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Vamvakoussi, Xenia; Vosniadou, Stella – Cognition and Instruction, 2010
We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…
Descriptors: Secondary School Students, Intervals, Numbers, Mathematics
Baroody, Arthur J.; Brach, Catherine; Tai, Yu-chi – Cognition and Instruction, 2006
A schema based view of addition development is compared with Siegler's latest strategy-choice model, which includes an addition goal sketch (a basic understanding of "the goals and causal relations" of addition; Siegler & Crowley, 1994, p. 196). This metacognitive component in the latter model is presumed to develop as a child practices a basic…
Descriptors: Arithmetic, Mathematics Instruction, Models, Cognitive Development