We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good…

An historical case is presented in which extra-mathematical certainties lead to invalid mathematics reasonings, and this is compared to a similar case that arose in the area of virtual education. A theoretical-methodological instrument is proposed for analysis of certainties. The article suggests the need for teachers to be aware that certainties…

Presents solutions at several different levels of sophistication for a problem involving 10 stools arranged in a row at a diner: how many different ways can the ten stools be occupied, discounting which of three persons sit on any stool, so that at least one stool is between two people? (AIM)

Although proof and reasoning are seen as fundamental components of learning mathematics, research shows that many students continue to struggle with geometric proofs. In order to relate pedagogical methods to students' understanding of geometric proof, this 3-year project focuses on 2 components of student understanding of proof, namely, students'…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

This paper aims, first, to describe the fundamental characteristics and workings of the AgentGeom artificial tutorial system, which is designed to help students develop knowledge and skills related to problem solving, mathematical proof in geometry, and the use of mathematical language. Following this, we indicate the manner in which a secondary…

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)

Describes experience of teaching truth tables and problems that exercise students' critical reasoning. (KHR)

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)

Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…

Investigates a way to assist students with learning differences. Considers mathematical connections appropriate in middle grades through college mathematics centered around the words "and" and "or" within the fields of logic, set theory, algebra, number theory, and probability. Teachers and students should be encouraged to investigate mathematical…

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)

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)