In this review, we are pitting two theories against each other: the more accepted theory, the
number sense theory, suggesting that a sense of number is innate and non-symbolic …

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability
to succeed in many professions. Unfortunately, these capabilities pose large difficulties for …

In various cultures and at all spatial scales, humans produce a rich complexity of geometric
shapes such as lines, circles or spirals. Here, we propose that humans possess a language …

We examined relations between symbolic and non-symbolic numerical magnitude
representations, between whole number and fraction representations, and between these …

Identifying the types of mathematics content knowledge that are most predictive of students'
long-term learning is essential for improving both theories of mathematical development and …

Mathematical competence rests on developing knowledge of concepts and of procedures (ie
conceptual and procedural knowledge). Although there is some variability in how these …

The number line estimation task is widely used to investigate mathematical learning and
development. The present meta‐analysis statistically synthesized the extensive evidence on …

" Reviewing the state of the science of learning disabilities (LD) and describing effective
educational practices, this authoritative text has been significantly revised and expanded …

The integrated theory of numerical development posits that a central theme of numerical
development from infancy to adulthood is progressive broadening of the types and ranges of …

Recent research on fractions has broadened and deepened theories of numerical
development. Learning about fractions requires children to recognize that many properties …