How Valid is it to Use Number Lines to Measure Children's Conceptual Knowledge about Rational Number?

Abstract

This study investigated validity of scores derived from the measurement procedure involving number lines by assessing its unique contributions to performance differences in criterion measures of rational number knowledge and skills, including fraction computation, application and explanation. A total of 413 5th and 6th graders participated in the study. Children's part-whole knowledge was measured with items of regional area representation, measurement knowledge with items involving number lines as well as those of fraction-size comparisons. It was found that when part-whole knowledge was accounted for, measurement knowledge assessed with number line items had no or negligible association with all of the three criterion measures. In contrast, measurement knowledge assessed with fraction-size comparisons demonstrated excellent incremental predictability. The results indicate that scores derived from the number line test items are poor estimators of children's understanding of the measurement aspect of rational number.