Compares sixth-grade American students to three samples of (Chinese, Japanese, and Taiwanese) sixth-grade Asian students to determine if the well-documented mathematical achievement of students from these Asian nations might be due in part to a greater understanding of mathematical representations. Indicates that all Asian samples scored…

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based "transition to proof" courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as…

The Colorado Model Content Standards for Mathematics were designed to serve as a guide for school districts as they define standards that will enable every Colorado student to develop the mathematical literacy needed for citizenship and employment in the 21st century. A new vision is provided of the content students should study in order to…

The focus of this activities book is on using calculators to solve problems, as a way of promoting better comprehension in mathematics in the intermediate grades. Problems of various types are presented, ranging from those based on everyday life such as shopping, schedules, meal planning, and sports, to those involving imaginary ideas.…

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)

This guide is for the use of teachers in the primary grades and is organized around six concepts: sets, numbers and numeration; operations, their properties and number theory; relations and functions; geometry; measurement; and probability and statistics. Objectives and sample activities are presented for each concept. Separate sections deal with…

This study examined the effects of number of illustrative examples and number of practice problems given on seventh graders' achievement in a unit on probability. Four treatment groups were used, one for each combination of two levels of number of examples and two levels of number of practice problems. Prior to treatment students were pretested on…

In an attempt to prepare students for units analysis in the solution of problems in high school chemistry and physics, the author developed learning packets on the factor label method. Thirty-three students used these packets individually during a regular tenth-grade geometry class. There were two packets, each to be used for two days. Prior to…

A criterion-referenced test battery was devised for use with the mathematics program of the Mamaroneck Public Schools (New York) in 1971. After two annual administrations, the tests were revised in four ways. The format was changed, and the number of items dealing with geometry was increased; some items were revised to conform better with the…

The possibilities that magazines have to offer in the teaching of mathematics with consumer-related problems are discussed. (JT)

Instructional techniques are given for the use of calculators in (1) finding prime numbers, (2) solving trigonometric equations, and (3) solving polynomial equations. (CP)

A variety of calculator activities is described for developing problem solving skills without getting involved in tedious computations. (JT)

Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)