This is part three of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text…

This teacher's guide is designed for use with the SMSG textbook "Calculus of Elementary Functions." It contains solutions to exercises found in Chapter 9, Integration Theory and Technique; Chapter 10, Simple Differential Equations; Appendix 5, Area and Integral; Appendix 6; Appendix 7, Continuity Theory; and Appendix 8, More About…

This is part one of a two-part manual for teachers using SMSG high school text materials. A chapter-by-chapter commentary on the text and answers to all the exercises are given. Chapter topics include the idea of the derivative, limits and continuity, differentiation, and applications of the derivative. (MP)

This is part two of a two-part manual for teachers using SMSG high school text materials. A chapter-by-chapter commentary on the text and answers to all the exercises are given. Chapter topics include: (1) area and integral; (2) basic integral theorems; (3) logarithmic and exponential functions; (4) growth, decay and competition; and (5)…

This guidebook on minimum course content was designed for students who have mastered the skills and concepts of analytic geometry. It is a short course in the basic techniques of calculus recommended for the student who has need of these skills in other courses such as beginning physics, economics or statistics. The course does not intend to teach…

The second in a four-part sequence for the student seeking Advanced Placement, this booklet emphasizes theory and applications of the derivative and the definite integral. Overall goals and performance objectives are speficied. A course outline, teaching suggestions, and references to state-adopted texts are given for each topic covered. A sample…

Techniques that can be used in solving various mathematical problems are illustrated by an optimization problem and the accompanying model and solution. (MP)

One lesson from a group of six computer-assisted lessons is described. The BASIC program is given along with a sample run. (MP)

Compared were the effects of two modes of instruction in the calculus: small group discovery and traditional lecture-discussion. The discovery mode was more effective in producing successful achievement in areas of manipulative skills, there were no differences in achievement as measured by a concepts test. (SD)

Calculus provides the language for expressing the differential equations that govern change and also the methods for solving them. In order to insure that more Americans qualify for science-related careers, the way calculus is taught must change. (MLW)

How the notion of limit can be developed through a meaningful approach is discussed. Selected portions of the high school calculus course are described, and errors on a test are analyzed. (MNS)

Shows how a simple spreadsheet program can be used to teach calculus concepts more effectively through simultaneous use of review questions and instructions, actual manipulation of data and formulas, and visual illustration of results. Concepts illustrated include the difference quotient and derivation of a function; difference and differential;…

Three activities with Knuth functions are discussed and illustrated, with sample computer programs listed. (MNS)

Presents three sample problems related to arithmetic and algebra, geometry, and calculus, indicating, in each case, similar problems that could be posed. Includes a discussion of positive benefits which result by asking students "Can you derive the result differently?" (JN)

Shows that Simpson's rule can be obtained as the average of three simple rectangular approximations and can therefore be introduced to students before they meet any calculus. In addition, the accuracy of the rule (which is for exact cubes) can be exploited to introduce the topic of integration. (JN)