Abstract
It is well known that the regulation of processes is an important factor in problem solving from Grade 7 to university level (cf. Mevarech & Kramarski, 1997; Schoenfeld, 1985). We do not, however, know much about the problem-solving competencies of younger children (cf. Heinze, 2007, p. 15). Do the results of studies also hold true for students below Grade 7? The study presented here strongly suggests that metacognition and process regulation is important in Grade 5 as well.The research questions are: How do the (more or less successful) problem-solving processes of fifth graders occur? What is the impact of metacognition and selfregulation on these processes? Are the transitions between phases in the problemsolving process closely connected to metacognitive activities?An analysis of approximately 100 problem-solving processes of fifth graders (aged 10–12) from German secondary schools will be used to help answer these questions. The videotapes that supplied the raw data were parsed into phases called episodes using an adapted version of the “protocol analysis framework” by Schoenfeld (1985, ch. 9). The junctures between these episodes were additionally coded with the “system for categorizing metacognitive activities” by Cohors-Fresenborg and Kaune (2007a). There is a strong correlation between(missing) process regulation and success (or failure) in the problem-solving attempts. Concluding suggestions are given for the implementation of the results in school teaching. These suggestions are currently being tested.
Highlights
Problem solving is important in everyday life, in situations where the solution path is not immediately obvious, as well as in mathematics, because “what mathematics really consists of is problems and solutions” (Halmos, 1980, p. 519)
Product Coding: In order to determine the pupils’ success in problem solving, their work results were graded into four categories: (1) no access, when the pupils did not work on the task meaningfully, (2) basic access, when they solved the problem but the solution had notable flaws, (3) advanced access, when they solved the problem for the most part, and (4) full access, when the pupils solved the task properly and presented appropriate reasons
Please note that 10 of the 19 pupils who worked on the “Squares on a Chessboard” task misinterpreted the formulation of the task and answered “64 squares” within less than 3 minutes. This is a sure sign of missing metacognition or control that leads to bad results
Summary
Problem solving is important in everyday life, in situations where the solution path is not immediately obvious (cf. OECD, 2003), as well as in mathematics, because “what mathematics really consists of is problems and solutions” (Halmos, 1980, p. 519). Problem solving is important in everyday life, in situations where the solution path is not immediately obvious (cf OECD, 2003), as well as in mathematics, because “what mathematics really consists of is problems and solutions” It is widely accepted that solving problems is of importance for the learning of mathematics, and it is part of many school curricula, e.g., in the United States and Germany (cf KMK, 2003; NCTM, 2000). In researching problem-solving, metacognition is an important factor to take into account 232), who was the first to describe this concept, the term metacognition “refers to one’s knowledge concerning one’s own cognitive processes and products or anything related to them, [...]. [It] refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes [...]” According to Flavell (1976, p. 232), who was the first to describe this concept, the term metacognition “refers to one’s knowledge concerning one’s own cognitive processes and products or anything related to them, [...]. [It] refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes [...]”
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