Merging Horizons: History of Mathematics and Cultural Diversity

Including history of mathematics into math teaching means entering the diversity of mathematical developments with a diverse population of students of diverse abilities. Students experience a new world with different motives for doing mathematics, different ways of thinking, and different linguistic and symbolic means. This may help to develop a more sustainable relationship to mathematics and an appreciation for other cultures. In a first step, the paper will discuss the frame for doing such work and, especially, what it means to read a (historical) source. The main result is that in a circular process of understanding, the reader of a (historical) source creates something new, different from the ideas of the author, or of other readers. In a second step, an illustrative example is discussed, the phases of the moon, a topic on the borderline of astronomy and geometry. This example played a fundamental role in Martin Wagenschein’s pedagogy as well as in Karl Popper’s philosophical thinking. Finally, we sketch a teaching unit for grade 8 based on a historical source (Cleomedes’ The Heavens) and naked-eye observations of the students. They describe verbally and via free hand drawings how one can understand the phases of the moon and their continual change in the course of a month. This offers chances of engagement for students of very diverse abilities.