Seven principles are presented for improving creative thinking, based on assumptions of creativity as a perceptual shift resulting from a metamorphic mental image. Principles include (1) the future initiates and pulls creative thought; (2) initial fact finding is best postponed; (3) problem redefinition is often retrospective; and (4) metaphors…

Many people are interested in computer aids to rhetorical invention and want to know how to evaluate an invention aid, what the criteria are for a good one, and how to assess the trade-offs involved in buying one product or another. The frame of reference for this evaluation is an "old paradigm," which treats the computer as if it were…

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

Museum objects can be the springboard for exercising critical thinking. There are four main thought processes associated with critical thinking: (1) fluent thinking, the ability to produce many ideas; (2) flexible thinking, the ability to view something in different ways; (3) original thinking, the ability to produce unique ideas; and (4)…

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)

Discusses how a single problem can be utilized to discuss mathematical skills and concepts at several different levels. Presents a problem involving fractions examined at the following four levels according to the abilities of the students: (1) finding solutions; (2) identifying methods for finding solutions; (3) exploring similar examples; and…

Previous research has shown a relationship between formal reasoning ability and science process skill attainment. It has been hypothesized that an increased emphasis on teaching process skills might enhance the formal thinking abilities of students. A variety of strategies have been proposed to better accomplish this task, most notable, the…

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

Describes the use and rationale of "Silent Teaching," a teaching technique in which the teacher remains silent as students generate and evaluate hypotheses while trying to understand an as-yet undiscovered concept. (MDH)

Describes the "number 2 arithmetic challenge," an activity in which students score points by creating examples using the number 2 that satisfy an unknown rule. Computers are utilized to verify and record examples. Conflicts with computer responses create situations to explore negative numbers, fractions, mixed numbers, the order of…