Approaches to studying and the effects of mathematics support on mathematical performance

  • Chetna Patel

    Student thesis: Doctoral ThesisDoctor of Philosophy


    The concern over undergraduate engineering students’ mathematical skills and the means of addressing this through the provision of mathematics support is the main driver of this research. With the emergence of mathematics support within mathematics education there has been an associated research community interested in measuring the effectiveness of mathematics support provision. Recent studies have measured improvements in mathematics performance for students who have used mathematics support against those who have not by comparing prior mathematical ability against examination results. This does not address the issue of individual differences between students and resulting changes in mathematical ability.

    However the provision of mathematics support for individual students is resource intensive hence evaluation of the effectiveness of the support is essential to ensure resources are efficiently used. This mathematics education research examines the effectiveness of mathematics support in addressing the mathematics problem. It does this by considering individual differences and the mismatch of mathematical skills for studying at University by analysing the effectiveness of mathematics support in improving mathematical skills.

    The dataset for the analysis comprises of over 1000 students from a Scottish Post-92 University, over 8% having made use of mathematics support, and nearly 2000 students from an English Russell Group University, with just over 10% having made use of the support. It was discovered that in both sets of data the students who came for mathematics support in comparison to their peers had a statistically significant lower mathematical skills base on entry to their course, and at the end of their first year had improved their mathematical skills base more than their counterparts. Although the analysis is based on data from UK Universities we believe the findings are relevant to the international community who are also engaged in the provision of mathematics support.

    However, this approach is open to criticism because it does not use a randomised sample. The sample was made up of nearly of all the students whose entry and exit (end of years 1 and 2) mathematics qualifications were known, some of whom had made use of mathematics support and some who had not. Hence a further study was undertaken to examine students’ preferences for different approaches to study as a differentiating factor. 122 students at the English Russell Group University completed a modified version of the Approaches to Study Skills Inventory for Students questionnaire, 34 of whom had used mathematics support. Considering performance of mathematics support students and non-mathematics support students in the light of their approaches to studying provides a means of addressing the bias introduced by the non-randomised data.

    The modified Approaches to Study Skills Inventory for Students questionnaire has two new subscales which are used to measure procedural deep and procedural surface approaches. These subscales are introduced to help provide a finer characterisation of approaches to studying in the mathematics discipline. It was discovered that the procedural deep subscale achieved internal reliability and as a result was placed within the overall deep approach scale but the procedural surface subscale did not achieve reliability and was discarded from further analysis in this study. Using these categories, it was found that the students who had shown a desire to gain deeper understanding were making more use of mathematics support. Additionally, changes in approaches to studying were investigated for a group of 25 students, out of the original 122, who had completed a shorter version of the questionnaire at the end of semester 1 as well. It was discovered that after one semester at university these students had changed their approaches to studying to a more surface approach. It is possible that the assessment process in Higher Education is more accommodating to students who can switch between approaches, especially in engineering where the learning of processes and meaningful understanding go hand-in hand. The change in approach to a more surface one in their first year adds to that the discussion that the deep approach is not necessarily better suited at level 1 for successful studying. Whether this is driven by the Higher Education assessment requirements is beyond the scope of this thesis but is worth consideration for future work.

    In conclusion, mathematics support was being used mainly by students who had weaker mathematics than their peers at both Institutes. However, there was another group of students namely those with a higher level of mathematical skills who were making use of the support centre but these were a minority in this study and a deeper review has not been undertaken here. We found that students taking advantage of mathematics support improved on their mathematical skills more than the students who had not made use of the support, though the improvement was not large enough to lead to out-performing students not making use of mathematics support. Additionally, students who had initially shown a desire to gain a deeper understanding in their learning had changed to a more surface approach after a semester at university.
    Date of Award2011
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorJim Tabor (Supervisor) & Peter Samuels (Supervisor)


    • Mathematics education
    • Mathematics skills
    • Mathematics support
    • Mathematics ability
    • Higher Education
    • University education

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