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 psychophysical function that best fits human data from number-line estimation is the
subject of a lively, on-going debate with important theoretical and practical implications. We …

The effectiveness of an experimental middle school fraction intervention was evaluated. The
intervention was centered on the number line and incorporated key principles from the …

How does understanding the decimal system change with age and experience? Second,
third, sixth graders, and adults (Experiment 1: N= 96, mean ages= 7.9, 9.23, 12.06, and …

The relation between short‐term and long‐term change (also known as learning and
development) has been of great interest throughout the history of developmental …

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) …

The number line task is often used to assess children's and adults' underlying
representations of integers. Traditional bounded number line tasks, however, have …

Children's ability to relate number to a continuous quantity abstraction visualized as a
number line is widely accepted to be predictive of mathematics achievement. However, a …

Numeric magnitudes often bias adults' spatial performance. Partly because the direction of
this bias (left‐to‐right versus right‐to‐left) is culture‐specific, it has been assumed that the …

When, how, and why students use conceptual knowledge during math problem solving is
not well understood. We propose that when solving routine problems, students are more …