Humans and other species have biologically endowed abilities for discriminating quantities.
A widely accepted view sees such abilities as an evolved capacity specific for number and …

Do children learn number words by associating them with perceptual magnitudes? Recent
studies argue that approximate numerical magnitudes play a foundational role in the …

We demonstrate a link between preschoolers' quantitative competencies and their school-
entry knowledge of the relations among numbers (number-system knowledge). The …

Learning the cardinal principle (the last word reached when counting a set represents the
size of the whole set) is a major milestone in early mathematics. But researchers disagree …

Children who achieve an early understanding of the cardinal value of number words
(cardinal knowledge) have a superior understanding of the relations among numerals at …

Effective curiosity-driven learning requires recognizing that the value of evidence for testing
hypotheses depends on what other hypotheses are under consideration. Do we intuitively …

Both recent evidence and research-based early mathematics curricula indicate that
repeating patterns—predictable sequences that follow a rule—are a topic of major …

We investigate number and arithmetic learning among a Bolivian indigenous people, the
Tsimane', for whom formal schooling is comparatively recent in history and variable in both …

How do children acquire exact meanings for number words like three or forty‐seven? In
recent years, a lively debate has probed the cognitive systems that support learning, with …

Perceptual representations of objects and approximate magnitudes are often invoked as
building blocks that children combine to acquire the positive integers. Systems of numerical …