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May 2004, Volume 35, Issue 3

FEATURES

Understanding Primes: The Role of Representation
Rina Zazkis, Peter Liljedahl
In this article we investigate how preservice elementary school (K–7) teachers understand the concept of prime numbers. We describe participants' understanding of primes and attempt to detect factors that influence their understanding. Representation  of number properties serves as a lens for the analysis of participants' responses. We suggest that an obstacle to the conceptual understanding of primality of numbers is the lack of a transparent representation for a prime number.

Middle School Children's Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective
Stephen J. Pape
Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem solving that integrates mathematical problem-solving and reading comprehension theories and using constant   comparative methodology (Strauss & Corbin, 1994), 98 sixth- and seventh-grade students' problem-solving behaviors were described and classified into five categories. Nearly 90% of problem solvers used one behavior on a majority of problems. Use of context such as units and relationships, recording information given in the problem, and provision of explanations  and justifications were associated with higher reading and mathematics achievement tests, greater success rates, fewer errors, and the ability to preserve the structure of problems during recall. These results were supported by item-level analyses.

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