Procedural and conceptual changes in young children’s problem solving

Voutsina, Chronoula (2012) Procedural and conceptual changes in young children’s problem solving. Educational Studies in Mathematics , 79, (2), 193-214. (doi:10.1007/s10649-011-9334-1).


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This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted with ten 5-6 year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures and arithmetic concepts when solving a multiple-step task, and how children’s application of different types of knowledge and overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions. The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals a dynamic interplay between children’s developing representation of the task, their improved procedures, and gradually their more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of the ‘iterative model’ hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s arithmetic problem solving.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s10649-011-9334-1
ISSNs: 0013-1954 (print)
1573-0816 (electronic)
Keywords: arithmetic, addition problem solving, procedural knowledge, conceptual knowledge, iterative model
Subjects: L Education > LB Theory and practice of education
Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Education > Mathematics and Science Education
Faculty of Social and Human Sciences > Southampton Education School > Mathematics, Science & Health Education (MSHE)
ePrint ID: 175337
Accepted Date and Publication Date:
9 June 2011Made publicly available
Date Deposited: 23 Feb 2011 09:31
Last Modified: 31 Mar 2016 13:33
Children Moving Beyond Initial Success in Problem-Solving
Funded by: ESRC National Centre for Research Methods (PTA-026-27-0697)
October 2004 to September 2005

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