Distributions of textbook problems predict student learning: Data from decimal arithmetic.

Abstract

This study investigated relations between the distribution of practice problems in textbooks and students’ learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal arithmetic problems were present across the 3 series: Addition and subtraction more often involved 2 decimals than a whole number and a decimal, but the opposite was true for multiplication and division. We expected children’s learning of decimal arithmetic to reflect these distributional biases. In Studies 2, 3, and 4, we tested the prediction that children would have more difficulty solving types of problems that appeared less frequently in textbooks, regardless of the intrinsic complexity of solving the problems. We analyzed students’ performance on decimal arithmetic from an experiment conducted in a different lab 35 years ago (Study 2), from a contemporary large-scale web-based learning platform (Study 3), and from a recent controlled experiment conducted in our own lab (Study 4). Despite many differences among the 3 studies, performance in all 3 was in accord with the predictions. These findings suggest that the distributions of practice problems in math textbooks may influence what children do and do not learn. Usefulness of analyzing textbook problem distributions as well as educational implications of the current findings are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved)