Low cost microcomputers with high resolution graphics provide students and educators with fast and accurate visual representations of mathematics relations and extend the benefits of discovery learning into the high school and college mathematics classroom. A recent challenge has been to use the computer in motivating students and teaching…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

Details are given of a method used by a student in discovering the relationships between the area under the sine curve and the unit circle. Two computer programs for the required calculations are included. (DT)

A set of programs, designed to supplement a high school or college course in trigonometry, is described. Student exploration is stressed. (MP)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)

The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

Describes an activity in which geometry and trigonometry are studied using pyramids. Identical model pyramids are constructed from card stock, along with pyramids of different proportions and cuboids to use as controls. Also includes an investigation of some apparently non-scientific claims. (DDR)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Gives an example of an open exploration using trigonometric relationships in which the law of cosines can be deduced from the law of sines. Discusses the characteristics and value of the exploration process. (MDH)

Presented is an example that allows students to investigate trigonometric ideas in a simple and practical way. (PK)

Presented are three methods to enrich the mathematics classroom. The first introduces an activity allowing students to discover the law of sines. The second gives eight distance-rate-time problems of value for their counterintuitive or elegant solutions. The third poses multiple answer questions that promote student interaction and communication.…

Examples of composite functions present students with intriguing questions that they can explore using calculators and computers, geometric and algebraic methods, and approximation techniques. Student-centered activities allow students to make discoveries about functions. (MLN)

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)