The application and development of an addition goal sketch

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).