Mathematics support—support for all?

Mathematics Support Centres are to be found in various forms in the majority of UK higher education institutions. They have been established in order to ease widespread and serious difficulties that a significant number of students have with mathematics, particularly at the school–university transition. They usually offer mathematics and/or statistics support to students across the full range of disciplines studied. Anecdotal evidence suggests that those students who make good use of such centres are not just those who struggle with mathematics. Many frequent users are quite competent and simply want to do better. The study reported here describes and analyses data from one cohort of engineering students. A novel aspect is the quantification of the proportion of support centre visitors who fall into these, and other, categories. We conclude of the cohort in the study, mathematics support has improved the pass rate by ∼3%. Of the failures, about half (∼4% of the sample total) could well have passed had they attended the mathematics support centre regularly. Furthermore, the majority of those attending were not students who were in danger of failing. This has important implications not only for the design of mathematics support provision, but also for the performance of the high fliers. The methodology offers one way tackling the difficult task of evaluating the effectiveness of mathematics support initiatives

Learning to be a postgraduate tutor in a mathematics support centre

The study reported here investigates the role, experiences and aspirations of a community of mathematics postgraduates as they learn to tutor in a mathematics support centre in a research-intensive university. This is achieved through in-depth interviews with nine postgraduate tutors all of whom had experience working in the centre. The data is analysed through the lens of communities of practice and presented through the voices of the postgraduates themselves. It sheds light on their personal trajectories as ‘newcomers’ to the peculiarities of tutoring within a mathematics support centre, and the ways in which they learn from, support and cooperate with each other in their common endeavour. As the postgraduates progress through their three or four years working in the centre the data reveals a growing confidence and, for some, a strong willingness to nurture and encourage their younger colleagues. Some of the ‘old timers’ go on to assist in the recruitment of new tutors and demonstrate insights into the ways their experience as tutors in the support centre will inform and influence their own future careers as academics. In particular, our work highlights the ways in which tutoring in the centre contributes to their own mathematical learning and personal development. The work is driven by a need to better understand the practices of postgraduate tutors in the growing field of university mathematics support and a desire to improve these. We consider how what we have learned can be put to use both in mathematics support centres and in university mathematics education more generally. By doing so we contribute to the solution of a widely reported ‘mathematics problem’ in higher education. At the same time this work strengthens what has been described as a ‘fragile’ relationship between mathematicians and educational researchers, bridging the gap between theoretical understanding and practice in a research-intensive university mathematics department

Progression within mathematics degree programmes

Several independent research projects report that the enjoyment of mathematics by many undergraduate mathematicians decreases as they progress through their degree programme and this decrease is accompanied by increasing disillusionment and disengagement with their course and alienation from mathematics itself. These are students who choose to study mathematics at university and who are relatively well-qualified. Moreover, it is often the case that students who report such feelings are not failing students – indeed many are doing rather well. Of course, many other students find their undergraduate experience of mathematics to be extremely rewarding but the prevalence of studies reporting disaffection suggests that this is an issue worthy of exploration within a book on transitional issues affecting undergraduate mathematicians. This chapter will review the evidence for this phenomenon and unpick the reasons students give for their changes in attitude to mathematics. After establishing the context for the chapter we present a brief review of the literature in this field. The evidence suggests that this state of affairs can be attributed, at least in part, to the mismatch between students’ hopes, expectations and aspirations and the reality of learning mathematics at university level. Sometimes, traditional pedagogies and practices can exacerbate this situation. We will go on to provide several examples of ways in which some lecturers and departments have attempted to modify practices in order to improve the student experience of university mathematics. We summarise the findings of selective activities and projects that provide pointers in the hope that they might inspire or provoke a discussion amongst individual lecturers and more widely within departments about ways in which disillusionment, disengagement and alienation might be ameliorated so that the experience of undergraduate mathematics is truly rewarding for all who choose to study it

