The report presents a summary of a mathematics project involving a system of individualized, laboratory and classroom instruction techniques for occupational and developmental college students. Continual diagnosis of student learning difficulties, flexible prescriptions of activities, and continual evaluation of student progress are incorporated…

There were three objectives of a revision and validation of the Iowa Algebra Aptitude Test (IAAT): (1) to reduce the importance of speed; (2) to improve the quality of the existing items; and (3) to replace a subtest with one of potentially greater predictive validity. The last of these goals involved the development of a new subtest composed of a…

Algebra I students were assigned to matched pairs according to scores on mathematical and verbal aptitude tests (high-math, Low-verbal; high-math, high-verbal; High-verbal, low-math; low-verbal, Low-math), then received programmed learning tasks designed to teach summing of series. Either learner was given the correct formula in both verbal and…

This curriculum guide outlines the mathematical content which whould be presented in grades 6, 7, and 8 - the new middle school organization. It is the result of a study made by a committee of principals and teachers of the needs and characteristics of adolescents. The following are included for each of the content areas: (1) topics which may be…

Listed are behavioral objectives for 86 topics in mathematics to be covered in grades seven through nine. For each topic a general objective is given and is followed by a list of specific objectives. Areas covered include number operations, geometry, number systems, set theory, and algebra. This work was prepared under an ESEA Title III contract.…

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…

Unit 17 in the SMSG secondary school mathematics series is a student text covering the following topics: number systems, coordinate geometry in the plane, the function concept and the linear function, quadratic functions and equations, complex number systems, equations of the first and second degree in two variables, systems of equations in two…

This paper reports a study which attempted to generalize earlier results obtained by Eastman to another mathematical content area. Two hundred eight ninth-grade algebra students were randomly assigned to one of the two treatments. The figural-inductive treatment presented concepts of logic through the use of Euler diagrams in an inductive mode;…

The effectiveness of an advanced organizer based on examples is compared with that of one based on counter examples. The counter examples strategy was found to be more effective for the unit on finite groups. (SD)

Examples illustrate the use of APL for teaching selected topics from logic, set theory, algebra, number theory, and calculus using the glass box approach. (MP)

These three brief articles concern problems students encounter in solving simple linear equations, children's conceptions of number, and the distinction between adding objects and adding numbers as illustrated by students' problems with Euler's formula. (SD)

The target point for the cue ball in a simplified game of billiards is computed through the use of line reflections and computations with complex numbers. (JT)

The principles of modern genetics are extended to study the extinction probabilities of such genetic diseases as sickle-cell anemia, Tay-Sachs disease, and cystic fibrosis. (JT)

One group of elementary education majors received an algebraic instructional treatment of a unit on linear absolute value equations while another received a geometric treatment. The hypothesis of an aptitude-by-treatment interaction was statistically confirmed. (MN)

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)