Describes a combinatorics problem involving pizza toppings. Includes three activity sheets. (Author/NB)

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

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

Presents a question designed to launch a discovery journey through conjecture, research, serendipitous encounters, proof, answers, and new questions. Reports some discoveries and suggests ways in which to incorporate this strategy into classrooms. Presents a geometry project that incorporates this problem-solving approach to mathematics. (JRH)

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,…

A series of 13 questions is offered for sequencing student writing activities according to a problem solving model of the composing process. The questions are organized in a cyclical framework for approaching any problem solving task that writing students may face. The questions fall into four progressively developed categories, including…

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…

Activities used with seventh and eighth grade students in Western Australia are described. The instructor guides pupils towards experimental solutions and encourages discovery of solutions for similar and more general problems. Investigations include study and construction of polygons, polyhedra, and one and two-sided surfaces. Commercial kits are…