Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

Describes the mathematical processes that occur during problem solving, reasoning, and communication. Provides examples from mathematics education research with preschoolers. (ASK)

A technique to teach cognitive skills to directly facilitate abstract and rational thinking is described. Based on George Kelly's theory of personal constructs, his Role Construct Repertory Test has students construe similarities and differences among important course concepts rather than provide individual definitions or examples of those…

This paper provides a brief overview of some of the current thought on teaching problem-solving and decision-making skills and presents selected exercises that have been used successfully in a graduate course in problem-solving and decision-making strategies. In addition to learning theories that are presented in order to help learners understand…

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

Recent research literature has highlighted the interest of both teachers and researchers in using analogies to aid students' conceptual understanding. This appears to be especially relevant in secondary chemistry education due to the many abstract concepts that are included in the curricula. This paper reviews recent literature and considers…

Argues that the emphasis in law courses on memorizing facts fails to teach the desired concepts of reasoning and problem-solving. Recommends the use of open-book tests. Suggests that because law is an imprecise subject, and there are no right or wrong answers, it should be taught in an open format. (LS)

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

Investigates different approaches of students from different cultures to problems and problem-solving strategies. Suggests ways to encourage students to use algebraic strategies. Provides some action research ideas for teachers to try in their classrooms. Contains 11 references. (ASK)

Intended for teachers across grade levels and disciplines, this monograph reviews research on the development of critical thinking skills and introduces a series of these skills that can be incorporated into classroom teaching. Beginning with a definition of critical thinking, the monograph contains two main sections. The first section reviews…

Describes the reasoning patterns characteristic of the abstract thinking required for higher levels of school science. Discusses control and exclusion of variables, ratio and proportion, conservation involving models, compensation and equilibrium, correlation, probability, combinatorial thinking, coordination of frames of reference, and…

This manual was developed to provide guidance to individuals working in Project SOAR (Stress on Analytical Reasoning), a pre-freshman summer program for science majors anticipating matriculation at Xavier University of Louisiana. Following an overview of Xavier University and Project SOAR and an outline of general instructions, specific…

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

The use of strategies is an important part of mathematical thinking. Presented are several games that help develop the reasoning strategies of hypothesis making and testing, proving and disproving, looking for patterns, and simplifying a difficult task. (MDH)