Geoff Wake

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.

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.

The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.

... Use of ICT. ... Speaking about a maths activity to the class Figure 8: How AS Use of Mathematics students perceive taking part in group work and discussing and talking about mathematics with others compared with their previous experience when studying GCSE These ...

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.

We describe the development of a curriculum construct ‘general mathematical competence’ which we have used in curriculum development of teaching materials in vocationally focused post-16 courses. This construct is designed to bridge the academic/vocational divide in the U.K. education system. It is now being used to define an assessment and accreditation system for applied mathematics units which are intended to attract students from both sides of this divide to study mathematics as an option.

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.

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 student's 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.

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.

We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view. We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that ‘open boxes’, we ‘outsiders and boundary-crossers’ sought to expose contradictions between College and work, induce breakdowns and identify salient mathematics. Typically, we find that mathematical processes have been historically crystallised in ‘black boxes’ shaped by workplace cultures: its instruments, rules and divisions of labour tending to disguise or hide mathematics. These black boxes are of two kinds, signalling two key processes by which mathematics is put to work. The first involves automation, when the work of mathematics is crystallised in instruments, tools and routines: this process tends to distribute and hide mathematical work, but also evolves a distinct workplace ‘genre’ of mathematical practice. The second process involves sub-units of the community being protected from mathematics by a division of labour supported by communal rules, norms and expectations. These are often regulated by boundary objects that are the object of activity on one side of the boundary but serve as instruments of activity on the other side. We explain contradictions between workplace and College practices in analyses of the contrasting functions of the activity systems that structure them and that consequently provide for different genres and distributions of mathematics, and finally draw inferences for better alignment of College programmes with the needs of students.

We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson; Lakoff & Nunes; and Schon, to formulate a perspective on mathematical models and modelling and show how dialogues can manifest (i) application of ‘dead’ models to new contexts, and (ii) generative modelling. In particular, we draw in some depth on one case study of the use of a double number line model of the ‘gas day’ and its mediation of communication within two dialogues, characterised by inquiry and pedagogical discourse genres respectively. In addition to spatial and gestural affordances due to its blend of grounding metaphors, the model translates between workplace objects on the one side and spreadsheet-mathematical symbols on the other. The model is found to afford generative constructions that mediate the emergence of new understandings in the dialogues. Finally we discuss the significance of this metaphorical perspective on modelling for mathematics education.