2024 Theses Doctoral

# Rebalancing Fraction Arithmetic Practice

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for studentsâ€™ poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with certain types of problems almost never presented (Braithwaite et al., 2017).

As a result, students often err when they attempt to solve those rare types of problems (Siegler & Pyke, 2013). Two experiments, a pilot study (n = 40 students in grades 5 through 7) and a larger study (n = 127 students in grades 6 and 7), were conducted. These experiments utilized a pretest-intervention-posttest design to empirically test the benefits of providing either a complement of the typical textbook distribution of problems (hyperbalanced practice) or an equal distribution of problems (balanced practice) compared to the benefits of providing a practice set that followed the typical distribution found in math textbooks.

A MANCOVA and follow-up ANCOVAs revealed significant differences between students in the textbook condition and students in the balanced and hyperbalanced conditions.For items involving adding fractions with unequal denominators, students who received typical textbook practice showed greater improvement and made fewer strategy errors than students who received hyperbalanced practice. For items involving multiplying two fractions with equal denominators, the opposite was true. Students who received hyperbalanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on items involving multiplying two fractions with equal denominators.

Finally, students who received fully balanced practice showed greater improvement and made fewer strategy errors than students who received typical textbook practice on problems involving multiplying one whole number and one fraction. This last finding was of particular interest since none of the practice conditions included practice with that item type.

The results of this study demonstrate that even a brief intervention in which students received extra practice with rare item types could improve performance. It also showed that gains in one type of item often resulted in decrements in others, which must be considered when making recommendations to textbook publishers and educators. In sum, this dissertation seeks to make a scholarly contribution to the field by discussing the role that textbooks play in student performance and by analyzing the benefits of supplementing typical textbook instruction with differently balanced fraction arithmetic practice.

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## Files

- Oppenzato_columbia_0054D_18292.pdf application/pdf 1.71 MB Download File

## More About This Work

- Academic Units
- Cognitive Studies in Education
- Thesis Advisors
- Siegler, Robert Stuart
- Degree
- Ph.D., Columbia University
- Published Here
- January 31, 2024