Abstract
Problem solving has been a main focus in mathematics education for several decades, yet it seems that its definition and classroom implementation are far from being consensual. We explore the views and approaches of a small community: the project leaders of five elementary mathematics curriculum development projects in Israel, working within a centralized system, which dictates the syllabus. We describe and analyze their views along six categories: What are problems? What are not problems? Classification of problems, problem solving and individual differences, the ratio of problem solving tasks to other tasks in the project, and the role of heuristics and metacognition in teaching problem solving. We describe, exemplify, interpret and discuss the (few) points of convergence and the many different approaches. Finally, we reflect on the possible role of research in settling those differences. We speculate that our analysis and results go beyond the local and the idiosyncratic.
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Notes
A search in the Educational Resources Information Center (ERIC) database for publications bearing the keywords ‘problem-solving’ and ‘mathematics’ in their titles yielded more than 500 publications worldwide between 1993 and 2007.
There are several definitions of the terms “curriculum” and “syllabus” (see, for example, Connelly & Lantz (1991) and Eash (1991). For us, curriculum is a conglomerate of materials designed to teach and learn mathematics. These materials share an implicit or explicit rationale on goals, nature of teaching and learning and mathematical activity. Syllabus is a list of the topics to be taught and the recommended number of hours for teaching each topic.
Devoting special booklets to ‘word problems’ may send the unintended message that problem solving is a topic in itself rather than an approach to the learning and teaching of mathematics.
In the textbook, this problem appeared under the heading “Comparison Problems”.
This problem is given to students before learning about the unfolding of a pyramid.
It is interesting to note that, the project leader who presented this problem reported that most students draw quadrilaterals with two equal opposite sides, and only a few construct quadrilaterals with two equal adjacent sides.
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Arcavi, A., Friedlander, A. Curriculum developers and problem solving: the case of Israeli elementary school projects. ZDM Mathematics Education 39, 355–364 (2007). https://doi.org/10.1007/s11858-007-0050-3
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DOI: https://doi.org/10.1007/s11858-007-0050-3