Calculus Self-Efficacy Inventory: Its Development and Relationship with Approaches to learning

Abstract

This study was framed within a quantitative research methodology to develop a concise measure of calculus self-efficacy with high psychometric properties. A survey research design was adopted in which 234 engineering and economics students rated their confidence in solving year-one calculus tasks on a 15-item inventory. The results of a series of exploratory factor analyses using minimum rank factor analysis for factor extraction, oblique promin rotation, and parallel analysis for retaining extracted factors revealed a one-factor solution of the model. The final 13-item inventory was unidimensional with all eigenvalues greater than 0.42, an average communality of 0.74, and a 62.55% variance of the items being accounted for by the latent factor, i.e., calculus self-efficacy. The inventory was found to be reliable with an ordinal coefficient alpha of 0.90. Using Spearman’ rank coefficient, a significant positive correlation ρ ( 95 ) = 0.27 , p < 0.05 (2-tailed) was found between the deep approach to learning and calculus self-efficacy, and a negative correlation ρ ( 95 ) = − 0.26 , p < 0.05 (2-tailed) was found between the surface approach to learning and calculus self-efficacy. These suggest that students who adopt the deep approach to learning are confident in dealing with calculus exam problems while those who adopt the surface approach to learning are less confident in solving calculus exam problems.

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

“…Similarly, the 13 items of the CSEI are hypothesized to expose a common latent factor (self-efficacy) and tested. The factor loadings are freely estimated, the factor variance is fixed to 1, two error covariances between item 09 and item 11 as well as between item 12 and item 13 are allowed in the model as recommended by Zakariya et al (2019) . Further, a maximum likelihood with robust standard errors (MLM) estimator was used instead of the WLSMV because the students’ responses on the CSEI are continuous and not categorical.…”

“…Following the task-specificity of the self-efficacy, the calculus self-efficacy inventory (CSEI) was adopted in the present study. The CSEI was developed with a specific purpose of exposing students’ self-efficacy in solving some mathematical tasks drawn from the first-year introductory calculus course ( Zakariya et al, 2019 ). According to the self-efficacy theory, such an inventory offers the best precision in exposing the construct ( Bandura, 2006 ).…”

“…The students rate their confidence, on a scale of 0–100, in their belief that they can successfully solve the mathematics tasks. The conceptualization, operationalization, and psychometric properties of the CSEI have been previously studied using factor analysis in FACTOR program coupled with Spearman’s rank correlation and well documented ( Zakariya et al, 2019 ). The CSEI was found to possess construct and discriminant validity, unidimensionality, and with a reliability index of 0.90 using ordinal coefficient alpha ( Zakariya et al, 2019 ).…”

Effects of school climate and teacher self-efficacy on job satisfaction of mostly STEM teachers: a structural multigroup invariance approach

“…internal convictions to perform tasks with an estimation of desired outcomes, has been linked to the works of Albert Bandura. It is postulated to have four sources of influence: mastery experience, vicarious experience, verbal/social persuasions and physiological or affective states (Bandura, 1997;Zakariya, Goodchild, Bjørkestøl, & Nilsen, 2019). It is an important affective factor that boosts job performance and a strong militating factor against attrition and absenteeism.…”

“…A conducive and inclusive school climate that is free of hostility and bullying enhances teachers' job satisfaction, boosts selfefficacy, improves teacher-student relationship, reduces attrition and burnout (Lee & Louis, 2019;Van Beurden, Van Veldhoven, Nijendijk, & Van De Voorde, 2017). School climate is equally beneficial not only to the teachers but also to students' behaviour, approaches to learning, total well-being and improved achievement (Zakariya et al, 2019). According to Ainley and Carstens (2018), school climate is a multidimensional construct that encapsulates "safety, relationships, engagement with teaching and learning, institutional environment, and school improvement activities" (pp.…”