Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…

This paper describes a design research study with ten second-grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked how they counted in multiple bases, specifically how they knew when to go to a new place value and why it was necessary to do so. All ten…

Two studies indicate that Oksapmin children progress from premediational to mediational phases in their use of body parts to compare and reproduce number and that this change generally occurs prior to the development of concepts of number conservation. A third study shows that this general change is manifested in culturally specific ways.…

College students, in three experiments, learned to recite a counting pattern in the base three number system. Although all subjects learned to a criterion of two errorless trials, learning with different rule systems resulted in different levels of understanding and performance on transfer tasks. (GDC)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

This document contains a workshop presentation for elementary mathematics teachers. The purpose of the workshop is to demonstrate methods for teaching computational concepts beginning with concrete materials and moving to expressing these concepts abstractly with numerical symbols. Section headings are: (1) "Introduction"; (2) "Sorting and…