Geoff Wake

The association between mathematics pedagogy and learners' dispositions for university study

We address the current concerns about teaching‐to‐the‐test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of ‘transmissionist’ pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers’ self‐reported pedagogy. We then use this measure in combination with the students’ survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students’ mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.

School or college mathematics and workplace practice: an activity theory perspective

This paper reports on a case study in which we detail how a college mathematics and chemistry student struggles to make sense of the graphical output of an experiment in an industrial chemistry laboratory. The students attempts to interpret unfamiliar graphical conventions are described and contrasted with those of college mathematics. Our analysis of this draws on activity theory to assist in understanding the position of the student in both the college and the workplace. This highlights the limitations of the experience of the student at college and we question how the mathematics curriculum might be adapted to assist students in making sense of workplace graphical output.

Mathematics students’ aspirations for higher education: class, ethnicity, gender and interpretative repertoire styles

This paper reports how students talk about their aspirations in regard to higher education (HE) and their mathematics, what ‘repertoires’ they use to mediate this discourse, and how students’ predominant ‘repertoire style’ relates to their cultural background. Our analyses draw on an interview sample (n=40) of students selected because they are ‘on the cusp’ of participation or non‐participation in mathematically demanding programmes in further and higher education. The interviews explored the students’ aspirations for their future in general and HE in particular, influences on these choices, and the place of mathematics in these. Thematic analysis revealed four interpretative repertoires commonly in use, which we call ‘becoming successful’, ‘personal satisfaction’, ‘vocational’, and ‘idealist’ repertoires. Most of the sample was found to use a single, predominant repertoire, which we call their repertoire ‘style’: what is more, this style is found to be strongly related to background factors independently obtained. The implications for policy and practice are discussed.

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.

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.

Considering Workplace Activity from a Mathematical Modelling Perspective

In recent years researchers investigating the mathematical activity of workers have highlighted how this is historically and culturally situated and consequently school mathematics often seems to provide inadequate preparation for the workplace. Here I draw on two case studies to illustrate how worker activity might be (re-)interpreted from a mathematical modelling perspective and suggest that such an approach may usefully be developed to inform future curriculum development in terms of mathematical modelling.

Teachers’ Professional Learning: Modelling at the Boundaries

This paper explores teachers’ professional learning in mathematical modelling using a range of theoretical tools. The study on which it is based gives a snapshot of the work of a development group of teachers near the outset of their journey into modelling. Narrative accounts of their development in terms of both their teaching and students’ learning are analysed using an instrument developed for this purpose. The results provide insight into important issues to consider when supporting professional learning in general and modelling in particular. This small scale study points to the importance for teachers of renegotiating the didactical contract of their classrooms when introducing modelling and consequently the need for professional learning that expands their repertoires in relation to both subject knowledge and particularly pedagogy more generally.

Theory Meets Practice: Working Pragmatically Within Different Cultures and Traditions

We explore the question of how a research community focused on mathematical modeling might best inform teachers’ practices from the viewpoint of an international collaborative project LEMA which seeks to develop a teacher training program for use in different countries with their distinctive cultures and traditions. Following identification of some of the key challenges, we illustrate these from the different perspectives of three of the partners involved. Then, we seek to identify where common ground and indeed differences might be used to enrich such a project. In doing so, we invite other researchers to reflect on their perspectives developed within their own cultural settings and to consider how they might help inform teacher education programs that seek to promote mathematical modeling.

Applying mathematics in the post-16 curriculum: teacher practices, student perspectives and emerging issues

In the light of new post-16 mathematics qualifications (Free Standing Mathematics Qualifications) and their associated curriculum innovation, we report a case study that illustrates how the implementation of new qualifications in a sixth form college affects a teachers classroom practices and her students’ perceptions of, and attitudes to, mathematics. In discussing the background to, and context of, the curriculum development at the centre of this case study, we highlight the current importance of such innovation to policy makers who are seeking to develop this area of the mathematics qualifications framework. Our findings suggest that these new qualifications, as implemented in this particular case, can effect the changes that were originally desired. However, we conclude that there is a need for further substantial research that builds on this study if proposed changes to post-14 qualifications in mathematics are to be informed by knowledge of how such innovation may be successfully implemented more widely.

Educational Interfaces Between Mathematics and Industry at School Level

The paper will report on the current debate on the educational interfaces between mathematics and industry at school level. Especially the approaches, which plead for the inclusion of mathematical modelling into mathematical education at school are described. Based on this description the educational consequences for a stronger connection between mathematics at workplace and school mathematics are discussed.