Tony Croft

Safety in numbers: mathematics support centres and their derivatives as social learning spaces

This article reports on data gathered from second and third year mathematics undergraduates at two British universities which have developed Mathematics Support Centres, primarily with a view to supporting skills development for engineering students. However, an unforeseen consequence of the support centres was the mathematics students’ colonisation of the physical space, and the development of group learning strategies which involve a strong community identity. Drawing on a socio‐cultural theoretical framework, based primarily in the concept of a figured world, the article explores the students’ perceptions of mathematics learning and their experiences of university‐level teaching, focusing on the ways in which they collectively build images of themselves as participants in an undergraduate mathematics community, resourced by the physical safe spaces that they have created, and which they now regard as essential sites of their learning.

Dealing with ‘fragile identities’: resistance and refiguring in women mathematics students

Many learners may be successful in mathematics but nevertheless see themselves as existing only on the margins of the practice, or as lacking stability in it – in this sense, they have what can be called a fragile identity. Although this kind of relationship with mathematics is not limited to girls and women, they do appear to express such fragile identities more often or more readily. Drawing on qualitative and quantitative data from undergraduates in three English universities, this paper presents an analysis of the way in which university mathematics is differentially experienced by men and women, and of the part this may play in women’s ongoing narratives of self as mathematicians. It is suggested that some women resist traditional positionings in the mathematics world, drawing on local resources which enable a sense of agency as successful students and a refiguring of their relationships with mathematics.

Can peer assisted learning be effective in undergraduate mathematics

We report the implementation and evaluation of a ‘peer assisted learning’ (PAL) scheme designed to reduce the so-called ‘cooling off’ phenomenon in undergraduate mathematics. ‘Cooling off’ occurs when mathematics undergraduates lose motivation and interest in their studies, despite having previously actively chosen to study it at higher levels. We found that, despite concerns about the novel didactic contract inherent in PAL schemes, a majority of students chose to engage with the scheme, and that the student leaders of the PAL sessions were generally capable of implementing a student-centred pedagogy. Furthermore, we found that students who attended the PAL sessions had higher achievement in their final examinations, even after controlling for their lecture attendance and prior attainment. We conclude by arguing that PAL may provide a useful mechanism for reducing the prevalence of the ‘cooling off’ phenomenon in some – but not all – groups of mathematics students.

'I'm worried about the correctness: undergraduate students as producers of screencasts of mathematical explanations for their peers ¿ lecturer and student perceptions

Undergraduate mathematics is traditionally designed and taught by content experts with little contribution from students. Indeed, there are signs that there is resistance from mathematics lecturers to involve students in the creation of material to support their peers – notwithstanding the fact that students have been successfully engaged as co-creators of material in other disciplines. There appears to be little research into what issues may lead to reservations to using student-created content in mathematics learning. This paper takes a case study approach to investigate the reasons for lecturers’ resistance to undergraduate student contributions to learning material, in particular with a view to the production of screencasts of mathematical explanations. It also investigates the views of students producing mathematical screencasts. This study is part of a larger research project investigating undergraduate involvement in mathematics module design. Four second-year students, who were producing mathematics screencasts as part of an internship, and five academics, were interviewed to gain an understanding of their views of the value of student screencasts. The interviews focused on the particular contributions students make to screencasts, outcomes for the students and level of lecturer acceptance of these resources. We argue that students benefit from creating screencasts for their peers by gaining deeper mathematical understanding, improved technological skills and developing other generic skills required of todays graduates. In contrast, we confirm lecturer resistance to using student-generated screencasts in their teaching materials. Lecturer reservations pertain to students’ lack of mathematical maturity and concerns over the mathematical integrity of the content that students produce. We conclude that close collaboration between students and lecturers during the design and production phases of screencasts may help lecturers overcome reservations, whilst preserving the benefits for students. In addition, we provide evidence that the process is a valuable professional development opportunity for the lecturers themselves.

Reshaping understandings of teaching-learning relationships in undergraduate mathematics: An activity theory analysis of the role and impact of student internships

This article presents an analysis of an intervention intended to address an aspect of undergraduate mathematics education that is frequently described as a situation of deadlock, between second-year undergraduates who are disillusioned with their university mathematics experience, and mathematics departments which describe many students as lacking interest in, and awareness of, the nature of university-level mathematics and how it is learned: whilst departments strive to support such students, the extent to which they can do so is often seen as limited. The SYMBoL project was designed to address this situation in terms of improving dialogue between students and staff through the introduction of undergraduate internships which challenged traditional hierarchical roles and relationships. Using third generation activity theory to analyse the nature and impact of the internship role, we show how the project legitimised the student voice as channelled through that of the interns, created shifts in perceptions of the problem, and began a process of transformational learning about possibilities in undergraduate mathematics teaching. We consider the implications for developing university mathematics teaching within the wider context of tensions across university systems.

