This guide is designed to aid the teacher in planning and teaching an eighth-grade mathematics course which should strengthen the student's understanding of the basic structure of mathematics through experience with and appreciation of abstract concepts. Thirteen units outlined are entitled: Numeration Systems; Natural Numbers and Zero; Integers;…

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Activities for teaching mathematics in kindergarten through grade 8 are included in this guide. Both original ideas and ideas gleaned from various sources, including teachers in the district, are presented. The introduction briefly discusses the importance of developing understanding of concepts, processes, and relationships, the need for…

One possible way of looking at the limit concept, from the learner's point of view, is proposed; it can easily be built up gradually with little risk of conscious or subconscious conflicts of concepts perceived to be closely related. (MN)

Fourth grade children (n=20) were matched on a pretest and randomly assigned to either a wooden base-10 block or computerized microworld group. Instruction was designed to establish relationships between notation and meaning, extending whole number numeration to decimal numeration. Neither group changed whole-number notational methods nor had…

This document reports on a small-group teaching experiment whose goal was to understand how fourth- and sixth-grade children develop concepts of common and decimal fractions. Both the Grade 6 and the Grade 4/5 children were taught common and decimal fractions through discussion and by using manipulatives, beginning with basic concepts of common…

This booklet was written to provide elementary-school teachers with an overview of some of the research results related to the development of computational skills, together with ideas for classroom activities which have grown out of research projects. The booklet is organized into twelve sections, the first of which is devoted to delineating the…

Described is a bingo-like game for classroom drill with fractions and their equivalents. (RS)

A proof is given of the irrationality of the square root of 2 which depends on notions of terminating and repeating decimals. (MP)

Several examples are given to show that the calculator can be a tool to enhance mathematical understanding. Expressing rational numbers (fractions) as decimals provides the content focus. (MNS)

A method of showing the meaning of decimal fraction without using fraction words or notation. One technique described in detail uses large squares, strips, and small squares; using the metric system and decimal coinage is also suggested. (DT)

Included in this section are brief articles on an algebraic puzzler, periodic decimal fractions with computers, and the arrow method of teaching logarithms. (MNS)

Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)