Graduates’ views on the undergraduate mathematics curriculum

In Winter 2011 we surveyed the views of 428 mathematics graduates from the 2008/9 graduating cohort. Each graduate was asked to reflect on the knowledge/skills they believed that they developed during their mathematical study, and to assess how useful these skills have been during their career to date. We were also able to benchmark these data against an earlier survey of incoming undergraduates’ expectations. Our overall goal was to determine whether the higher education mathematics syllabus adequately prepares students for the workplace. We found a mixed picture: • An overwhelming majority of graduates believed that they successfully developed generic cognitive skills during their studies (e.g. logical reasoning, critical thinking and problem solving). Furthermore, there was widespread agreement that these skills are useful in the workplace. • However, fewer students believed that their studies had developed generic non-cognitive skills such as making presentations, oral and written communication, team working or computer literacy. All these skills were considered to be useful in the workplace, but are apparently not well developed by studying undergraduate mathematics. Furthermore, we found that incoming undergraduates expected to develop these non-cognitive generic skills during their mathematical study, suggesting that there is a mismatch between students’ expectations and outcomes. • When asked to select what skill graduates wished they had had the opportunity to develop more during their mathematical studies, the most commonly selected was “applying mathematics to the real world”. Over 90% of incoming undergraduates expected to develop this skill, whereas only around 60% of graduates believed that they had. This report raises two issues to consider. First, whether the mathematical community is (or should be) satisfied with the range of skills that graduates perceive the current higher education curriculum to develop. And second, if the community is satisfied by the current situation, how the apparent mismatch we observed between incoming students’ expectations and graduates’ perceived outcomes can be addressed

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

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

Student perceptions of screencast feedback on mathematics assessment

Although feedback is a very important component of assessment in higher education, there is substantial evidence that students view traditional methods of feedback as deficient in a number of respects. In this paper we explore how students perceive generic feedback on a mathematics assignment provided via screencasts. Our study is based on a Differential Equations module taught to first and second year students at a United Kingdom university. Our analysis of a student survey of this novel approach to feedback indicates that some students prefer screencast feedback to written feedback for a number of reasons: it is perceived to be more personal, it provides a richer experience than handwritten comments, it can be accessed anytime and replayed and paused as needed, it assists with learning how to communicate mathematics and it helps develop mathematical thinking skills. In fact, we show that this form of feedback is effective according to Sadler’s (Instructional Science 18:119–144, 1989) definition of effective feedback

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

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

“This is what you need to be learning”: an analysis of messages received by first-year mathematics students during their transition to university

This paper explores the messages that first-year mathematics students receive in the context of their academic studies during their transition from school to university mathematics. Through observations of lectures and discussions with first-year mathematics undergraduates in an English university, we identified and analysed the messages that two of their lecturers transmitted to them during this transitional phase. The results suggest that strongly framed messages are more easily perceived by students and affect them during their transition. Additionally, messages that have been received in the school context continue to have control over students’ thinking and on many occasions can impede adjustment to the new setting

Engineering students understanding mathematics

ESUM (Engineering Students Understanding Mathematics) is a developmental research project at a UK university. The motivating aim is that engineering students should develop a more conceptual understanding of mathematics through their participation in an innovation in teaching. A small research team (the authors) has both studied and contributed to innovation which included small group activity, a variety of forms of questioning, an assessed group project and use of the GeoGebra medium for exploring functions. The main study took place in the academic year 2010-11, but development is ongoing

Community perspectives of mathematics and statistics support in higher education: building the infrastructure

Over the last two decades, mathematics support has, increasingly, been seen by higher education institutions as a vital mechanism for helping students enhance their mathematical and statistical skills, particularly as they make the transition to university study. Several studies have shown the growth of mathematics support across the higher education sector within the UK, Ireland and beyond. Others have demonstrated its impact upon learners. However, few have explored the extent to which mathematics support is embedded within institutions or the extent to which it is likely to be sustainable. Such analyses are important for both the institutions themselves and the many colleagues who are working to develop mathematics support into an area of study in its own right. Here, we report on a survey of 47 institutions offering mathematics and statistics support within the UK. Findings show that, within many institutions, mathematics support is now embedded as part of student-focused institutional support provision. Further, its impacts are increasingly extending beyond those students who access the support: there is evidence that mechanisms are in place for feeding findings from mathematics and statistics support into mainstream teaching and learning and curriculum development. Significantly, the analysis shows that mathematics support offers good potential for sustainability such that the legacy of national endeavours to establish it more widely will continue to exist into the future