Fraction Instruction That Fosters General Multiplicative Reasoning

Lee Vanhille

Farmington (Utah) Bay Youth Center

vanhille@davis.uswest.net

Arthur J. Baroody

University of Illinois, U-C

baroody@uiuc.edu

Research indicates that students are relatively unsuccessful on tasks that require multiplicative reasoning, including those involving operations on fractions or proportional reasoning. The present study was undertaken to see if an instructional program on fraction operations--one that emphasized multiplicative relations--would transfer to unpracticed multiplicative problems, including proportionality.

The 51 participants in this study consisted of volunteers from three sixth-grade classes. Two control classes received traditional textbook-based fraction instruction, and the experimental class received instruction developed and piloted by the first author. The experimental instruction had the following features: (1) partitioning experiences with objects and extensive use of drawings that represented the partitioning; (2) partitioning experience that dealt with noninteger factors and complex ratios; (3) experience with ratio tables; and (4) instruction for multiplying a mixed number by a whole number based on a distributive model.

Participants were pre- and posttested using four dependent measures. Three measures were group-administered, paper-and-pencil tasks: computation of simple fractions, equivalent fractions with noninteger factors, and missing-factor sentences. The fourth measure was an individually administered oral test of contextualized proportionality problems.

ANCOVA analyses indicated that the experimental class did equally well as the control classes on fraction computation (p=.412). There was a significant difference among the other measures (all ps=.000), with the experimental class outscoring the control classes. Analyses of interview protocols indicated that the experimental participants were able to apply multiplicative reasoning to unfamiliar proportion problems.