Early algebraic thinking is the reasoning engaged in by 5-to 12-year-olds as they build
meaning for the objects and ways of thinking to be encountered within the later study of …

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 …

For some time now, the study of cognitive development has been far and away the most
active discipline within developmental psychology. Although there would be much …

This study examined relations between children's conceptual understanding of
mathematical equivalence and their procedures for solving equivalence problems (eg, 3+ 4+ …

Given its important role in mathematics as well as its role as a gatekeeper to future
educational and employment opportunities, algebra has become a focal point of both reform …

The studies presented in this book should be of interest to anybody concerned with the
teaching of arithmetic to young children or with cognitive development in general …

In a series of two in vivo experiments, we examine whether correct and incorrect examples
with prompts for self-explanation can be effective for improving students' conceptual …

Explaining new ideas to oneself can promote transfer, but how and when such self‐
explanation is effective is unclear. This study evaluated whether self‐explanation leads to …

This study examined whether knowledge of arithmetic contributes to difficulties with
equations. In Experiment 1, children (ages 7–11) completed tasks to assess their adherence …

Students hold many misconceptions as they transition from arithmetic to algebraic thinking,
and these misconceptions can hinder their performance and learning in the subject. To …