Shares a series of problems designed to provide students with opportunities to develop an understanding of applications of the definite integral. Discourages Template solutions, solutions in which students mimic a rehearsed strategy without understanding as the variety of problems helps prevent the construction of a template. (Author/ASK)

To build understanding of, and the ability to use, first-year science and engineering calculus, students were introduced to differential equations and asked to carry out research on differential equation modeling projects. Describes a model for the research paper; appendices provide a copy of the student handout and five examples of student…

Investigates issues of mathematics instruction of problems in blocks. Discusses the best way to construct mathematical problems with connections to one another as parts of a coherent whole and how to reflect on the types of connections that can arise between them. (Author/KHR)

Describes an attempt to increase business calculus students' desire to learn by overcoming typical low levels of mathematical preparation and motivation utilizing a corporate structure managed by the students. Includes 10 sample problems from fictitious corporations. (JJK)

Short essay questions are introduced into the calculus course as a technique to involve students with their own learning. Provides (1) instructions to the student for writing the report; (2) results of using the technique; and (3) reasons for using writing in mathematics classes. (MDH)

Presents examples of questions and answers arising from a hands-on and exploratory approach to discrete mathematics using cuisenaire rods. Combinatorial questions about trains formed of cuisenaire rods provide the setting for discovering numerical patterns by experimentation and organizing the results using induction and successive differences.…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

This paper describes the use of cooperative groups in teaching calculus. It discusses benefits and drawbacks of group techniques and presents reactions from both students and the author. (Author)

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)