The shadow reckoning problem from ancient society as context for learning Trigonometry

Abstract

In this article, we explore the shadow observations and reckoning from various ancient societies, especially form china and medieval Islam, as inspiration in developing a learning design. We used the evolution of trigonometry from old shadow reckoning techniques to arrange instructional tasks for tenth-grade secondary education students and analyse how its role in supporting students’ understanding of trigonometry. We choose Design Research as a method to reach the purpose. However, we restrict our discussion to a part of one phase, namely pilot experiment, from three main phases of design research. The idea of the learning design is involving students in old mathematical activities that concern with concept of shadow ratio as the beginning of basic trigonometry. This research was involving six Indonesian high school students. We developed an instructional design which consists of several activities’ that begin with solving history-based problem using Chong Cha procedure (double difference) from ancient china, where the calculation method is using shadow assistance from two poles as a gnomon to determine the height or depth and distance of an inaccessible object (e.g. mountains or valleys), and followed by solving a problem by using a tool and method from medieval Islam in the surveying process which is actually also developed from the concept of shadow calculations. The result indicated that the use of ancient problems and method can provide valuable insight for the students and give them an opportunity to learn the trigonometric ratio meaningfully. Furthermore, by using history as a context, students got more opportunities to improve their mathematics literacy performance through formulating various contextual mathematics problems into formal mathematics form.