Title: Investigating the Rate of Change Development of Two Latina Undergraduate Students from an Anti-Deficit Perspective: A Cultural Approach to Mathematical Caring Relations
Abstract:
This study introduces cultural mathematical caring relations (CMCRs) as a framework that extends Hackenberg’s (2005b) mathematical caring relations by integrating two tenets of culturally relevant pedagogy (Ladson-Billings, 1995): academic achievement and cultural competence. Framed within radical constructivism, CMCRs prioritize students’ cognitive growth and development while affirming their cultural and experiential identities by embedding their funds of knowledge into the learning process. Through a constructivist teaching experiment with two students, Yari and Jocelyn, this research investigates how working to establish and maintain CMCRs can influence Latin* students’ rate of change development.
Findings illustrate that CMCRs supported the development of Yari and Jocelyn’s rate of change reasoning, even when their progress did not align neatly with traditional developmental frameworks. The study also identifies four key factors that shaped the success and challenges of working to establish and maintain CMCRs: (1) teacher decisions, (2) the role of students’ funds of knowledge in their mathematical reasoning, (3) witness-researcher support, and (4) external influences on students’ mathematical growth.
Ultimately, this work challenges deficit discourses about Latin* students in mathematics by showcasing how CMCRs highlight the assets in their cultural and lived experiences, as well as the strengths in their mathematical reasoning. It demonstrates that CMCRs can maintain mathematical rigor while simultaneously valorizing students’ funds of knowledge, inviting a reimagining of what counts as “meaningful” in cognitive research.