Language syntax is discussed, followed by an overview of algbraic syntax. Evaluating algebraic expressions was chosen as the means to investigate the psychological basis of syntactic skills. Subjects' ability to perform evaluative tasks appropriately using standard algebraic notation was ascertained; then similar tasks were presented using a…

The academic success of students enrolled in remedial English and mathematics programs was compared at two large state universities, California State University, Northridge, and San Diego State University. The sample consisted of three successive freshmen classes, those entering in fall semesters 1981, 1982, and 1983. The remedial English programs…

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

This document explores two methods of obtaining numbers that are approximations of certain definite integrals. The methods covered are the Trapezoidal Rule and Romberg's method. Since the formulas used involve considerable calculation, a computer is normally used. Some of the problems and pitfalls of computer implementation, such as roundoff…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

The purpose of this project was to develop a Master of Science program in Applied Mathematics designed specifically to meet the needs of students wishing to prepare for careers in business, industry, or government. The program emphasizes problem-solving, mathematical modeling, and areas of mathematics such as differential equations, computing, and…

This document deals with the observation of students in a direct translation scheme in the solution of word problems in a university freshman-level Intermediate Algebra class. It is felt that since successful problem solvers of algebraic equations often have as much difficulty in solving word problems as do other students in the classes, the…

The purpose of this study was to uncover information about and gain a greater insight into the extent to which students who are successful in a basic algebra course: l) demonstrate a reversibility of reasoning processes when solving algebraic problems; 2) demonstrate a flexibility of reasoning processes when solving algebraic problems; 3)…

These worksheets suggest activities through which secondary school students may be introduced to the ideas of simulation. All can be played as games to give students a feel for the situation modeled; most use coins or dice and a few use random digits. Directions are detailed for each of the 17 worksheets, with variations suggested for many. (MMS)

The research described here seeks to characterize the "managerial" aspects of expert and novice problem-solving behavior, and to describe the impact of managerial or "executive" actions on success or failure in problem solving. A framework for analyzing protocols of problem-solving sessions based on "episodes" of…

Minorities have for some time faced underrepresentation in the technical professions. However, recent statistics indicate that many more minorities are enrolled in higher education than ever before. This report centers on identifying the particular difficulties that bilingual Hispanic students majoring in technical subjects have in performing…

The regenerative model for the mathematics education of elementary school teachers that is presented is an interactive model that recognizes the need to consider local and national professional concerns as well as local preservice and in-service teacher concerns. A process for identifying and utilizing these concerns is described. Other models…

Conducted during the 1979-80 school year, this study gathered statistical information as to the success of the developmental mathematics program at Arkansas State University (ASU). The investigation focused on a comparison between Foundation Mathematics students who took Basic Mathematics as a follow-up course and pupils who enrolled in Basic…

In order to make recommendations for improvement of the mathematics laboratory at Mira Costa College, questionnaires were mailed to 100 community colleges. Of the 40 responding, 17% had completely self-paced labs, 20% combined open labs with individualized instruction, 20% had no lab instruction, and the remainder had a variety of offerings.…

Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in college arithmetic. Topics covered include: whole numbers, decimal fractions, fractions, ratio and proportion, percent, powers and roots, and the metric system of measurement.…