Everyone agrees that environments influence learning, but only a small percentage of
studies of cognitive development relate children's specific learning environments to their …

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 …

This article describes UMA (Unified Model of Arithmetic), a theory of children's arithmetic
implemented as a computational model. UMA builds on FARRA (Fraction Arithmetic Reflects …

This study's first purpose was to investigate effects of a fourth-and fifth-grade “next-
generation” fraction intervention, which included six enhancements over a previously …

The number one plays a special role in mathematics because it is the identity element in
multiplication and division. The present findings, however, indicate that many middle school …

To advance understanding of the gap in fraction learning between students in high-
achieving East-Asian countries and the United States, we examined both intended curricula …

Historically, efforts to foster strong awareness of tax issues among citizens have been
largely driven by the challenges of tax evasion and widespread ignorance of tax obligations …

Many US students possess only a weak knowledge of fraction arithmetic. I hypothesize that
textbooks are a critical reason for students' poor performance on fraction arithmetic. This is …

This thesis presents a comprehensive exploration of rational number arithmetic in primary
education, encompassing five distinct studies aimed at enhancing both understanding and …

Hopkins, S., Russo, J., & Siegler, RS (2022). Is counting hindering learning? An
investigation into children's proficiency with simple addition and their flexibility with mental …