A recent classroom revelation caused us to reconsider the adequacy of the instructions offered in our textbooks for one of our most elementary quantitative methods. Specifically, we found that many students were mystified concerning how to pick an initial objective function value when plotting an isoprofit line in order to graphically solve a…

A THEORY OF STRUCTURE IS ESSENTIAL TO AN OBJECTIVE ORGANIZATION OF BASIC PEDAGOGIES IN DESIGN. THE PURPOSE OF THIS STUDY WAS TO ASSESS THE STRUCTURAL THEORY OF MATHEMATICIAN K.L. WOLF AND TO TRANSLATE THIS THEORY INTO A VISUAL PRODUCT THAT COULD BE USED BY BEGINNING DESIGN STUDENTS. WOLF DESCRIBES 6 ISOMORPHIC COVERAGE OPERATIONS AND 7…

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

This paper is a report of a symposium on research in mathematical learning and teaching held during the annual meeting of the California Mathematics Council in 1966. Speakers and their topics were: Professor Frederick J. McDonald - "The Teaching of Mathematics"; Dr. John E. Coulson - "The Learning of Mathematics"; Professor Zoltan P. Dienes -…

This paper reports on the answers indicated by research studies to nine questions concerning the teaching of multiplication and division. (1) Should multiplication facts be memorized? Answer: Yes, at an appropriate time. (2) How should multiplication be conceptualized? Answer: Normally addition of equal addends; sometimes arrays or…

This study investigated the effect an advanced organizer, a post organizer, or knowledge of a behavioral objective has on learning the mathematical concept of network tracing. Self-instructional booklets on network tracing were given to eighth grade students. The booklets were designed so that the instruction and posttest could be completed within…