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

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.

High-quality tasks for e-assessment in mathematics

“…However, in such an instance, some researchers (e.g., Kline, 2016) have recommended that if the ratio of the chi-square value to the degree of freedom (df) is less than 3, then the model exhibits an appropriate global fit. More so, the RMSEA value is a little above .06 but it poses no problem to the model fit since the 90% confidence interval includes .06 (Zakariya, 2021). Interestingly, the results show that the effect of age-group on the attitude towards mathematics construct is not significant.…”

Improving students' mathematics self-efficacy: A systematic review of intervention studies

“…Also, mathematics self-efficacy predicts performance in mathematics better than intelligence test scores, personality traits (i.e., agreeableness, conscientiousness, emotional instability, extraversion, and openness), and self-esteem (Zuffianò et al, 2013 ). There seems to be a consensus that mathematics self-efficacy has a substantial positive association with students' performance in mathematics (Pajares and Miller, 1995 ; Yurt, 2014 ; Roick and Ringeisen, 2018 ; Zakariya, 2021 ). That is, high mathematics self-efficacy is associated with high performance in mathematics while low mathematics self-efficacy is associated with poor performance in mathematics.…”

“…That is, high mathematics self-efficacy is associated with high performance in mathematics while low mathematics self-efficacy is associated with poor performance in mathematics. Going a step further, Zakariya ( 2021 ) uses an innovative instrumental variable approach of structural equation modeling to show that students' mathematics self-efficacy on mathematics tasks has a causal relation with students' performance in mathematics.…”

The reciprocal relationship between mathematics self-efficacy and mathematics performance in US high school students: Instrumental variables estimates and gender differences

“…One recent study by Zakariya (2021) aimed to derive evidence of a causal relationship between self-efficacy and performance in mathematics, using an instrumental variable approach to structural equation modeling. Unfortunately, besides the small sample size, the findings (large bidirectional effects between math self-efficacy and math performance) are not generalizable, as the focus is on first-year engineering students following a mathematics course at a Norwegian university.…”