Self-Efficacy Between Previous and Current Mathematics Performance of Undergraduate Students: An Instrumental Variable Approach to Exposing a Causal Relationship

Abstract

Purpose: Self-efficacy has been argued theoretically and shown empirically to be an essential construct for students' improved learning outcomes. However, there is a dearth of studies on its causal effects on performance in mathematics among university students. Meanwhile, it will be erroneous to assume that results from other fields of studies generalize to mathematics learning due to the task-specificity of the construct. As such, attempts are made in the present study to provide evidence for a causal relationship between self-efficacy and performance with a focus on engineering students following a mathematics course at a Norwegian university.

Method: The adopted research design in the present study is a survey type in which collected data from first-year university students are analyzed using structural equation modeling with weighted least square mean and variance adjusted (WLSMV) estimator. Data were generated using mainly questionnaires, a test of prior mathematics knowledge, and the students' final examination scores in the course. The causal effect of self-efficacy was discerned from disturbance effects on performance by using an innovative instrumental variable approach to structural equation modeling.

Results: The findings confirmed a significant direct effect of the prior mathematics knowledge test (β = 0.52, SE = 0.01, p < 0.001) on self-efficacy, a significant direct effect (β = 0.43, SE = 0.19, p = 0.02) of self-efficacy on performance, and a substantial mediating effect (β = 0.22, SE = 0.10, p = 0.03) of self-efficacy between a prior mathematics knowledge test and performance. Prior mathematics knowledge and self-efficacy explained 30% variance of the performance. These findings are interpreted to be substantial evidence for the causal effect of self-efficacy on students' performance in an introductory mathematics course.

Conclusion: The findings of the present study provide empirically supports for designing self-efficacy interventions as proxies to improve students' performance in university mathematics. Further, the findings of the present study confirm some postulates of Bandura's agentic social cognitive theory.

Keywords: causal model analysis; instrumental variable approach; prior mathematics knowledge; self-efficacy; undergraduate learning.