A model of how automated and controlled processing can be mixed in computer simulations of problem solving is proposed. It is based on previous work by Hunt and Lansman (1983), who developed a model of problem solving that could reproduce the data obtained with several attention and performance paradigms, extending production-system notation to…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 56th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education is covered. Ten reports deal with problem solving, four are concerned with instructional methods, three…

These two modules cover aspects of the coding process and algebraic coding theory. The first unit defines coding as a branch of information and communication science, which draws extensively upon many diverse mathematical fields, primarily abstract and linear algebra, number theory, probability and statistics, and combinatorial theory. Aspects of…

This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

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 survey represents an attempt to indicate how much is known about all aspects of research in mathematics education. For each topic, a brief description of the variable is provided and the kinds of experiments or other empirical studies which have been used to investigate them are indicated. At the end of each chapter is a bibliography and a…

An overview of a variety of interesting teaching techniques is given to assist school personnel in strengthening their overall mathematics programs in the first eight grades. The problem-solving approaches recommended are so designed that they should be useful in every subject. The materials could also be used as a basis for teacher in-service…

This publication is a study guide prepared for use in a National Science Foundation (NSF) Chautaugua-Type Short Course for College Teachers. The purpose of the guide is to provide college teachers with a variety of modeling methods that can be used with problem solving. Mathematical applications and illustrations are included, along with listings…

The message of this article is that there are many types of problems ordinarily requiring advanced techniques or special insight to solve which can now be done as simple programming exercises on inexpensive programmable calculators. Several examples appropriate for the secondary school curriculum are given. These are: (1) evaluating polynomials;…

This is the teacher's guide to accompany the student guide which together comprise one of five computer-oriented environmental/energy education units. This unit explores U.S. energy consumption; is applicable to Mathematics, Social Studies, and Ecology or Science Studies with Mathematics background; and is intended for use in grades 9 through 14.…

This is the student guide in a set of five computer-oriented environmental/energy education units. Contents are organized into the following parts or lessons: (1) introduction to power and energy; (2) energy consumption and supply; (3) energy conservation and distribution; (4) energy flow and the question of transportation; and (5) computer models…

Many problems and activities which can be worked with a calculator are contained in this booklet. The problems include: pattern recognition, combinations of operations, estimation, squares and square roots, rate problems, area, and volume. Chapter topics include: getting to know the calculator, single-step problems, using formulas, and…

These background papers are written to provide information for the teacher on technical problems that might arise as students carry on various USMES investigations. Background papers are also written which include information about the types of investigations which may provide good opportunities for learning in specific areas. This set includes…

A programed sequence for teaching students to solve word problems was developed using a combination of the information processing and structural variables approaches. Students using the sequence proceeded individually through mastery of a sequence of objectives. In order to evaluate the program, fourth and fifth graders were randomly selected from…