In the study reported here, I examined the diagrams that mathematically capable high school students produced in solving applied calculus problems in which a diagram was provided in the problem statement. Analyses of the diagrams contained in written solutions to selected free-response problems from the 1996 BC level Advanced Placement Calculus…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

An experienced mathematics teacher in a rural high school in the United States was studied as she first implemented a reform calculus curriculum. Her instruction was compared to her previous practice using a curriculum not constructed with the reform movement in mind. Despite her early attempts to make her instructions more student-centered, the…

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in…

This article describes a calculus project that exposes students to the concept of retirement annuities in both the saving and withdrawal phases, via revenue streams represented by integrals. Students use modeling skills to solve several related problems as the assumptions of the original problem are changed, and the project requires them to use a…

Heuristic training alone is not enough for developing one's mathematical thinking. One missing component is a mathematical point of view. This study reports findings regarding outcomes of a historical approach calculus course to foster Taiwanese college students' views of mathematical thinking. This study consisted of 3 stages. During the initial…

This project was coordinated and funded by the California Partnership for Achieving Student Success (Cal-PASS). Cal-PASS is a data sharing system linking all segments of education. Its purpose is to improve student transition and success from one educational segment to the next. Cal-PASS' standards deconstruction project was initiated by the…

This study explored personality variables measured by the 16 Personality Factor (16PF) test and their relevance to success, as defined by the final course grade, in college calculus courses with 94 students. Two personality variables were significant predictors of success as determined by the final course grade. A Statistical Analysis System…

This paper discusses the assumptions required by the item response theory (IRT) true-score equating method (with Stocking & Lord, 1983; scaling approach), which is commonly used in the nonequivalent groups with an anchor data-collection design. More precisely, this paper investigates the assumptions made at each step by the IRT approach to…

Structural covariance models that would explain the correlations observed among mathematics achievement and participation measures and related cognitive and affective variables were developed. A sample of college calculus students (N=268; 124 females and 144 males) was administered a battery of cognitive tests (including measures of spatial-visual…

This document explores two methods of obtaining numbers that are approximations of certain definite integrals. The methods covered are the Trapezoidal Rule and Romberg's method. Since the formulas used involve considerable calculation, a computer is normally used. Some of the problems and pitfalls of computer implementation, such as roundoff…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

Fifteen research reports related to mathematics education are abstracted and analyzed. Six of the reports deal with aspects of learning theory, four with areas in mathematics instruction (calculus, elementary mathematics for students of economics, and planning for topics for kindergarten children), and two with assessment or prediction of…

Contained in these proceedings are: (1) two lectures; (2) reports from four working groups, three review groups, and three special groups; and (3) a list of participants. Lecture I, by Caleb Gattengo, was entitled "Reflections of 40 Years of Work on Mathematics Teaching." Lecture II, by David Hawkins, was entitled, "Understanding…

This report compares the results of three successive second year calculus classes, in which part of each class was taught the concept of uniform convergence of a sequence of functions by an interactive COMIT module, while the remainder was given lectures in the traditional manner. An outline of the teaching techniques used in the module is…