Development of a Mathematics Self-Efficacy Scale: A Rasch Validation Study

The main objective of this study is to develop and validate a sources of mathematics self-efficacy (SMSE) scale to be used in a polytechnic adopting Problem Based Learning (PBL) as its main instructional strategy. Based on socio-constructivist learning approach, PBL emphasizes collaborative and self-directed learning. A non-experimental cross-sectional design using a questionnaire was employed in this study. The validation process was conducted over three phases. Phase 1 was the initial development stage to generate a pool of items in the questionnaire. In Phase 2, a pilot test was performed to obtain qualitative and quantitative feedback to refine the initial pool of items in the questionnaire. Finally, in Phase 3, the revised scale was administered to the main student cohort taking the mathematics module. The collected data from the questionnaire was subjected to empirical scrutiny, including exploratory factor analysis (EFA) and Rasch analysis. The participants for this study were first year polytechnic students taking a mathematics module. There were 29 participants taking part in Phase 2 of the study, comprising 12 (41%) females and 17 (59%) males. For Phase 3, there were 161 participants, comprising 91 (57%) males and 70 (43%) females. The EFA yielded a three-factor solution, comprising (a) personal experience; (b) vicarious experience; and (c) psychological states. The items in the SMSE scale demonstrated good internal consistency and reliability. The results from the Rasch rating scale analysis showed an acceptable item and person fit statistics. The final 23-item SMSE scale was found to be invariant across gender. Finally, the study showed that the SMSE scale is a psychometrically reliable and valid instrument to measure the sources of mathematics self-efficacy among students. PBL educators could use the results from the SMSE scale in the study to adopt appropriate interventions in curriculum design and delivery to boost self-efficacy of students and hence improve their mathematics achievement.