The refiguring of students’ mathematical identities: a mixed methods study of three tailored calculus courses

Abstract

This study explores how the goals and enactment of three tailored calculus courses, referred to as course variations (standard calculus, life sciences calculus, and physics calculus), at the same university impact students’ mathematical identity. In this mixed-methods study, we draw on the framework of figured worlds to interpret how students’ mathematical identities can be refigured by the enactment of three calculus course variations. Results demonstrate that students in life sciences calculus had opportunities to refigure their identity as capable learners and doers of mathematics yet still viewed the subject as ancillary to their disciplinary interests. Students in physics calculus sustained their mathematical identity through strong peer collaborations. Finally, students in standard calculus shifted their identity as survivors of mathematics, conveying a sense of received knowing from their instructor. The ability of any particular course variation enactment to provide opportunities for refiguring mathematical identities resides within the goals, structures, students, and instructors that help to form these figured worlds. The results presented here provide insights into course variation instructional design and instructional practices that can positively affect students’ mathematical identities, and in turn, their persistence in mathematics and science.

KEYWORDS:

• Mathematical identity
• figured worlds
• course variations
• calculus

Acknowledgments

This manuscript would not have been possible without the contributions and efforts of the entire Progress through Calculus project team. The authors also want to thank Athina Thoma for feedback and suggestions on an earlier version of this manuscript presented at the 11th Congress of European Society for Research in Mathematics Education (Voigt et al., 2019). MV carried out the data collection, led the writing and analysis of the manuscript. CR carried out the data collection and contributed to the writing and analysis of the manuscript. AM contributed to the writing and analysis of the manuscript. All authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Availability of data and materials

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

1 The term major refers to the academic discipline or programme of study to which an undergraduate student formally commits.

2 Names of all students in the three course variations are pseudonyms.

3 AP calculus is a first course in differential calculus offered through the advanced placement system, which is a programme in the US and Canada that offers university level curricula and examinations to secondary school students.

Additional information

Funding

This material is based upon work supported by the National Science Foundation (NSF) under [grant number 1430540]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.