This paper presents the results of research that compared the academic achievement of high school students enrolled in an integrated Advanced Placement Biology/Advanced Placement Calculus course with students enrolled in traditional Advanced Placement Biology and Advanced Placement Calculus courses. Study subjects included high school students…

A method of nonmetric multidimensional scaling is described which minimizes pairwise departures from monotonicity. (Author)

A report on the development and use of a course developed by the Center for Research in College Instruction of Science and Mathematics (CRICISAM) at Florida State University. (MM)

Reports basic research on the meaning and measurement of family attitudes and the development of a new measurement instrument, the Family Motivation Test. Theoretical system is called the Investment-Subsidation Model. (Author/DB)

A simple way to introduce natural logarithms and e is presented. The standard approach is outlined, followed by the approach via differentiating the exponential functions that the student knows about. (MNS)

The effectiveness of a distributive model and the conventional method for assigning homework in a first-semester course in calculus is examined. Results indicated a pay-off for the distributive model in terms of improved performance of the student of average or below-average mathematics ability. (MP)

It is noted that all graphs of cubic equations are symmetric about their inflection points. This is proven through the use of some calculus and the fundamental theorem of algebra. A table sums up the nature of symmetry for polynomials of any degree. (MP)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

This discussion deals with the question, are there integral rectangles such that a box of maximum volume is obtained by removing an integral-sided square from each corner? An equation to solve the problem is generated and a table of values presented. The material appears suitable for beginning calculus students. (MP)

Results are presented of an impromptu exploration of polar formulas for volumes of revolution for certain plane regions. The material is thought to be unique, and to offer room for student exploration. It is felt pupil investigation can lead to increased pupil interest in both polar coordinates and calculus. (MP)

A logically and empirically valid structure of knowledge for differential calculus was made by textbook analysis and by collecting data from a first semester college calculus course. (MP)

Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)

Detailed examples of the kind of interdisciplinary activity involving differential equations and the computer that are highly motivating to many pupils and can be easily integrated with current materials are provided. It is felt the projects illustrated can work well within courses and are not excessively time-consuming. (MP)

An experimental program in Calculus I at the University of Southern California (USC) is described. It is concluded that it is possible to give a meaningful program in which computer use is incorporated. The intent is to set up all USC calculus courses with some use of microcomputers. (MP)

During the summers of 1978 and 1979, mathematics classes sponsored by SMPY (Study of Mathematically Precocious Youth) were held for seventh graders with the goal that participants learn as much precalculus mathematics as was feasible during the eight-week program. (SB)