Finding patterns in the relationship between the number of sides in a polygon and the total number of diagonals is used as vehicle to discuss discovery learning. (DT)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Different regular-polygon-shaped candles wound with a sheet of paper are cut through obliquely. When the papers are unwound, unique patterns are revealed. Investigation of these patterns leads to the discovery of geometric concepts. (JP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

Presented are a series of conjectures and proofs resulting from an examination of patterns and relationships among natural numbers. (JP)

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

An investigation of patterns in magic triangles leads to a number of discoveries concerning the sums of sides and corners. (MP)

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.…

Suggests that by using elementary concepts and arithmetic methods it is possible to find many interesting aspects of mathematics. The activities could be used to allow students to make individual discoveries about mathematics. (PK)

Discusses the use of computer visualization to motivate and support mathematical dialogues. Describes the "Scientific Visualization Software Suite," a set of public domain visualization tools from the National Center for Supercomputing Applications. (Author/MDH)