No abstract
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 counting based procedure for calculating sums and to subsequently 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 procedure 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 development, and a nuanced instructional theory of addition (i.e., one that goes beyond the direct instruction vs. discovery learning debate).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 advanced procedures they themselves have never used? In instructional terms, is direct 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 developmental readiness when teaching addition procedures and focus on promoting the conceptual underpinnings of more advanced procedures? The main purpose of this study is to address these theoretical and practical questions.Researchers generally agree that children use increasingly sophisticated and abstract counting based procedures to determine sums (e.g.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.