This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

A series of questions can be posed and resolved in the process of teaching that the decimal expansions of rationals are terminating or repeating. (SD)

Divisibility facts, greatest common divisors, least common multiples, and relative primes are explored through the use of lattice diagrams. (JT)

Beginning with peg manipulation the author sets up a different multiplication system and set of primes. (JM)

The history of Hawaiian number systems is examined, and answers to questions regarding Hawaiian number words, including their origin and factors that influenced their development, are covered. A brief guide for pronouncing Hawaiian words is also provided. (MP)

Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

The purpose of this report is to make a tentative contribution to the knowledge of students' understanding of the significance of numerical information. The article relates to a study made by the author. (Author/MK)

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

Extensive studies have documented various difficulties with, and misconceptions about, decimal numeration across different levels of education. This paper reports on pre-service teachers' misconceptions about the density of decimals. Written test data from 140 Indonesian pre-service teachers, observation of group and classroom discussions provided…

One of the best known numbers in mathematics is the number denoted by the symbol [pi]. This column describes activities that teachers can utilize to encourage students to explore the use of [pi] in one of the simplest of geometric figures: the circle.

A key area of weakness in individuals with fetal alcohol spectrum disorder (FASD) is working memory, thus the goal of this study was to determine whether teaching children (aged 4-11) with FASD verbal rehearsal would increase their memory. Rehearsal training has been effective in other populations with working memory difficulties, so we…

We review recently published papers that have contributed to our understanding of how the preverbal infant represents number, area and time. We review evidence that infants rely on two distinct systems to represent number nonverbally and highlight the similarities in the ratio-dependent discrimination of number, time and area. Contrary to earlier…

This article looks at how the activity of decomposing number--having students write numerical expressions equivalent to the number of days in school--can help students develop understanding of place value. (Contains 3 figures.)

The balance between the preservation of early cognitive functions and serious transformations on these functions shifts across time. Piaget's writings, which favored transformations, are being replaced by writings that emphasize continuities between select cognitive functions of infants and older children. The claim that young infants possess…