Fingerräkningsstrategier och talbegreppets utvecklingsnivåer

Abstract

Aim The main aim was to find out the character of the relationship between the pupils' finger-counting strategies and their levels of cognition for understanding the number-concept.

Main questions What finger-counting strategies do pupils use? · What are the pupils' respective levels of cognition for understanding the number-concept? · Is there a relationship between the pupils' finger-counting strategies and their levels of cognition for · understanding the number-concept?

Method Pupils' ways of thinking when counting on their fingers was our main focus. Therefore a qualitative approach seemed appropriate. 60 pupils, 7 and 8 years old, from three schools were interviewed to select 15 of them who used their fingers when counting. In order to facilitate the analyses of these pupils' finger-counting, we videotaped the pupils' counting on their fingers during the interviews. Then six of them, who displayed different strategies, were selected to be analyzed. The pupils were also observed during their mathematics lessons in order to give us the opportunity to see whether their respective finger-counting strategies were actually made use of as a habit of theirs. The analyses will take Fuson's research categories for understanding of the concept of number as a point of departure.

Results Connections between pupils' finger-counting strategies and their respective cognitive levels of understanding the concept of number have been identified during the study. Four different strategies were found, `the changing between the ordinal and cardinal aspect', `the coordinated ordinal and cardinal aspect', `the undivided number- word of five' and `the part-hole comprehension'. For example, `the changing between the ordinal and cardinal aspect' turned out to be a basic strategy according to which the pupils finger-counted those numbers that corresponded to the number in the mathematics operations. Another aspect of finger-counting that was discerned was that finger-counting seems to give the opportunity for extending the domain of subitizing with the help of finger-patterns.

Teaching applications Knowledge about different finger-counting strategies can be of great importance for mathematic teachers, since it can be a useful tool for getting better understanding of pupils' individual levels of understanding the concept of number. This in turn means that the teachers can make the pupils take advantage of the various supportive finger-counting strategies. Another positive aspect of finger-counting is the possible extension of subitizing, the ability of immediate quantity-comprehension, which is an ability of great importance when it comes to understanding the number concept.