This series of units is designed to help middle, junior high, and high school students use LOGO computer language as a tool to explore concepts in geometry, estimation and problem solving. The format of the unit was designed so that the instruction can be provided by the classroom teacher. The lessons are constructed so that, with some teacher…

The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…

This workbook was designed as an easy-to-read, slower-paced text for students who have learning, reading, and language problems. As one of five workbooks to aid low achievers in problem solving, it focuses on strategies for solving one step and multistep word problems in mathematics. Students use skills learned in the four previous workbooks in…

This paper presents an examination of the construction of logic in multidigit subtraction. Interviews were conducted with 90 grade 2 and grade 3 students to determine whether they understood the logic of borrowing and whether the construction of the logic was related to procedural expertise or corresponding conceptual knowledge. Of 34 students…

The Educational Technology Center has attempted to develop a series of computer based learning environments to support the learning and application of multiplicative reasoning. The work and software described in this paper, including the teaching experiment that generated the error phenomena examined, is part of a larger ongoing research project.…

High school students (N=213) of various ability levels enrolled in first-year algebra classes were presented lessons concerning geometry concepts. The lessons were varied according to the degree of complexity of the examples that were presented. Students then were tested over their understanding of the concepts. The test questions ranged from…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

This document is designed to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. The approach used is to: (1) develop the material in terms of full-rank factorizations and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) include…

Research on the use of calculators in mathematics classes is reviewed. It is noted that calculators were initially too high-priced and of too low an availability to be viewed in terms of widespread use in classrooms. Technological and manufacturing advances have since made wide use possible. Proponents of calculator use see this technology as a…

Young children's responses to a velocity inference task based on static pictorial stimuli giving cues of proximity and ratio were examined. Subjects (N=65) in preschool through second grade viewed pictures of snails moving horizontally or spiders suspended vertically and were asked to estimate which competitor would reach its destination first.…

Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…

Five open-ended problems are suggested which lead students to investigate basic number properties and numeration characteristics. (JP)

Presented is a graphical approach to teaching higher degree, rational function, and absolute value inequalities that simplifies the solution of these inequalities and thereby reduces the amount of classroom time that has to be devoted to this topic. Applications are also given for signum functions, maximum-minimum, and points of inflection…

This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5)…

This document is a collection of reports presented at a programable calculator symposium held in Seattle, Washington, in April, 1980, as part of the annual meeting of the National Council of Teachers of Mathematics (NCTM). The session was designed to review whether the programable calculator has a place in the school mathematics program, in light…