The Transition from Counting-All to Counting-on in Addition

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  • 1 Northwestern University

An analysis of the transition from counting-all to counting-on identified three subskills: (a) counting-up from an arbitrary point, (b) shifting from the cardinal to the counting meaning of the first addend, and (c) beginning the count of the second addend with the next counting word. First-grade children were given tests to classify them as counting-all versus counting-on followed by tests of the subskills. Adequate subskill performance was strongly related to counting-on: All 28 count-on children demonstrated all three subskills or incorporated Subskill 2 into Subskill 3, whereas 36 of 45 count-all children failed to demonstrate one or more subskills. A posttest indicated that the subskills assessment alone had induced counting-on for 7 of the 9 count-all children who demonstrated all subskills. A random half of the children who initially lacked Subskills 2 and 3 were taught them in a single session and retested. Seven of the 8 instructed children counted-on, compared to 1 of 8 not instructed. The conceptual bases for the subskills are discussed.

Journal for Research in Mathematics Education


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