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May 2009, Volume 40, Issue 3


Preservice Elementary School Teachers’ Conceptions of Multidigit Whole Numbers
Eva Thanheiser
Although preservice elementary school teachers (PSTs) lack the understanding of multidigit whole numbers necessary to teach in ways that empower students mathematically, little is known about their conceptions of multidigit whole numbers. The extensive research on children’s understanding of multidigit whole numbers is used to explicate PSTs’ conceptions of these numbers. A grounded theoretical approach leads to the development of a framework for PSTs’ conceptions of multidigit whole numbers, and that framework facilitates description of their conceptions and their difficulties in the context of the standard algorithms. The framework also enables discussion of the PSTs’ performance in other contexts.

The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems
Swee Ng; Kerry Lee;
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. The authors describe the model method and a three-phase theoretical framework supporting its use. The findings offer avenues of support in word problem solving to children of average ability.

Facilitating the Transition from Empirical Arguments to Proof
Gabriel Stylianides; Andreas Stylianides
Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, the authors discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the limitations of empirical arguments as methods for validating mathematical generalizations and see an intellectual need to learn about secure methods for validation (i.e., proofs). The development of the instructional sequence was part of a 4-year design experiment conducted in an undergraduate mathematics course, prerequisite for admission to an elementary teaching certification program.