The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

Recently, the nature of children's mental number line has received much investigation. In the number line task, children are required to mark a presented number on a physical number line with fixed endpoints. Typically, it was observed that the estimations of younger/inexperienced children were accounted for best by a logarithmic function, whereas…

In this study, Piagetian theory is extended to explore ways in which children construct their understanding of our notational system and place value. Eighty children aged 4 to 9 were asked to group objects, draw pictures of grouped quantities, write numerals to indicate amounts, and theorize about the relationship between their written numerals…

A mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing…

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

This brief report from the Indigenous Mathematics Project focuses on the way in which numerical reasoning is changing in the Oksapmin community of Papua New Guinea as a function of participation in new social institutions: economic exchange with currency and enrollment in school. Each of these new institutions means that arithmetic problems are…

AN ATTEMPT WAS MADE TO ASSESS THE EFFECTS ON ADULT LEARNING OF DIFFERENTIALLY STRUCTURED INTRODUCTORY COGNITIVE LEARNING TASKS AND MATERIALS, AND THE INTERACTION OF INTELLIGENCE WITH THE EXPERIMENTALLY MANIPULATED MATERIAL AND TASK CATEGORIES. ABOUT 96 ADULTS WHO WERE UNFAMILIAR WITH THE CONCEPT OF NUMBER BASES WERE CLASSIFIED ACCORDING TO A 4X3X4…