These syllabuses for grades 7-12 were written, evaluated, and revised by a team of writers from the Orange County Science Education Improvement Project (OCSEIP). OCSEIP is a cooperative enterprise of the University of California (Irvine), California State College at Fullerton, the Orange County Schools Office, and local districts throughout Orange…

Presented is an elementary approach to areas, columns and other mathematical concepts usually treated in calculus. The approach is based on the idea of average and this concept is utilized throughout the report. In the beginning the average (arithmetic mean) of a set of numbers is considered and two properties of the average which often simplify…

Increasingly higher education is confronted with the task of educating a population of students whose entry aptitudes and skills have grown more heterogeneous. Perhaps nowhere is this diversity of abilities more apparent, and at the same time more difficult to deal with, than in courses in introductory calculus. This paper outlines an experimental…

A three-factor design was used to determine the effects of testing frequencies and feedback delays on college students' achievement in a beginning calculus course. Four test-period frequencies--daily quizzes (5-10 minutes), weekly quizzes (20-30 minutes), three midterm exams, or one midterm exam--were used. Two feedback-delay-levels for test…

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…

This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…

The purpose of this article is to point out some of the problems that arise in the use of calculators to illustrate derivatives, due to rounding or truncation, by the calculator. Several illustrations of numerical differentiation techniques are also given. (Author/MP)

This paper is a report on experimental courses in calculus and linear algebra which have been given for the past three years at Swarthmore College. Computing is used to represent the ideas and concepts of calculus and linear algebra and to facilitate their analysis and exploration. APL is used as the notation. (MN)

Infinite geometric series are related to the time-motion paradox involving a football team advancing halfway to a goal line on each successive play. (MN)

Elementary differential calculus is used to analyze and to discuss some complex economic situations. (JT)

A theorem with proof is given for L'Hopital's Rule for the indeterminate form "infinity divided by infinity." The theorem takes advantage of the fact that this form is first encountered after the "zero divided by zero" case has been proved. (MN)

An application of the formula for finding the sum of an infinite geometric series is described through the use of Pierre Fermat's method for finding the area under a curve. (JT)

The author presents a method of teaching the concept of limit. (SD)

Calculus must be made more relevant and understandable to students if the nation is to maintain a strong scientific and technological enterprise. A national effort should be launched to bring calculus education into the computer age by developing curricula incorporating calculators and other innovative tools. (MLW)