Abstract
Symbolic subtraction problems such as 14 − 8 =? were interpreted to children as story problems with dot pictures that supported count-up solutions. Children in first-grade mathematics classes were taught with considerable success to solve such symbolic subtraction problems by counting up from the smaller number to the larger (“8, 9, 10, 11, 12, 13, 14; 6 more make 14”) while keeping track of the number counted up by using one-handed finger panerns. The children improved quire considerably on a rimed test of the more difficult subtraction combinations, and this improvement held up over a month. Interviews indicated that almost all children could count up to solve subtraction combinations they did not know. Many used counting up to solve subtraction story problems with different semantic structures: performance on compare, separate (take-away), and equalize (how many more to make the same?) story problems was similar and good.
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