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PA 25 Unterricht und Lernen II
A Design of Exploring Mathematical Proof in Secondary School
Geometry: A Perspective on German and Taiwanese Textbooks
Mittwoch (7.9.2011), Raum V.1.01, 09:00 Uhr - 09:30 Uhr
Yu-Ping Chang, Kristina Reiss, Stefan Ufer
Technische Universität München
yuping.chang@tum.de
Geometry is an important topic for proof and argumentation in secondary school. However,
the complexity of geometric proof frustrates many students. An interview study (Heinze, 2004)
analyzing proof instruction in Germany reported that even high-achieving students at grade
8 in Germany, taught a unit on reasoning and proof (congruence-related content), had difficulties
in generating a proof idea and combining arguments to a proof. Besides, Lin (2003)
and his research group conducted an investigation, about the development of adolescents’
competence in mathematical argumentation (DACMA) in Taiwan, and found that even though
students could organize their knowledge learned in elementary school to solve difficult and
inexperienced questions, they could not retrieve a simple principle to judge and explain why a
property was true.
We present an analytical framework in order to explore how knowledge of mathematical concepts
and proving competencies are built within geometry content. This study presents preliminary
results regarding the content arrangement in comparison of Germany and Taiwan. We
analyzed texts from textbooks by problem-driven content analysis, and restricted the analysis
to textbook content from grade seven to nine. Six individual editions of textbooks from Germany
and Taiwan, three from one country respectively, are analyzed based on this framework.
We discuss the choice of analytic units as well as the choice of variables for the framework with
some examples.
Heinze, A. (2004). Schülerprobleme beim Lösen von geometrischen Beweisaufgaben – ein Interviewstudie. ZDM,
36 (5), pp. 150-161.
Lin, F.-L. (2003). Development of adolescents’ competence on mathematical argumentation (Technical Report).
Taipei: Department of Mathematics, National Taiwan Normal University. [In Chinese]