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

Scientific ideas are often expressed as mathematical equations. Understanding the ideas
contained within these equations requires making sense of both the embedded mathematics …

This paper reviews research on learners' knowledge of three arithmetic principles:
Commutativity, Relation to Operands, and Inversion. Studies of arithmetic principle …

Recent functional neuroimaging studies have begun to clarify how the human brain
performs the everyday activities that require mental calculation. We used fMRI to test the …

When reasoning about rational numbers, people sometimes incorrectly apply principles or
rules for natural numbers. Many factors affect whether participants display this natural …

Abstract The Common Core State Standards in Mathematics recommends that children
should use visual models to represent fraction operations, such as fraction division …

Past research has shown that both contrasting cases instruction and prompts to self-explain
promote students' learning in mathematics. However, it is not clear whether these …

This study examined children's learning from implicit and explicit analogies during
instruction. In all conditions, 6th grade children learned about fraction division from a …

The current study investigated the relation between spatial ability and children's math
performance, as well as the potential mechanisms underlying this relation including …

Previous studies have shown that even preschoolers can solve inversion problems of the
form a+ b− b by using the knowledge that addition and subtraction are inverse operations. In …