and ‘world-making’ is used to examine these narratives. Differences between the two narratives include (i) their histories of compliant or oppositional identities as learners, and subsequently as teachers; (ii) their different experiences of ‘understanding’ and ‘tricks’, and (iii) their different use of figures as role models or anti-heroes in their self-authoring as teachers. It is argued that these narratives might ‘make worlds’ and provide future teachers in turn with figures for their own professional identity work.
Williams, J. (2011) Teachers telling tales: the narrative mediation of professional identity. Research in Mathematics Education 13:2, pages 131-142.
Figures in our worlds: a response to articles by Hernandez-Martinez et al. and Williams
Etienne Wenger, (2011) Figures in our worlds: a response to articles by Hernandez-Martinez et al. and Williams. Research in Mathematics Education 13:2, pages 143-146.
Enrolment, achievement and retention on ‘traditional’ and ‘Use of Mathematics’ pre-university courses
This paper investigates enrolment, attainment and drop-out rates for two different English pre-university advanced mathematics, AS-level, courses, a ‘traditional’ and an innovative ‘Use of Mathematics’ pre-university course. Very different student profiles were found for those enrolled on each course, and a model of attainment at the pre-university level showed a relatively complex relationship with prior achievement at the end of compulsory schooling. Although those pupils who had relatively high prior achievement tended also to achieve relatively highly on the pre-university courses, this relationship was not evident for lower scores. Those pupils with ‘mid-range’ prior attainment tended to make the smallest gains. Taking prior attainment into account, the difference in attainment outcomes between the two courses is small. However, these courses do differ with respect to the number of students retained, with the ‘Use of Mathematics’ course retaining a significantly higher proportion of the students. Contextual factors are discussed, suggesting implications for policy and practice in mathematics education.
Graeme D. Hutcheson, Maria Pampaka & Julian Williams, (2011) Enrolment, achievement and retention on ‘traditional’ and ‘Use of Mathematics’ pre-university courses. Research in Mathematics Education 13:2, pages 147-168.
Measuring mathematics self-efficacy as a learning outcome
We report the construction and validation of a self-report ‘Mathematics self-efficacy (MSE)’ instrument, designed to measure this construct as a learning outcome of students following post-compulsory mathematics programmes. The sample ranged across two programmes: a traditional preparation for university study in mathematical subjects (Advanced level) and an innovative ‘modelling’-based programme intended to widen participation in mathematics through use of technology and coursework. We report Rasch measurement and Generalised Linear modelling analyses of large scale survey data, and occasionally we draw on learners' interviews for triangulation. We found that MSE is related to students' mathematical attainment and gender, as well as their dispositions to further study mathematics. We also show significant differences between students' development of MSE in the two programmes. In conclusion, we propose that MSE deserves further attention as a measure of valued learning outcomes.
Maria Pampaka, Irene Kleanthous, Graeme D. Hutcheson & Geoff Wake, (2011) Measuring mathematics self-efficacy as a learning outcome. Research in Mathematics Education 13:2, pages 169-190.
The way forward for mathematics 16–19? A response to articles by Pampaka et al. and Hutcheson et al.
Margaret Brown, (2011) The way forward for mathematics 16–19? A response to articles by Pampaka et al. and Hutcheson et al.. Research in Mathematics Education 13:2, pages 191-195.
Mathematics coursework as facilitator of formative assessment, student-centred activity and understanding
We seek to illuminate reasons why undertaking mathematics coursework assessment as part of an alternative post-compulsory, pre-university scheme led to higher rates of retention and completion than the traditional route. We focus on the students’ experience of mathematical activity during coursework tasks, which we observed to be qualitatively different to most of the other learning activities observed in lessons. Our analysis of interviews found that these activities offered: (i) a perceived greater depth of understanding; (ii) motivation and learning through modelling and use of technology; (iii) changes in pedagogies and learning activities that supported student-centred learning; and (iv) assessment that better suited some students. Teachers’ interviews reinforced these categories and highlighted some motivational aspects of learning that activity during coursework tasks appears to provide. Thus, we suggest that this experience offered some students different learning opportunities, and that this is a plausible factor in the relative success of these students.
Paul Hernandez-Martinez, Julian Williams, Laura Black, Pauline Davis, Maria Pampaka & Geoff Wake, (2011) Mathematics coursework as facilitator of formative assessment, student-centred activity and understanding. Research in Mathematics Education 13:2, pages 197-212.
Looking back, looking forward: valuing post-compulsory mathematics education
This final article of the special issue looks back on our work on the ESRC projects, especially Keeping Open the Door to Mathematically-Demanding Courses in Further and Higher Education (published here and elsewhere), and looks forward to that of the ‘Transmaths’ projects under way – a collection of work on post-compulsory mathematics education during adolescence. I argue that this phase of mathematics education is dominated by two factors. First, there is the ‘value’ of mathematics to the learner and to society at large, which shapes all choices, decisions and strategies. Second, there is the fact of adolescence and the special demands on mathematics education this poses, for theoretical thinking, for identity, and for relationships. In our project, we adopted mixed methods approaches to capturing the ‘whole person’ of the mathematics learner (and teacher): their sense of self and motivation, their disposition to learn mathematics, and their mathematics self-efficacy. The key contradiction that emerges is that, between the use and exchange value of mathematical knowledge, whether for the learner, the teacher, the institution, or wider society and culture. I discuss the prospects for a theory of value in Activity theory and in Bourdieu's sociology.
Julian Williams, (2011) Looking back, looking forward: valuing post-compulsory mathematics education. Research in Mathematics Education 13:2, pages 213-221.
The Transmaths website has been developed as part of the project:
Promoting participation and engagement in post-compulsory mathematics education for STEM
ESRC Award: RES-189-25-0235