Computer programming is considered an important competence for the development of higher-order thinking in addition to algorithmic problem solving skills. Its horizontal integration throughout all educational levels is considered worthwhile and attracts the attention of researchers. Towards this direction, an exploratory case study is presented…

Problem solving, introduced in every grade and practiced throughout elementary school, is an essential foundation on which students build their understanding of mathematical ideas, operations, and relationships. This article discusses 1-2-3 Time, an instructional mode that promotes multimodal math learning in ways that engage and sustain students'…

The concept of proof is discussed from a "human" viewpoint. The author concludes that "a good proof is one which makes us wiser." (MP)

A review of the statement and history of the Four-Color theorem is followed by an explanation of Appel and Haken's solution of the problem with a computer-aided proof. This is seen as the first proof in mathematics that would not be done without a computer. (MP)

A traditional question is whether or not computers shall ever think like humans. This question is redirected to a discussion of whether computers shall ever be truly creative. Creativity is defined and a program is described that is designed to complete creatively a series problem in mathematics. (MP)

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

The use of a computer program written in BASIC to help prove a theorem in geometry is discussed. Ideas used in this example could be applied to writing programs for other geometric proofs. (MP)

The mathematics curriculum in the first 2 years of college is a tool created to assist in solving problems. The current mathematics curriculum has changed little; the same topics, tied to the engineering and science curriculum, are taught as they were being taught in 1945. The problems that students need to solve have changed however. Both the…

The use of the Computer to Help In Problem Solving (CHIPS) is described, along with Small Computers Aiding Mathematical Problem-solving and Investigations (SCAMPI). Sample activities involving combinations and "shuffles" of elements are used to highlight the use of computers, with the BASIC programing language featured. (MP)

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

Women tend to subscribe to a belief that they are less inclined than males to handle numbers, logic, or problem-solving tasks. Upward mobility in occupations is seen to be dependent on math. A list of math anxiety, math avoidance, and math reentry programs given around the country is provided. (MLW)

This document describes how to teach a computer to add numbers using the LOGO programing language. The programing project is described in the way a student might develop it. The model of developing the program uses humans as an anthropomorphic model for the computer, and the computer as a model for people. The document has an unorthodox style, as…

THIS GUIDE EXPLAINS HOW A COMPUTER MIGHT BE USED IN MATHEMATICS EDUCATION IN CONJUNCTION WITH THE REGULAR COURSE OF STUDY. STARTING WITH THE PREMISE THAT A CHILD WHO LEARNS TO OPERATE A COMPUTER IS LED BY HIS NEW SELF ESTEEM TOWARD A GREATER INTEREST IN HIS COURSES, THE AUTHORS STATE THAT COMPUTER EDUCATION WILL ALSO MEET THESE OBJECTIVES--(1)…

This final report summarizes research findings and presents a model for generative computer assisted instruction (CAI) with respect to its usefulness in the classroom environment. Methods used to individualize instruction, and the evolution of a procedure used to select a concept for presentation to a student with the generative CAI system are…

As momentum for change in U.S. education continues to grow, questions about the nature and goals of mathematics education take on increasing urgency. This report proposes a framework for reform of school mathematics mainly through reshaping of the mathematics curriculum. Chapters included are: (1) "A Rationale for Change," describing changing…