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

Yusuf F Zakariya

doi:10.3389/fpsyg.2020.556607

Abstract

PurposeSelf-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.MethodThe 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.ResultsThe 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.ConclusionThe 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.

Highlights

There has been a growing interest in research on students’ affective factors and their contributions to learning outcomes at all levels of education
The preliminary analysis in the present study shows that PKMT is the only variable that satisfies the properties (a)–(c), and it was selected as an instrument to discern the true effect of self-efficacy on the performance from the omitted causes in the model
The first set of results are from the evaluations of one-factor models for each of the prior mathematics knowledge test and the calculus self-efficacy measurement models

Summary

Introduction

There has been a growing interest in research on students’ affective factors and their contributions to learning outcomes at all levels of education. Apart from the fact that some of these affective factors, e.g., self-efficacy, satisfactorily predict students’ performance, an explanation for the growing interest may be ascribed to the ease of developing interventions that influence such factors (Czocher et al, 2019). A high sense of self-efficacy has been linked with the adoption of deep approaches to learning, high learning motivation, positive attitude toward mathematics. A low sense of self-efficacy has been linked with the adoption of surface approaches to learning, high mathematics anxiety, and low interest in mathematics (Bandura, 1997; Rozgonjuk et al, 2020; Zakariya et al, 2020b). Schukajlow et al (2019) demonstrate an approach through which constructing multiple solutions to real-life problems can be used as an intervention to influence students’ self-efficacy in mathematics. Student-centered instructional methods have been linked with high self-efficacy (Lahdenperä et al, 2019)

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