NOMAD 9(2), 2004. The quality of conceptual change in mathematics: The case of number concept

 

KAARINA MERENLUOTO and ERNO LEHTINEN

Abstract
In this article, the main results are presented from a number concept test in which 538 students from 24 randomly selected Finnish upper secondary schools took part. The test included identification, classification and construction problems in the domain of rational and real numbers. In addition, the students were asked to explain their answers and estimate their certainty about them. The theories of conceptual change and of mathematics concept formation were used to categorize students’ explanations into different levels. The results indicate the clearly restricted nature of students’ prior thinking of whole numbers and of their everyday experiences of counting and continuity. On the basis of the results, we claim that the problems that students have with these difficult concepts are not only due to the complexity or abstract nature of the concepts to be learned, but also to the quality of their prior knowledge, which is not sufficiently taken into account in traditional teaching.

Sammanfattning
I denna artikel beskrivs de viktigaste resultaten från en studie, där elevers förmåga att uppfatta matematiska tal testades. 538 elever (i medeltal 17,2 år) från 24 slumpmässigt valda finska gymnasier deltog i studien. Eleverna svarade på frågor som innehöll identifierings-, klassificerings- och konstruktionsproblem inom området för rationella och reella tal. Eleverna ombads också förklara sina problemlösningar med egna ord och uppskatta svarens säkerhet. Teorier om begreppsförändring (Vosniadou, 1999) och matematisk begreppsutveckling (Sfard, 1991) användes för att klassificera studenters förklaringar. Majoriteten av eleverna hade stora svårigheter med begreppen. Resultatet indikerar att elevernas tidigare föreställningar begränsade deras insikter. Utgående från resultatet hävdar vi att de problem som elever har med de svåra begreppen inte bara förorsakas av begreppens komplexa natur, utan också av kvaliteten på deras tidigare kunskap. Detta har inte tillräckligt beaktats inom den traditionella undervisningen.

KAARINA MERENLUOTO
Dr. Kaarina Merenluoto is a senior researcher in the field of education at the Department of Teacher Education of University of Turku. Her scientific work is aimed at the research on problems of learning and conceptual understanding in mathematics on secondary level; and at the dynamics of cognitive and motivational processes in conceptual change.

ERNO LEHTINEN
Erno Lehtinen is professor of education at the University of Turku and is currently the vice rector of the University. His scientific work is aimed at combining basic research on cognition and motivation with the practical development of learning environments. He was the President of the European Association for Research on Learning and Instruction (EARLI) in 2001–2003.