Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

Suggests that, when teaching statistics, research supports linking concrete experiences to procedures, giving students the opportunity to develop language, giving students a variety of problem types, using problems that represent the data in various forms, having students collect and summarize their own data, and using calculators for…

Outlines an instructional approach that can be used to teach students to apply a strategy known as subgoal generation to multistep problems. (PK)

Forty-eight students with no previous exposure to probability or statistics read one of three textbooks that varied in emphasis placed on rote and conceptual learning of basic elementary probability concepts. Findings, among others, show students who read textbooks emphasizing conceptual learning tended to be less sensitive to surface features.…

Presented are geometry activities which require only colored construction paper cut into simple shapes, paste or glue, and large sheets of newsprint or art paper on which to paste designs. The activities, which may be done alone or in groups, are varied in content and difficulty. (JN)

Promotes the use of the microcomputer in mathematics instruction, reviewing approaches to teaching nonlinear equations. Examples of computer diagrams are illustrated and compared to textbook samples. An example of a problem-solving program is included. (ML)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

Incorporating writing into mathematics classes is promoted, with numerous suggestions on using writing to help students recall procedures, develop story problems, and plan computer programs, among other things. (MNS)

An activity that involves pattern finding, generalizing, and deductive thinking is detailed. The activity is thought to provide students with experience in these areas and to have potential for exploration at several levels. It is noted that, for small sums of money, it is not difficult to find all possible representations. (MP)

Three closely related problems are presented, which can be solved using only the formula for circumference. It is felt the solving of these genuine problems with the mathematical tools at their command should give pupils a feeling of power and accomplishment and a sense that mathematics is a useful subject. (MP)

Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

A word problem concerning weights of a pail containing different amounts of nails appeared in January 1997 issue of Mathematics Teaching in the Middle School. Teachers were invited to try the problem with classes and submit examples of students' work with a brief analysis. This article contains three student solutions. Argues that posing such…

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)

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)