Student understanding of functions of two variables: A reproducibility study

• Published in: The Journal of mathematical behavior 2022-06, Vol.66, p.100950, Article 100950
• Main Authors: Borji, Vahid, Martínez-Planell, Rafael, Trigueros, María
• Format: Article
• Language: English
• Subjects: APOS; Conceptual Understanding; Didactic characteristics; Function of two variables; Genetic decomposition; Reproducibility
• ISSN: 0732-3123; 1873-8028
• DOI: 10.1016/j.jmathb.2022.100950

In this Action-Process-Object-Schema (APOS) study, we aim to study the extent to which results from our previous research on student understanding of two-variable functions can be replicated in a different institutional context. We conducted the experience at a university in another country and with a different instructor than in previous studies. The experience consisted in comparing two sections of the same course; one taught through lectures and the other using activities designed with APOS theory and the ACE didactical strategy (Activities, Class discussion, Exercises). We show the results of a comparison of students’ performance in both groups and give evidence of the generalizability of our previously obtained research results and the possible replication of didactic aspects across institutions. We found that using the APOS theory didactical approach favors a deeper understanding of two-variable functions. We also found that factors other than the activity sets and teaching strategy affected the replication. •Replication study of student understanding of two-variable functions.•Activities and didactic strategy to help students understand two-variable function.•Factors that may influence the replication study are considered.•Found unexpected differences between students in original and replication studies.•Shows that deciding what a research-based innovation encompasses can be non-trivial.