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Center for Educational Policy Studies Journal, v4 n3 p111-129 2014

The purpose of this study is to determine how Finnish pupils' problem-solving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other. The purpose of the formulation of the problem was to help the pupils to find how many solutions for a certain answer exist. The participants in the study were 348 third-graders and 356 fifth-graders. Pupils' fluency, i.e. ability to develop different solutions, was found to correlate with their ability to solve the problem. However, the proportions of the pupils (17% of the 3rd graders and 21% of the 5th graders) who answered that there were an infinite number of solutions are of the same magnitude. Thus, the pupils' ability to solve this kind of problem does not seem to have developed from the 3rd to the 5th grade. The lack and insufficiency of pupils' justifications reveal the importance of the teacher carefully listening to the pupils' ideas in order to be able to promote pupils' understanding of the concept of infinity, as well as the basic calculations.

Descriptors: Foreign Countries, Elementary School Students, Problem Solving, Mathematics Skills, Skill Development, Grade 3, Grade 5, Pretests Posttests, Followup Studies, Mathematical Aptitude, Subtraction, Arithmetic, Creative Thinking, Comparative Analysis

University of Ljubljana, Faculty of Education. University of Ljubljana Kardeljeva plošcad 16. Slovenia. Tel: +386-1-5892-344; e-mail: editors[at]; Web site:

Autor: Laine, Anu; Näveri, Liisa; Ahtee, Maija; Pehkonen, Erkki


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