Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

According to the Merriam-Webster dictionary, a planimeter is "an instrument for measuring the area of a plane figure by tracing its boundary line". Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by "walking" on the boundary. For someone who has…

Two packages in computer graphics are described that can represent three-dimensional surfaces in two dimensions. (MP)

Demonstrates how microcomputers can be used in teaching differential calculus, iteration, integral calculus, graphs, and statistics. Several ideas for putting this information into practice are outlined. Sample computer programs are included for the discussions on differential calculus, integral calculus, and iteration. (JN)

Describes the principles underlying computer programs designed to improve undergraduate calculus instruction. The programs were produced for teacher use on a single microcomputer for when there are not enough microcomputers available to allow students to have access to them. (JN)

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Discusses a way to help children retain the desire to understand mathematical ideas and to carry out routine procedures. Describes a method using computers to teach linear equations and calculus. Eight references are listed. (YP)

Discusses the use of computer graphics to introduce the concepts of derivative and tangent line using the iteration of functions, especially linear functions. (MKR)

An advanced placement calculus program is described that incorporates IBM personal computers, conference telephone connections, modems that transmit computer signals over the phone lines, OPTEL graphics that allow the users to "write" on their computer screens, and a sophisticated package of calculus software used for homework…

Reviews for three software packages are given. Those packages are: 20/20 Statistics, Graphing Equations, and COMPUCALC. The first package is a set of programs for use in introductory statistics, the second contains four programs for studying the graphing of equations, and the third contains examples and techniques from calculus. (PK)