Learning pythagorean theorem from ancient China: A preliminary study

Abstract

In this article, we explore how History of the Pythagorean theorem, especially from ancient China, as a source of inspiration for learning design. Based on historical examples and problem solving from the history of mathematics, we try to arrange instructional tasks for seventh-grade secondary education students and how its role in supporting students’ understanding of Pythagorean theorem. We focus on explaining the preliminary studies or the first phase of the three main phases in design research. The basic idea of instructional design is to introduce historical geometric diagrams and solve the right triangle problem in the manner of Liu Hui (3rd century CE). The purpose of introducing geometric diagrams is to connect students’ symbolic algebraic thinking with visual thinking about geometric shapes especially in the case of right triangles. In this study, we also conducted interviews and debrief sessions with teachers and tested the student’s history-based tasks to several students for initial investigation in the matter of developing the Hypothetical Learning Trajectory. Results of this study show that teachers have a positive response toward the history-based instructional task developed. On the other hand, we find the resolution of Right Triangles problems with diagrams by the students involving three steps: translation, transformation, and diagrammatic reasoning.