Portion of the chapter on Numerals" from author's forthcoming book on Japanese and the Other Altaic Languages". Paper delivered at the March 1969 meeting of the Association for Asian Studies on The Periphery of the Japanese Language". (DS)

The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

Discusses mastery goals and developmental levels of students aged 3-7 for learning numbers in informal situations. (KHR)

Demonstrates how to use graphing calculators to explore rational number approximations to irrational numbers. (Author/NB)

Describes the kinds of computational abilities achieved by a class of 4th grade students who were part of a research program for teaching rational numbers. In this program, students build on intuitive understandings of percents and proportions for the development of overall understanding of the number system and are encouraged to invent their own…

Analysis of characteristics of rational numbers in magazines written for children, teenagers, and adults indicated that difficult mathematical concepts that appear in the media are much more prevalent in adults' magazines than in the others. Discusses numeracy demands of everyday life. Appendix contains coding scheme. (34 references) (Author/MKR)

In this article we investigate how preservice elementary school (K-7) teachers understand the concept of prime numbers. We describe participants' understanding of primes and attempt to detect factors that influence their understanding. Representation of number properties serves as a lens for the analysis of participants' responses. We suggest that…

This paper examines what children believe about unmapped number words--those number words whose exact meanings children have not yet learned. In Study one, 31 children (ages 2-10 to 4-2) judged that the application of "five" and "six" changes when numerosity changes, although they did not know that equal sets must have the same number word. In…

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists…

These Proceedings are a written record of the research presented at the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2011) held in Reno, Nevada, October 20-23, 2011. The theme of the conference is Transformative Mathematics Teaching and Learning. The Proceedings…