Numerical Cognition

Cross-validating whether distributions of assigned problems that students encounter parallel distributions of textbook problems
Rational Numbers
Textbook Analysis

Carnegie Mellon University


March 31, 2022

Biased Problem Distributions in Assignments Parallel Those in Textbooks: Evidence From Fraction and Decimal Arithmetic

Tian, J., Leib, E.R., Griger, C., Oppenzato, C.O. , & Siegler, R.S. (2022)

Imbalances in problem distributions in math textbooks have been hypothesized to influence students’ performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all problems in textbooks and because teachers present problems from sources other than textbooks. To test whether distributions of problems that students encounter parallel distributions of textbook problems, we analyzed fraction and decimal arithmetic problems assigned by 14 teachers over an entire school year. Five of the six documented biases in textbook problem distributions were also present in the classroom assignments. Moreover, the same biases were present in 16 of the 18 combinations of bias and grade level (4th, 5th, and 6th grade) that were examined in assignments and textbooks. Theoretical and educational implications of these findings are discussed.

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