NOMAD 11(3), 2006. The use of reasoning in the resolution of geometric problems

Skapad: 2006-10-31. Ändrad: 2006-11-02  

NOMAD 11(3), 2006. The use of reasoning in the resolution of geometric problems

EUGENIA KOLEZA and ELISABETH KABANI

Abstract

The cognitive processes of 15-year-old students, when they solve geometrical problems involving the construction of isosceles triangles, and the different forms of reasoning which they use, are investigated in this paper. First we explore the large variety of reasoning processes which appear, categorize them in three approaches (visual, heuristic and theoretical) and look at the language which is used by each one. Then we focus on the weaknesses of students' reasoning and examine their reasons. The analysis of the data intends to support teachers to recognize and understand the relationship between students' reasoning (nature of justification) and their
geometrical thought.

Sammenfatning

Artiklen undersøger kognitive processer hos 15-årige elever under deres arbejde med geometriske problemer i forbindelse med konstruktion af ligebenede trekanter. Tre forskellige ræsonnementsformer er udviklet til kategorisering af elevernes problemløsning; nemlig visuel, heuristisk og teoretisk ræsonneren. Inden for hver ræsonnementsform analyseres elevernes sprogbrug, grundlaget for og svaghederne ved deres ræsonnementer. Analyserne har som intention at støtte lærere i at genkende og forstå relationen mellem elevernes ræesonneren og deres geometriske tænkning og forståelse. En sådan viden kan anvendes som grundlag for at støtte og udfordre elevernes problemløsning inden for geometri på en relevant måde.

EUGENIA KOLEZA
Eugenia Koleza is Associate Professor and Ph.D. in Mathematics education in the Department of Primary Education, University of Ioannina, Ioannina, Greece. She is the Director of the Laboratory of Research in Mathematics Education of the University of Ioannina. She has served the editorial boards of Hellenic and international journals and has published books for elementary mathematics teachers and over 60 articles. Her main research interests are focused on the epistemological and sociological aspects of Mathematics Education.

ELISABETH KABANI
Elisabeth Kabani, who has been a mathematics teacher for 26 years, is the headmistress of the 5th High School of Alimos. She has a Master and Ph.D. in didactics of mathematics. She has participated in the group of implementation, supervision and support of innovative educational programs in Greek High Schools, and in many European Programs (Lingua, Comenius, Arion).