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Structuring versus counting: critical ways of using fingers in subtraction

Journal article
Authors Camilla Björklund
Angelika Kullberg
Ulla Runesson Kempe
Published in ZDM - Mathematics Education
Volume 51
Issue 1
Pages 13-24
ISSN 1863-9690
Publication year 2019
Published at Department of Education, Communication and Learning
Department of Pedagogical, Curricular and Professional Studies
Pages 13-24
Language en
Keywords Part-Whole relations, Preschool, Spontaneous finger use, Structuring numbers, Subtraction, Variation theory
Subject categories Pedagogy, Didactics


The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4–5-year-olds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children’s finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

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