Presents techniques and materials for instruction at secondary school and upper elementary grades in mathematical concepts of number systems structure. Grouping is used as a simple algebraic system to illustrate structure. Closure, inverse, identity, commutative and associative properties are examines relative to manipulation of geometric figureS.…

Procedures to help algebra students solve problems more efficiently are discussed, using linear programing graphs. (MNS)

Mathematical concepts used in modern algebra are shown to be useful in modeling syndetic structure employed in information retrieval systems. The equivalence relation can represent "see also" components of traditional library catalogs; partial orderings and mappings assist in modeling syndetics in sophisticated systems such as thesauri.…

Production rules used to build a problem-solving system and a tutorial interface that controls interaction between user and system are described. The tutorial interface controls the rule- based problem solver used to emulate a student's steps, while the system provides a flexible framework for algebraic problem solving. (Author/MBR)

A computer program that uses determinants to solve simultaneous systems of equations is presented. The purpose is to show teachers how to use topics from algebra, geometry, and programing to lead pupils to appreciate the beauty and unity of mathematics. (MP)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

A process for eliminating the xy term in a quadratic equation in two variables is presented. The author feels this process will be within the reach of more high school students than more commonly used methods. (MK)

Forty second-year algebra students were interviewed while solving eight problems. Data from the interviews included frequencies of problem-solving processes and scores on the test. Conceptual knowledge accounted for 50 percent of the variance. (MP)

The transfer between problems having related structures was investigated. The results indicated that transfer occurred for both algebraic and puzzle problems, and significant transfer resulted when the generalization was solved first. (MP)

The use of a multiple approach using both geometric and algebraic contexts is suggested in teaching concepts. Several examples are given including area and multiplication, length and number, and functions and power. (MP)

Sidelights and extensions of factorability are presented. (DT)

The organization of a self-paced algebra course is described and testing procedures are discussed. (DT)