Four techniques used to incorporate writing and active learning into mathematics classrooms are described. They include summary sheets, short focused writing, medium length writing, and student presentations. Examples of how each technique can be used are included. (KR)

This article describes a calculus lesson that illustrates the nature of cycles in simple systems of nonlinear differential equations through the use of the Lotka-Volterra predator-prey model as incorporated in the computer software package, Phaser (version 1.0). (JJK)

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 the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

When students are working with hand held technology, such as graphics calculators, we usually only see the outcomes of their activities in the form of a contribution to a written solution of a mathematical problem. It is more difficult to capture their process of thinking or actions as they use the technology to solve a problem. In this paper we…

This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed…

This study investigated the cognitive benefits of learning how to program by determining the degree of cognitive transfer of programming skills at a construct level to solving analogous problems in other domains. Subjects, who were students enrolled in four sections of the beginning Pascal programming course and two sections of a calculus course,…

The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

These proceedings include two lectures followed by working group and topic group contributions in reduced format. The two lectures were by Heinrich Bauersfeld, speaking on contributions to a fundamental theory of mathematics learning and teaching, and Henry Pollak, speaking on the relationship between applications of mathematics and the teaching…

This monograph presents 13 papers dealing with various aspects of elementary problem solving. They are: (1) "Training for Effective Problem Solving" (Gary A. Davis); (2) "Patterns of Problem Solving--A Campus-Wide Course at UCLA" (Moshe F. Rubinstein, L. Robin Keller, Edward A. Kazmarek); (3) "A Taxonomy of Problem-Solving Activities and Its…

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

This report contains papers from the Nordic Conference on Mathematics Teaching (NORMA-94). The first three papers are plenary talks aimed at giving the participants an opportunity to form a coherent view of the new theories of learning. The themes of the paper sessions addressed a variety of topics on different levels from elementary school to…

The benefits of high-level mathematics packages such as Matlab include both a computer algebra system and the ability to provide students with concrete visual examples. This paper discusses how both capabilities of Matlab were used in a multivariate calculus class. Graphical user interfaces which display three-dimensional surfaces, contour plots,…

A mathematical preview program in physics was developed at the Arkansas School for Mathematics and Sciences to introduce students to mathematical concepts, then use these as tools in physics while concurrently studying them in mathematics. The topics and time frame for the mathematical preview in calculus-based physics courses is presented, along…

Calculus can be taught using meaningful problems and active participation, with provocative problem situations and large-scale projects. An Ithaca College (New York) introductory calculus course uses this problem-based learning approach to develop understanding of central concepts (differentiation, integration, approximation) with less of the…