Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

The purpose of this article is to discuss specific techniques for the computation of the volume of a tetrahedron. A few of them are taught in the undergraduate multivariable calculus courses. Few of them are found in text books on coordinate geometry and synthetic solid geometry. This article gathers many of these techniques so as to constitute a…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…

We solve two problems that arise when constructing picture frames using only a table saw. First, to cut a cove running the length of a board (given the width of the cove and the angle the cove makes with the face of the board) we calculate the height of the blade and the angle the board should be turned as it is passed over the blade. Second, to…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

This note could find use as enrichment material in a course on the classical geometries; its preliminary results could also be used in an advanced calculus course. It is proved that if a , b and c are positive real numbers such that a[squared] + b[squared] = c[squared] , then cosh ( a ) cosh ( b ) greater than cosh ( c ). The proof of this result…

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Designed to serve as a supplement for high school level mathematics, this publication contains activities which aim to enhance mathematical knowledge and skills and to assist students in understanding aerospace technology and its achievements. This volume updates an earlier supplement that was published in 1972. Problems are grouped into chapters…