Digraphs, graphs, and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability. Mathematical structure was defined as the relationship between concepts within a set of abstract systems. The word association technique was used to measure the existing relations (cognitive structure) in S's memory…

The purpose of the study was to devise a taxonomy of moves and strategies found in the teaching of a skill venture at the secondary school level. Fifty-seven hours of classroom instruction were audiotaped from a sample consisting of teachers of various preparation, age, and experience levels from schools of various sizes, location, and…

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…

The purpose of this study was to investigate the effectiveness of guided discovery and concrete materials on mathematics learning. From the seventh grade of one school, 40 students were selected who were at least one standard deviation above or below the mean on two mathematics achievement tests. Five high ability and five low ability were then…

This is one of a series of reports on the National Longitudinal Study of Mathematical Abilities (NLSMA). It is the report of a dissertation that sought to identify characteristics correlated with problem solving. The type of problem used was classified as "insightful," meaning nonroutine and challenging but not of a trick or puzzle type.…

Part I of the teachers' guide for "Detecting Patterns" gives a brief description of the mathematical skills needed for the unit, lists the substantive areas touched on by the problems in the pamphlet, suggests classroom uses for the booklet, and gives background information on the individual chapters of the unit. Part II provides complete…

This curriculum guide is specifically designed for the slow learning students in grade 10. It is one of a series of course guides for grades 6-11. The intent of the curricular designers was to outline mathematical experiences which would be appropriate for the characteristics of these students. The areas of mathematical content included are: 1)…

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…

This document is a source book for those who see the need to provide more meaningful mathematical experiences for students who have experienced little or no success in traditional programs. It is in four parts. In the first part, three innovative general mathematics projects are described. The second part outlines the mathematics laboratory…

The first part of this volume reports on the 1959 Royaumont Seminar on secondary school mathematics, an important factor in the spread of "New Mathematics" at the beginning of the last decade. Key addresses on Reform in School Mathematics (Stone) and New Thinking in School Mathematics (Dieudonne) are reported in full, and there are summaries of…

Reported are the results of an investigation of mathematical achievement of students enrolled in modern and traditional mathematics programs. To be included in the comparative study, students had to have been continuously in a modern program or a traditional program during grades ten, eleven, and twelve. The experimental group (141 students) had…

This is the first workbook-text in a two-part series written for deaf students. It is remedial in nature, aimed at the secondary level, and covers addition, subtraction, multiplication, and division of whole numbers. The use of the number 10 in explaining the concepts presented is stressed throughout. For the second workbook, see SE 015 828, and…

This study compares the postulational approach to tenth grade geometry by three textbooks: one synthetic, one transformational, and one vectional. The development of incidence, order, distance, separation, congruence, parallelism, and similarity are discussed, and the different approaches illustrated. Special consideration is given to theorems in…

This document reports the present status of the Comprehensive School Mathematics Program (CSMP). Three major components are described: (1) the criteria used for content selection and the role of staff and consultant mathematicians in its analysis; (2) the rationale for choosing the activity packages, organizational plans for producing and testing…

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.…