Conceptual versus procedural approaches to ordering fractions

This paper reports the performance of 30 rising seventh-grade girls on a task in which they were asked to order four fractions from least to greatest. Less than three-fifths attained correct answers. The performance gap was widest between students who attended Title I schools and those who did not, the latter being much more likely to attain correct answers. The achievement gap was less prominent by race/ethnicity, family socioeconomic status, and community type (suburban/urban versus rural). Participants tended to use conceptual and procedural approaches equally, but conceptual approaches were more successful. The most common conceptual strategy was making drawings that illustrated part-whole concepts, and the most common procedural strategy was converting fractions to equivalent fractions. The most problematic fractions to place in order of relative size were the two middle fractions, which were somewhat closer to each other in size than other adjacent pairs and were farthest from the benchmarks of 0 or 1. Based on these and other research findings, we conclude that it would benefit students to possess a greater repertoire of specific strategies, especially conceptual strategies such as use of number lines, benchmarks, and set models, for working with fractions.