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…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

This is volume one of a three-volume SMSG junior high school mathematics text. This volume contains units concerned with the structure of the number systems of arithmetic. Unit topics include: (1) numeration; (2) natural numbers and zero; (3) factoring and primes; (4) supplementary tests for divisibility and repeating decimals; (5) the…

This is the first of two guidebooks for Grade 7 recommended to build fundamental concepts necessary for success in algebra. Topics covered include numeration systems, operations in non-decimal bases, whole numbers, factors and primes, and fractions. Goals for the course are stated, then, for each topic, performance objectives, a course outline,…

Suggests that good number sense is fundamental for success in estimation, approximation, and problem solving. Further, large-number concepts are appropriate for development in upper elementary school, high school, and beyond. Presents examples to enhance a sense of large numbers in middle and high school students. (PK)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Virtual organisms animated by a computational theory of selection by consequences responded on symmetrical and asymmetrical concurrent schedules of reinforcement. The theory instantiated Darwinian principles of selection, reproduction, and mutation such that a population of potential behaviors evolved under the selection pressure exerted by…

We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his…

The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and…