A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

Considers how elementary school classroom teachers can employ exploration methods (gathering, evaluation, and synthesis of data related to a specific topic) to help students develop readiness for intellectually complex problem solving. (Author/DB)

Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)

Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)

Activities designed to aid pupils explore the Fibonacci sequence are presented in worksheets. (MP)

Discusses the mathematics education philosophy of J. W. A. Young and how it compares to the principles in the National Council of Teachers of Mathematic's "Curriculum and Evaluation Standards for School Mathematics." Elaborates on Young's views concerning rote learning, establishing connections between mathematics and other disciplines,…

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

An approach which seeks to stimulate interest in mathematics by enabling a student to use his knowledge in a nontrivial application is discussed. An example of how the approach was implemented is presented with an assessment of the results as measured by student reactions. (Author/TG)

This resource book contains 18 magic number tricks that spark the interest and imagination of students as they are led through a variety of mathematical computations and discoveries. Following each activity, students are asked to write about their discoveries and create their own magic tricks. A matrix of skills for all the activities and lists of…