Theories of self-efficacy and approaches to learning are well-established 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 self-efficacy 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.