Baroody_et_al._Mixed_Methods - COGNITION AND INSTRUCTION...

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The Application and Development of an Addition Goal Sketch Arthur J. Baroody and Sirpa H. Tiilikainen Department of Curriculum and Instruction University of Illinois at Urbana–Champaign Yu-chi Tai College of Optometry Ohio State University A schema based view of addition development is compared with Siegler’s latest strategy-choice model, which includes an addition goal sketch (a basic understand- ing 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 counting based procedure for calculating sums and to sub- sequently affect strategy choice by identifying correct and incorrect procedures. A study of 20 kindergartners was undertaken to examine key assumptions of this model. Participants were individually interviewed to determine their own proce- dure use and their ability to evaluate correct and incorrect procedures. The results did not support a central prediction of the strategy-choice model—that children who possess a goal sketch should recognize as correct a relatively advanced (counting-on) procedure they themselves do not use. These results are consistent with the schema based view that accurately evaluating or learning such advanced procedures requires a qualitative leap in conceptual development. Theoretical, methodological, and instructional implications include a case for a simulation that models assimilation (a cognitive process underlying developmental readiness and conceptual development), a conceptually based taxonomy of addition develop- ment, and a nuanced instructional theory of addition (i.e., one that goes beyond the direct instruction vs. discovery learning debate). COGNITION AND INSTRUCTION, 24 (1), 123–170 Copyright © 2006, Lawrence Erlbaum Associates, Inc. Correspondence should be addressed to Arthur J. Baroody, Department of Curriculum and Instruc- tion, University of Illinois at Urbana–Champaign, 310 Education Building, 1310 South 6th Street MC-708, Champaign, IL 61820–6990. E-mail: [email protected]
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When and how do children construct the conceptual understanding necessary to evaluate and adopt new counting based procedures for determining sums? Once children construct a basic understanding of the purpose (goals) and nature (causal relations) of addition, does this goal sketch empower them to comprehend, assess, and learn any new counting based procedure, even relatively sophisticated or ad- vanced procedures they themselves have never used? In instructional terms, is di- rect instruction (modeling by, e.g., a parent, early childhood teacher, older sibling, or television character) sufficient for learning all such procedures or accelerating addition development? Or, does a goal sketch enable children to assimilate, judge, and internalize basic procedures but not more advanced procedures that require a deeper conceptual understanding? That is, must educators take into account devel- opmental readiness when teaching addition procedures and focus on promoting the conceptual underpinnings of more advanced procedures? The main purpose of
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Baroody_et_al._Mixed_Methods - COGNITION AND INSTRUCTION...

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