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 …

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

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 …

This article proposes an integrated theory of acquisition of knowledge about whole numbers
and fractions. Although whole numbers and fractions differ in many ways that influence their …

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 …

Understanding of numerical development is growing rapidly, but the volume and diversity of
findings can make it difficult to perceive any coherence in the process. The integrative theory …

Arithmetic is still hugely important in many aspects of modern life, but our personal attitudes
to it differ greatly. Many people struggle with the basic principles of arithmetic, whilst others …

In this review, we attempt to integrate two crucial aspects of numerical development:
learning the magnitudes of individual numbers and learning arithmetic. Numerical …