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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.

Theories of self-efficacy and approaches to learning are wellestablished in the psychology of learning. However, studies on relationships between the primary constructs on which these theories are developed are rarely reported in mathematics education research. Thus, the purpose of the current study is to provide empirical evidence for a potential causal relationship between perceived self-efficacy and approaches to learning. The present study adopts a cross-sectional survey research design that includes 195 engineering students enrolled on a first-year introductory calculus course. The data are collected using two well-developed and validated instruments with established high psychometric properties. Two hypotheses are formulated and tested using a structural equation modelling approach coupled with a weighted least square mean and variance adjusted estimator. The findings show that a high sense of perceived self-efficacy has a strong tendency to induce a deep approach to learning mathematics. In contrast, a low sense of perceived selfefficacy induces a surface approach to learning mathematics with a strong effect. This study represents a shift from the usual correlational studies that characterize quantitative research in mathematics education literature to causal relation research. Therein, causal assumptions are made and tested against the collected data, and some recommendations are made for future studies.

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