Students' Overuse of Proportionality on Missing-Value Problems: How Numbers May Change Solutions

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. We investigated whether (besides the missingvalue formulation of word problems) the numbers appearing in word problems are part of the superficial cues that lead students to (over) use proportionality. A test containing proportional and nonproportional word problems was given to 508 4th, 5th, and 6th graders. Numbers in these problems were experimentally manipulated so that the internal and external ratios were either integer or not. For proportional problems, performances decreased as a result of noninteger ratios. For nonproportional problems, noninteger ratios led to a decrease in the overuse of proportionality; only in the case of additive nonproportional problems was this decrease accompanied by an increase in correct answers. This effect decreased from 4th grade to 6th grade. Implications of this study for research and practice are discussed.