Missing Input: How Imbalanced Distributions of Textbook Problems Affect Mathematics Learning

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students perform surprisingly poorly on seemingly simple fraction and decimal arithmetic problems that are seldom seen in textbooks. Next, we describe imbalanced distributions in textbooks of mixed notation arithmetic and comparison problems, and we hypothesize similar relations between the frequency of those types of problems and student accuracy on those tasks. Finally, we review findings about relations between textbook input and student performance in whole number arithmetic and mathematical equality, and we propose a hypothesis regarding when imbalanced distributions of problems are most detrimental. We conclude that presenting more balanced distributions of problems and helping children understand mathematical principles that differentiate legitimate from flawed solution strategies offer promising ways of improving mathematics education.