A long tradition of research on mathematical thinking has focused on procedural knowledge,
or knowledge of how to solve problems and enact procedures. In recent years, however …

Researchers have speculated that children find it more difficult to acquire conceptual
understanding of the inverse relation between multiplication and division than that between …

The last decade has seen a rapid growth in our understanding of the cognitive systems that
underlie mathematical learning and performance, and an increased recognition of the …

Early elementary schooling in 2nd and 3rd grades (ages 7–9) is an important period for the
acquisition and mastery of basic mathematical skills. Yet, we know very little about …

When reasoning about rational numbers, people sometimes incorrectly apply principles or
rules for natural numbers. Many factors affect whether participants display this natural …

This study investigated whether instruction that involves comparing the equal sign with other
relational symbols is more effective at imparting a relational interpretation of the equal sign …

A major goal of the first years of schooling is students' development from using counting
strategies to using calculation strategies–or even recall–to solve addition or subtraction …

Arithmetic problem solving is a crucial part of mathematics education. However, existing
problem solving theories do not fully account for the semantic constraints partaking in the …

We propose to assess conceptual knowledge of mathematical notions by having recourse to
isomorphic word problems. We assumed that failing to solve isomorphic problems is an …

This study investigated the promotion of children's understanding and acquisition of
arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved …