Presents mathematical games that involve a problem-solving matrix, multicolored cubes, and three-dimensional dominoes. The work of Alexander MacMahon is highlighted. (MA)

Activities are presented that focus on the topic of problem solving using the strategies of: (1) patterning; (2) working backwards; (3) making a chart, table, or graph; and (4) diagraming and elimination. (RH)

The vast majority of people are most familiar with arithmetic in base ten. This article presents a follow-up on a problem with several divisibility tests valid in base ten which are related to Freitag's general test and which follow directly from it. Base 13 is also explored. (Author/MA)

The author arranges 26 current states of mathematical knowledge (in relation to solving a problem) in an informal taxonomy and comments on them. (MNS)

Methods for solving logic puzzles which focus on thought-free procedures that facilitate solution are discussed. Two of the procedures noted pertain to the interior of any submatrix, whereas others span several submatrices. A puzzle is presented at the conclusion as an exercise for practicing the methods promoted. (MP)

Presents activities designed to provide students with an informal introduction to deductive logic through the use of the problem-solving skill of "eliminate possibilities." Includes rationale for the activities, background information, list of materials needed, objectives, four ready-to-copy student worksheets, and instructional…

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

What are often missing for children in classroom instruction are experiences with numbers that stretch beyond computation skills and word problems. This lesson models such an experience for third graders. Students use small boxes of raisins in several problem-solving activities. Children apply whole number operations, estimate, consider…

Data were collected in the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems. The children were interviewed three times during the school year. The influence of problem structure on children's solution strategies appears more extensive and decisive than that…

A project designed to stimulate analytical reasoning skills in elementary school students is described, with a sample of the developed exercises. The materials were found to generate and maintain an enthusiastic response from the group of gifted eight-year-olds with which they were used. (MP)

The creation of "false laws" of mathematics by many pupils as they attempt to rephrase new ideas and make them understandable and useful is discussed. The reasons for these mistakes and some ways teachers can help students adopt correct rules are reviewed. (MP)

Many students appear to enjoy mysteries at the same level that they hate proofs. It is felt that the solutions of the two can be so alike that their diagrammatic forms will coincide. One geometry and three mystery problems involving logic for solution are presented. (MP)

Describes ways of finding the answer to a problem for the possible sum of the three-digit numbers without using the same number repeatedly. Describes the classroom applications of the problem. Provides a computer program to obtain the solutions of the problem. (YP)

Compares two approaches to the teaching of mathematics, rote versus reasoning. Discusses the way to teach mathematics as reasoning in elementary classroom as stated in the NCTM Standards. (YP)