A Logo-based Task for Arithmetical Activity
Résumé
Young children attend to answer-getting readings of arithmetical notation. This is evidenced by many children's exclusive acceptance of a + b = c syntaxes that lend themselves to computational readings (e.g. Behr et al., 1976; Carpenter & Levi, 2000; Knuth, Stephens, McNeil & Alibali 2006). Even those children who do accept a wider variety of syntaxes, such as a + b = b + a and c = a + b , adhere to a computational view involving getting answers to both sides of the equals sign and checking they are the same (Jones, 2006). I report here on the trialling of a Logo-based task (see screenshot below) designed to foster meaningful engagement with the structural properties of arithmetical equality statements. The design rationale is that of diagrammatic reasoning where arithmetic inscriptions onscreen are observed and manipulated according to precise operational rules. The dual functionality of selecting equality statements and substituting terms is intended to afford the specific diagrammatic activities of iconic matching and transformation making towards the construction of purposeful meanings for differing statement syntaxes. The data show that the children's readings of arithmetic notation were broadened from computation to iconic matching during trialling. This pattern-based observation of notation combined with the activity of transformation making resulted in commutative and partitional meaning-making for a + b = b + a and c = a + b syntaxes respectively. The data also suggest that various factors impacted on the diagrammatic strategies developed by the children to complete the task. These factors included blind experimentation, systematic testing, existing computational readings, and emergent commutative and partitional readings.
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