A description of the development of three-valued logic includes construction of truth tables. (MK)

Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

Discusses the application of induction using a two-player game with sticks. Describes a winning strategy for the game with n sticks; number of moves to complete the game; and changing the rules of the game. (YP)

Provides a teacher's guide and activity sheets designed to introduce students to three patterns of reasoning in inferential logic. Students learn to construct arguments from diagrams and, given an argument, illustrate the argument with a Venn diagram, then study the diagram to see if the argument is valid or invalid. (MKR)

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)

A study at Cleveland State University (Ohio) compared the effectiveness of conventional mathematics instruction given to 190 students with an alternative course in mathematical reasoning given to 120 students as preparation for a required course in real analysis. Results show the alternative method effective in raising both pass rate and grades in…

College students who were either monolingual speakers of English or bilingual Hispanics participated in two studies dealing with the comprehension of sentences containing negations. Both the influence of different sentence constructions on comprehension, as well as the heuristics and misconceptions exhibited by subjects as they attempted to…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

Games and activities which involve problem solving are presented in order to help teachers develop the numeric, geometric, and logical thought processes of elementary school students. The activities and games (many of which are pencil-and-paper) require using logic, plan-ahead strategies, spatial reasoning, strategies based on prior patterns or…

Examines the hypothesis that there are preliminary stages in problem solving that are often neglected in teaching chemistry. Discusses correlations calculated between the student's ability to handle disembedding and cognitive restructuring tasks in the spatial domain and ability to solve chemistry problems. (TW)

Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…