TLRP: Multi-dimensional structure of a (use of) mathematics self efficacy instrument
This paper forms part of a larger study aiming to understand how cultures of learning and teaching can support learners in ways that help widen and extend participation in mathematically demanding courses in Further and Higher Education; this involves contrasting a traditional ‘mathematics’ programme with a new ‘use of mathematics’ programme in the U.K. The particular interest in this paper is self-efficacy, given that social science literature on widening participation suggests that a positive disposition towards a subject is crucial to continuing to study a subject (Bandura and Cervone, 1983; Bandura and Locke, 2003). This paper is reporting on the development of an instrument to measure mathematical self-efficacy of college students studying ‘traditional mathematics’ and ‘use of mathematics’ programs. We will focus on the measurement issues emerging during the validation process with regard to the dimensionality of the construct. An instrument was built to measure self-efficacy (s.e.) of 16-17 year old students in relation to their use of mathematics, a ‘soft’ learning outcome measure that is expected to provide important information when contrasting subgroups following a ‘mathematics’ and a ‘use of mathematics’ programme. Analysis revealed significant DIF between the two subgroups. Further, multi-dimensional analysis suggests that ‘pure (P)’ and ‘applied (A)’ scores might better be reported separately (in addition to the overall ‘maths (M)’ s.e. score). Furthermore the subgroup score means P and A are significantly different in the expected direction (i.e. the use of maths group is significantly more confident on the Applied dimension and vice versa), while the relation of M (A, P) is nearly invariant across subgroups.