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)

Presented is an example of how a child adopted an incorrect method for solution to arithmetic sentences. Methods for detecting and correcting this behavior are discussed. (JP)

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

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)

Introduces the Fibonacci sequence using examples from nature. Describes some fascinating mathematical patterns using multiples and GCFs that exist among these numbers. (KHR)

Examines the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems, including an experimental and control group each consisting of 34 elementary students, in Japan. The experimental group showed a significantly better performance on the retention test…

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)

Presents activities to find Pythagorean triples using the TI-83, a graphing calculator. (KHR)

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

Magic squares are used both as a vehicle for arithmetic drill and the development of mathematical concepts for second-grade students. By searching for patterns within the squares, additional number concepts are developed along with the concept of symmetry. (JP)

Postulated here is the notion that the exploration of number patterns with calculators is a valuable mathematical learning activity that should be commenced in the primary grades. Various activities are presented that make use of the constant function key, which is available on many of the inexpensive four-function calculators. (JJK)

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…

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)

Pascal's triangle can be used as early as grades five and six to teach children to recognize mathematical patterns. Children can be guided to discover patterns or sequences of numbers if they begin with pictures or physical objects which they can manipulate and count. (Author/BB)