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

Many children and adults have difficulty gaining a comprehensive understanding of rational
numbers. Although fractions are taught before decimals and percentages in many countries …

When school students compare the numerical values of fractions, they have frequently been
found to be biased by the natural numbers involved (eg, to believe that 1/4> 1/3 because 4> …

Abstract Knowledge of fractions is thought to be crucial for success with algebra, but
empirical evidence supporting this conjecture is just beginning to emerge. In the current …

An important issue in understanding mathematical cognition involves the similarities and
differences between the magnitude representations associated with various types of rational …

Many students' knowledge of fractions is adversely affected by whole number bias, the
tendency to focus on the separate whole number components (numerator and denominator) …

To understand the development of mathematical cognition and to improve instructional
practices, it is critical to identify early predictors of difficulty in learning complex mathematical …

The standard number system includes several distinct types of notations, which differ
conceptually and afford different procedures. Among notations for rational numbers, the …

How children's understanding of numerical magnitudes changes over the course of
development remains a key question in the study of numerical cognition. In an ongoing …

Fraction and decimal concepts are notoriously difficult for children to learn yet are a major
component of elementary and middle school math curriculum and an important prerequisite …