Competence and autonomous motivation as motivational predictors of college students’ mathematics achievement: from the perspective of self-determination theory

Abstract Background Applied Calculus courses serve hundreds of thousands of undergraduates as quantitative preparation and gatekeepers across diverse fields of study. The current study investigated how motivational factors are associated with students’ learning outcomes in Applied Calculus courses from the perspective of self-determination theory—a sound comprehensive motivation theory that has been supported by considerable research in psychology and education. In order to have a nuanced understanding of students’ motivation and learning in Applied Calculus courses, we used three different types of learning measures to investigate students’ mathematics achievement, including course grades, a standardized knowledge exam, and students’ perceived knowledge transferability. Results We tested the relationships between motivational factors and learning outcomes with a multi-semester sample of 3226 undergraduates from 188 Applied Calculus classrooms. To increase the precision of our analysis, we controlled for three demographic variables that are suggested to be relevant to mathematics achievement: gender, minority group status, and socioeconomic status. With a series of multilevel modeling analyses, the results reveal that: (1) competence satisfaction predicts college students’ mathematics achievement over and above the satisfaction of needs for autonomy and relatedness; and (2) autonomous motivation is a more powerful predictor of college students’ mathematics achievement than controlled motivation and amotivation. These findings are consistent across different types of learning outcomes. Conclusions Self-determination theory provides an effective framework for understanding college students’ motivation and learning in Applied Calculus courses. This study extends self-determination theory in the field of mathematics education and contributes to the dialogue on advancing undergraduate science, technology, engineering, and mathematics (STEM) education by providing evidence to understand how motivational factors are associated with students’ learning outcomes in undergraduate mathematics courses.