Teaching and Learning the Derivative in Senior High School

A Cross-Cultural Comparison of Instructional Approaches and Students’ Understanding of Derivatives in Taiwan and Germany

The teaching of derivatives occupies an important place in upper secondary mathematics education, yet the ways in which this topic is introduced and developed differ substantially across educational systems. Differences in curricula, textbook traditions, instructional practices, and expectations regarding mathematical reasoning may provide students with fundamentally different opportunities to develop an understanding of derivatives.

This project compares the teaching and learning of derivatives in Taiwan and Germany, two educational contexts with distinct traditions in mathematics education. The cross-cultural comparison will examine how derivatives are represented and introduced in the respective educational systems and how these differences are reflected in students’ opportunities to engage with conceptual aspects of differentiation. The project combines analyses of curricular and instructional materials with empirical investigations of students’ mathematical knowledge. By relating characteristics of the learning opportunities provided in the two educational contexts to students’ understanding, the project aims to identify how different approaches to teaching differentiation may shape the development of mathematical knowledge. The comparison between Taiwan and Germany will provide a broader perspective on how educational traditions influence the teaching of a central topic in calculus. The findings are expected to contribute to a better understanding of which characteristics of instruction and learning opportunities may support the development of a robust conceptual understanding of derivatives.

Kristin Litteck, Aiso Heinze (IPN Kiel, Germany)

Pin-Chen Guo, Kai-Lin Yang (National Taiwan Normal University Taipei, Taiwan)