Widening participation in higher education: student quantitative skills and independent learning as impediments to progression

Abstract

The UK government's widening participation strategy, and the concomitant development of a mass higher education system, has imposed a variety of pressures on higher education institutions. Not least of these is the changing nature of the student population, and the assumptions that can be made about its skills and knowledge base. It should not be surprising that this rapid expansion of the higher education system has resulted in declining student progression and retention rates. This paper takes a case study approach and attempts to identify the range of factors that might explain the variability of student performance on a first year undergraduate introductory statistics module. The paper concludes that there are no simple predictors of success or failure. However, there is evidence to suggest that any innovations in delivery need to take account of individual student development and that the presumption that students can rapidly become independent learners upon initial entry to higher education is an unrealistic one.

Notes

We use the terms numeracy/mathematical literacy/quantitative skills interchangeably, and interpret them as being generic in the sense of describing a general facility for undertaking numerically-based educational programmes. While recognizing that the specialist educational literature draws a distinction between these concepts, we do not consider these distinctions to be relevant within the context of the present study.

General Certificate of Secondary Education, the public examination taken at age 16 in the UK.

This information was unavailable in the sense that while students had to demonstrate that they had achieved a minimum threshold level in mathematics upon application to the university, the specific mathematical qualification achieved was not subsequently recorded on the individual computerized student records – the qualification recorded was the broad qualification that formed the basis for admission.

The ethnic categorization derives from students defining their own ethnicity upon enrolment.

In terms of the specific entry qualifications in table 3, Matriculation Qualifications would be defined as standard entry qualifications for HE, and includes A-levels for England and Wales and their equivalent in Scotland and Ireland. This category also includes a range of equivalent overseas qualifications, such as the baccalaureate. The second category in table 3 – Vocational Qualifications – are here specific to the UK, and include General National Vocational Qualifications/National Vocational Qualifications at Level 3 (GNVQ/NVQ). These qualifications are more vocational in their orientation than A-levels and their equivalent, but are still considered to be a valid qualification for entry to HE. This category also includes BTEC National Certificates/Diplomas (BTEC NC/ND), a more established vocational qualification at post-16 level. Access/Foundation Courses are designed for mature students, generally without formal qualifications, or standard-age students who have not obtained matriculation qualifications, and provide a general orientation for HE study. The ‘None – Mature Student’ category would cover those mature students who have considerable work experience at a level considered appropriate to allow for direct entry to HE. The ‘Other (Overseas)’ category covers a range of overseas qualifications that do not fit neatly into the other categories, but are considered appropriate for HE entry.

The questionnaire was included with the coursework for the module, and students were requested to submit a completed questionnaire when they submitted their coursework. However, students were guaranteed anonymity in the sense that the questionnaire was removed from the coursework before the coursework was passed on for marking.

Repeat students were omitted from the analysis in order to focus upon the experience of those students taking the module for the first time. The grade recorded for each student is the best grade achieved at either the initial assessment point or the reassessment point.

The correlation between this variable and the final grade achieved on the module is 0.47, and thus while certainly statistically significant, is perhaps not as high as might have been expected, and in particular, not so high as to swamp all other influences.

It might be expected that students may have found it difficult to draw such a distinction between these two aspects of the study demands of the module. However, the correlation between these two variables was just 0.16, which would suggest that this was not the case.

These factors were found to be not statistically significant in all subsequent statistical analyses, and therefore will not be discussed any further. In the case of ethnicity this is consistent with the relevant literature (not reported here) which suggests that any apparent differences in student performance by ethnicity can be explained in terms of social class and educational backgrounds.

The logarithm of assessment hours was used as its statistical performance was superior to that of the simple level of assessment hours. This can be rationalized by arguing that the log attenuates the impact of those small numbers of students who undertook very large numbers of assessment hours – there were declining marginal returns to the hours spent on assessment preparation. A similar effect was in evidence with regard to age – the impact of age on performance also appeared to have a declining marginal impact.

The impact of commitment to paid employment was evaluated in a variety of ways. Initially, the variable was used in its raw and continuous form, as the reported number of hours worked. In general, this variable worked satisfactorily in the sense that it exerted a negative and statistically significant impact on performance in most of the regressions. However, in the context of the literature suggesting the possibility of a discrete effect – that students can undertake some modest level of paid employment with no effect on performance – various dichotomized versions of the variable were also tested. In general these produced superior statistical results in the sense of generating higher t-statistics. The dichotomized variable became statistically significant when students worked more than 10 to 12 hours per week, a finding that is consistent with the literature.

A range of non-linear variants of the age variable were tested, including quadratic and cubic formulations, but the formulation used here was the only one that proved to be consistently statistically significant.

See Note 5 with regard to the nature of BTEC NC/ND qualifications.

The regression package used to generate these statistics is Microfit 4.1. See Pesaran and Pesaran [43] for a description of these tests.

Probit regressions were also run in which the dependent variable simply reflected the pass/fail outcome – that is, the dependent variable took the value 1 if the student achieved 40% or more on the assessment, 0 otherwise. The results were broadly consistent with the regressions in tables 5 to 7, although there were some differences. No gender effects were identified, and age effects were restricted to just males and mature students. Thus, while age and gender appear to have an impact on grade achieved, they have a very limited impact on the probability of passing the module. In general, hours spent on seminar and assessment preparation had a much more limited impact on the probability of passing, as compared to the results in tables 5 to 7.