Paul Hernandez-Martinez

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.

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.

Against the odds: resilience in mathematics students in transition

This paper examines ‘resilience’ of mathematics students in transition from a sociocultural perspective, in which resilience is viewed as relational and in particular as a function of the social and cultural capital students may bring to the new field. We draw on two students’ stories of transition, in which we recognise elements traditionally viewed as ‘risks’ for mathematics students in transition into institutions where new demands are made. However, in each case it seems that some of their apparent background ‘risk factors’—coming from poorer socioeconomic backgrounds and disadvantaged schools—have come to serve to constitute capital, buttressing their particular resilience, as they provide a crucial kind of autonomy that is particularly valued in the new institution. We identify the learners’ reflexivity as having been crucial to this accumulation of capital and we discuss some educational implications.

Mathematics and Its Value for Engineering Students: What Are the Implications for Teaching?.

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[1] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.

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.

Using focus groups to investigate the presence of formative feedback in CAA

The aim of this project is to examine the effectiveness of feedback offered by computer-aided assessment (CAA). CAA provides practice tests for undergraduates, and feedback to help them improve their scores and mathematical understanding. However, there is a lack of evidence-based literature on the effect of formative feedback in mathematics learning (Crockett et al. 2009), and so a desire for research to examine the effectiveness of the feedback that CAA provides (Sangwin 2007). We refer to Ramaprasad (1983), Taras (2002) and Yorke (2003) when defining formative feedback to comprise: (1) a judgement made against a given standard; (2) advice for the student to close the gap between current performance and this standard; and (3) evidence to demonstrate an improvement has been made. Mathematics undergraduates working with CAA at Loughborough University may access practice tests multiple times for a limited period usually a week prior to a summative testing period. The questions in the practice tests are similar to those in the following summative test. The CAA system marks each attempt, and returns a score with feedback for each question. Feedback usually comprises full worked solutions. We ask the following questions.

“I did use to like maths…”: Emotional Changes Toward Mathematics During Secondary School Education

This chapter seeks to explore the role of emotions in students’ dispositions toward mathematics throughout their secondary school education. Drawing on data from a recent mixed methods longitudinal study in England, we first illustrate how the concept of emotions relates to that of mathematics dispositions from a measurement perspective and then provide evidence of a clear decline in these dispositions. Further qualitative evidence shows the intrinsic role of emotions in this decline: many students expressed negative emotions toward pedagogic practices that are common in secondary mathematics education. In contrast, positive emotions were expressed in relation to pedagogies that encourage diversity of practices, often linked to a social, “relaxed” atmosphere; but these practices were scarce. The challenge is then for institutions and teachers to develop environments that allow students a variety of experiences with mathematics that facilitates socializing and connecting of mathematics to their interests, aspirations, and ways of being.

I did use to like maths

Abstract This chapter seeks to explore the role of emotions in students’ dispositions toward mathematics throughout their secondary school education. Drawing on data from a recent mixed methods longitudinal study in England, we first illustrate how the concept of emotions relates to that of mathematics dispositions from a measurement perspective and then provide evidence of a clear decline in these dispositions. Further qualitative evidence shows the intrinsic role of emotions in this decline: many students expressed negative emotions toward pedagogic practices that are common in secondary mathematics education. In contrast, positive emotions were expressed in relation to pedagogies that encourage diversity of practices, often linked to a social, “relaxed” atmosphere; but these practices were scarce. The challenge is then for institutions and teachers to develop environments that allow students a variety of experiences with mathematics that facilitates socializing and connecting of mathematics to their interests, aspirations, and ways of being.