The Interaction between Intuitive Interpretations, Linguistic Knowledge and Algorithmic Components in Children´s (Aged 7-9) Subtraction Errors

Aims: In the present paper, we have examined the interaction between formal, intuitive and algorithmic knowledge in the solution for the subtraction operation (Fischbein, 1994).
Study design: Qualitative analysis.
Place and duration of study: Department of Didactic, Organization and Investigation Methods (University of Salamanca), between February 2005 and July 2006.
Methodology: We included the verbal protocols of nine children aged between seven and ten years old who solved a total of 180 subtractions were analyzed. The volume of data obtained via verbal protocols has allowed us to study the influence of the conceptual framework and the way in which the children interpret algorithmic process in the first stage of teaching.
Results: The results have allowed certain suggestions to be made with regard to the relation between formal, procedural and intuitive components that have a bearing on the generation of errors, and offer deep insights into how teachers influence the acquisition of mathematical concepts in the primary education stage.
Conclusion: we consider as influential in the origin of the subtraction error is that the child’s intuitive interpretations formed in structural schemata, the vocabulary that forms part of these, and the semantic interpretation of zero uphold the sources that generate analogue transfer. It is important to consider its influence in order to improve the algorithmic teaching processes.