This student discussion guide is intended to accompany "Explorations in Mathematics," a text for teachers. The materials in this booklet relate mainly to variables, graphs, signed numbers, logic, identities, functions and matrices. The materials were designed to be used as supplementary materials with students in grades 5 through 9. (RP)

This report presents a more detailed elaboration and discussion of the mathematical content of the central concepts which have been designated as the Mathematical Strands of the Mathematics Curriculum for grades K-8. In Part I of the report there is a discussion of the pedagogical philosophy which the committee felt was to have an importance equal…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program see ED 086 545. In this guide, the teacher is provided with objectives for…

The purpose of this study was to investigate the effects of the addition of geometry and geometric illustrations as a supplement to the teaching of factoring second-degree polynomials. Sixty eighth-grade students with certain prerequisite skills were randomly assigned to six treatment groups. Each group was taught factoring of quadratic…

LOGO is a programming language developed at Bolt, Beranek and Newman, Inc., specifically for use in teaching. It provides the student with a set of numerical and symbolic primitives as elements for gradually building extended, complex program structures. The building of these structures is facilitated by a procedure-oriented programming heuristic…

A method for teaching students to solve complex algebraic equations is described. The method, which relies on sequentially reducing the complexity of the problem has been successfully used with secondary students and in remedial college courses. (SD)

An application of functions and their inverses is described--the coding and decoding of messages, or cryptographs. The helpfulness of computers is noted, with two programs listed. (MNS)

A general model for solving algebra word problems requiring a linear solution in one variable is described. A step-by-step approach is illustrated, with a worksheet included. (MNS)

Use of the calculator to create a series of iterations to approximate i to some desired degree of accuracy is illustrated with three problems on interest rates. (MNS)

Suggested is the presentation of problems for which student teams are to write computer programs which will reveal the results of guesses at the answer by users of the program. Illustrative problems and programs are included. (MNS)

The purpose of this paper is to offer a framework for categorizing and describing the different types of processes that undergraduates use to construct proofs. Based on 176 observations of undergraduates constructing proofs collected over several studies, I describe three qualitatively different ways that undergraduates use to construct proofs. In…

This paper compares a number of different Computer Algebra Systems (CAS) in their solution of one-step and multi-step problems. The CAS programs considered include DERIVE, Maple, Mathematica, and MuPAD while the problems are taken from the final examinations of grades 9 and 12 in Estonian schools. The different outputs to one-step problems with…

The choice of teaching an effective method--one that most students can master--or an efficient method--one that takes the fewest steps--occurs daily in Algebra I classrooms. This decision may not be made in the abstract, however, but rather in a ready-to-hand mode. This study examines how teachers solve linear equations when the purpose is…

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…

A strategy game is presented that teachers (1) logical reasoning; (2) how to formulate a clear verbal argument that explains your reasoning; (3) basic mathematical skills and (4) computational skills. The game is adaptable for many levels of instruction. (JP)