The authors propose that conceptual and procedural knowledge develop in an iterative
fashion and that improved problem representation is 1 mechanism underlying the relations …

This study examined relations between children's conceptual understanding of
mathematical equivalence and their procedures for solving equivalence problems (eg, 3+ 4+ …

This study examined whether the quality of first graders'(mean age= 7.2 years) numerical
magnitude representations is correlated with, predictive of, and causally related to their …

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 …

Engaging young children in mathematics: Standards for early childhood mathematics education
Page 2 Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics …

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

Interactions between conceptual and procedural knowledge influence the development of
mathematical competencies. However, after decades of research, these interrelations are …

Background/Context Most reforms in elementary education rely on teacher learning and
improved instruction to increase student learning. This study increases our understanding of …

The chapter reviews research on infants' and children's developing mathematical
competencies—from the ability to determine sizes of small sets to the solving of word …

Researchers have speculated that children find it more difficult to acquire conceptual
understanding of the inverse relation between multiplication and division than that between …