| Abstract: | During the past decade, rather than studying the outcomes of mathematics learning in experimentation with specific teaching strategies, cognitive psychology has been advancing understanding of the fundamental nature of mathematics learning. The promise of cognitive theories for instruction is illustrated by reviewing several studies on elementary mathematics. This research illuminates the formal structure of a mathematical procedure such as counting and the hierarchy of its subprocedures, the diagnosis of consistent errors in subtraction and decimals and the discovery of their underlying sources, the formulation of the role of schemata in executing arithmetic skills, and the comprehension of word problems. The development of mathematics skills is considered in terms of the distinction between procedural and propositional knowledge. Implications of a cognitively based understanding of mathematical learning for the effective design of instruction are discussed. (67 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved) |