Engineering students’ self-confidence in mathematics mapped onto Bandura’s self-efficacy

Abstract In the UK since the early 1990s, there has been widespread concern and extensive reporting about the difficulties encountered by engineering students with the mathematical elements of their university courses. Students’ lack of previously expected mathematical skills is of particular concern and has prompted the provision of mathematics support in many UK institutions. A related problem is students’ lack of self-confidence (or self-efficacy) in their mathematical capability, and this paper seeks to explore how this has arisen and how it affects students’ learning, and proposes suggestions for improvement. Interviews were conducted with final year engineering students at Harper Adams University College in 2009. These explored students’ experiences of and self-confidence in learning and using mathematics before and during university and what they anticipate in the future. The seven students interviewed exhibited a range of self-confidence and achievement and their responses about self-confidence and mathematics support were analysed. Despite their wide ranging backgrounds, all of the students achieved well in their first year university engineering mathematics modules, which naturally increased their self-confidence. Several students described how using the mathematics support provision had helped them with mathematics and improved their confidence. In addition to analysing the interview scripts thematically, Bandura’s model of self-efficacy (Bandura, 1997) was used as a conceptual framework with which the students’ accounts were cross-matched. Bandura’s model proposes four sources of self-efficacy (past achievement; comparison with others; what others tell you; feelings or physical states) and four mediating processes (cognitive; motivational; affective; selective processes). Additional sources of self-confidence outside of Bandura’s model were also described by the students, in particular working with peers, appropriate speed of teaching and small group sizes. The most important source of self-efficacy was found to be students’ past experience of success or failure, and all four of Bandura’s mediating processes were referred to by the students. There was no mention, however, of verbal persuasion, and it is argued that lecturers and support tutors might do more to develop students’ confidence through this means. Most importantly, students’ opportunities for success should be maximised, including careful provision of challenging tasks at the right level, in order to build students’ self-confidence in mathematics.

The Mathematics Learning Support Centre at Loughborough University: staff and student perceptions of mathematical difficulties

Abstract From a census of academic and academic-related staff in the School of Mathematics at Loughborough University, most of whom work in the Mathematics Learning Support Centre, and a survey of the students who frequently use this facility we investigate the difficulties that are encountered with mathematics and the growing need for support with this subject. This paper reports the raw data results obtained from a selection of the questions that were posed. Responses were obtained from 29 mathematics staff and 37 students from mathematics, engineering and physics departments. We detail findings from the questions pertaining to perceptions of pre-knowledge, areas of difficulty and reasons for using the Centre. The results show that in some cases the opinions and perceptions of staff and students are almost diametrically opposite and in some cases students are unaware that the difficulties they are experiencing stem from a lack of fluency in areas of basic mathematics. What is also shown is that staff need to be aware of the mathematical content contained in the wide range of qualifications that students may enter university with. These findings have important consequences for those involved with mathematics education in the Higher Education sector and will also prove informative for universities who provide similar support.

Senior management perspectives of mathematics and statistics support in higher education: moving to an ‘ecological’ approach

ABSTRACT This article explores the perspectives of three senior managers in higher education institutions in England regarding their mathematics and statistics support provision. It does so by means of a qualitative case study that draws upon the writing of Ronald Barnett about the identity of an ‘ecological’ university, along with metaphors associated with the notion of organisations as living ‘organisms’, suggested by Gareth Morgan. Using these ideas as a heuristic sheds light upon the view that whilst outwardly universities appear to represent a uniform landscape, mathematics and statistics support alternatively, can be seen as different ‘species’ within the higher education system. The study illustrates how three universities occupying contrasting ecological ‘niches’ are responding to the challenges they face by providing and planning different forms of learning support for mathematics and statistics. In conclusion, it is recommended that senior managers reflect upon the possibilities offered by the idea of ‘ecological’ identities in order to explore how they might respond strategically to a rapidly changing environment. This includes adapting various solutions and the further development of innovative ways of supporting students’ transitions throughout the academic lifecycle. In addition, an ecological approach could also aid the formation of the co-creational relationships and networks required for the future success of those developments.