The process of knowledge re-description as underlying mechanism for the development of children’s problem-solving strategies: an example from arithmetic

Abstract

This paper reports on a study which aimed at exploring ways by which 5-6 year-old children organise different pieces of knowledge to develop strategies for solving a specific arithmetical task and furthermore, ways by which children move beyond their successful problem solving approaches to the acquisition of increased control over the procedural and conceptual knowledge that supports their problem solving success. The paper considers the emerging theory of Representational-Redescription which supports the idea of ‘success-based’ cognitive change and argues that new knowledge can be constructed by a process of internal exploitation of knowledge that already exists in the cognitive system of the problem solver.

In problem solving, the notion of Representational-Redescription has been studied in spatial, physics, linguistic and notational tasks but currently, it is under-researched in mathematics. The paper presents outcomes from a study which focused on ten cases. The microgenetic method was used for the study of changes in children’s problem solving. This entailed the design of a sequence of sessions during which children were individually involved in solving a specific form of additive task, more than once, and after they had been successful in solving it. The microgenetic method was combined with the clinical method of interviewing.

The paper presents a specific path of after-success strategy change. This path of change indicated children’s movement from initial success-oriented behaviour to an organisation-oriented phase during which new strategies were introduced or known strategies were evolved procedurally and conceptually. The paper explains the general analytical direction which was followed to reveal different levels of knowledge accessibility and explicitness which supported children’s main strategy during the after-success change process. These findings support the idea that learning follows not only from failure but also from success, and that the Representational-Redescription theory can offer an additional insight to the complex nature of learning processes

More information

Identifiers

ORCID for Chronoula Voutsina: orcid.org/0000-0003-2196-5816

ORCID for Keith Jones: orcid.org/0000-0003-3677-8802

Catalogue record

Export record