Eighteenth Century Land Surveying as a Context for Learning Similar Triangles and Measurement

Abstract

In our study, we investigated the value and applicability of the history of mathematics as a didactical tool for teaching mathematics. Recent literature has disclosed conceptual, cultural, and motivational arguments for including historical mathematical texts and methods in the mathematics curriculum. We explored how these theoretical assumptions worked out when designing historically-based instructional material and when using this material for teaching. The focus was on teaching measurement skills and the application of similar triangles to eight- and ninth-grade students. The profession of the Dutch land surveyor in the 18th century served as a historical context. Analyses of the data indicated that several aspects of this historical context were helpful for teaching these subjects. The practical activities along the 18th century lines appeared to have a positive effect on the students' motivation and on their conceptual understanding. The ninth-graders reacted more positively to the historically inspired text than the eighth-graders. The integration of historical elements, especially the need to read the old language, was generally not applauded, nor did we observe a positive cognitive effect. Even so, the practical activities inspired by the context appeared significantly effective and were judged positively by the students.