Opportunities to Learn Mathematical Proofs in Geometry

This monograph provides an outlook on the similarities and differences of introducing mathematical proofs in German and Taiwanese mathematics textbooks. The author conducted two comparisons, the general comparison and the specific comparison, on geometry content between three German and three Taiwanese textbook series from grades 7 to 9. With respect to the general comparison, she developed an analytic framework to analyze textbooks in a quantitative perspective. In order to zoom in the differences of introducing mathematical proofs between Germany and Taiwan, she selected and analyzed three mathematical statements independently, the Pythagorean theorem, the sum of the interior angles of a triangle, and the Thales theorem, in six textbook series for the specific comparison. These three statements are introduced very different between German and Taiwanese textbooks. In summary, this study unveils different sequences of geometry content and different emphases in designing mathematical proofs in German and Taiwanese mathematics textbooks.