Abstract
Teaching mathematical proof is one of the most challenging topics for teachers. Several empirical studies revealed repeatedly different kinds of students’ problems in this area. The results give support that students’ abilities in proving are significantly influenced by their specific mathematics classrooms. In this paper we will present a method for evaluating proof instruction and some results of a video study that describe proving processes in mathematics classrooms at the lower secondary level from a mathematical perspective.
Kurzreferat
Der Beweis im mathematikunterricht ist eine der größten Herausforderungen für Mathematiklehrer. Empirische Studien haben wiederholt verschiedene Schülerprobleme in diesem Bereich aufgezeigt und lassen annelumen, dass die Schülerfähigkeiten im Beweisen signifikant durch den spezifischen Unterricht beeinflusst werden. In diesem Beitrag präsentieren wir eine Methode zur Evaluation von Unterrichtsbeweisen sowie Ergebnisse einer Videostudie zum Beweisen im Mathematikunterricht der Sekundarstufe I.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baumert, J.; Lehmann, R.; Lehrke, M. et al. (1997): TIMSS—Mathematisch-naturwissenschaftlicher Unterricht im internationalen Vergleich. Opladen: Leske+Budrich.
Boero, P. (1999): Argumentation and mathematical proof: a complex, productive, unavoidable relationship in mathematics and mathematics education. International Newsletter on the Teaching and Learning of Mathematical Proof, 7/8.
Deutsches PISA-Konsortium (2001): PISA 2000: Basiskompetenzen von Schülerinnen und Schülern im internationalen Vergleich. Opladen: Lesk+Budrich.
Hanna, G.; Jahnke, H. N. (1996): Proof and proving.—In: Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., Laborde, C. (Eds.), International handbook of mathematics education. Vol. 4, Pt. 2. Dordrecht: Kluwer, pp. 877–908
Healy, L.; Hoyles, C. (1998): Justifying and Proving in School Mathematics. Technical report on the nationwide survey. Institute of Education, University of London.
Heinze, A. (in preparation); Schülerprobleme beim Lösen geometrischer Beweisaufgaben—eine Interviewstudie.
Klieme, E.; Schümer, G.; Knoll, S. (2001): Mathematikunterricht in der Sekundarstufe I: “Aufgabenkultur” und Unterrichtsgestaltung.—In: Bundesministerium für Bildung und Forschung (BMBF) (Ed.), TIMSS—Impulse für Schule und Unterricht Bonn: BMBF, pp. 43–57
Lin, F.L. (2000): An approach for developing well-tested, validated research of mathematics learning and teaching.—In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1. Hiroshima: Hiroshima University, pp. 84–88
Manin, Y. (1977): A course in mathematical logic. New York: Springer.
Reiss, K.; Hellmich, F.; Reiss, M. (2002): Reasoning and proof in geometry: prerequisites of knowledge acquisition in secondary school students.—In A.D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education Vol. 4. Norwich: University of East Anglia, pp. 113–120
Reiss, K.; Klieme, E.; Heinze, A. (2001): Prerequisites for the understanding of proofs in the geometry classroom.—In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education Vol. 4. Utrecht: Utrecht University, pp. 97–104
Stigler, J.; Gonzales, P.; Kawanaka, T.; Knoll, S.; Serrano, A. (1999): The TIMSS videotape classroom study. U.S. Department of Education. National Center for Education Statistics, Washington, DC: U.S Government Printing Office.
de Villiers, M. (1990): The role and function of proof in mathematics. Pathagoras, 24, pp. 17–24.
Author information
Authors and Affiliations
Additional information
This research was funded by the deutsche Forschungsgemeinschaft in the priority program “Bildungsqualität von Schule (Educational Quality of School)” (RE 1247/4).