In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

This research was based on the assumption that the teaching of broadly generalizable cognitive skills should be a primary goal of education--that students can be taught to be better insight problem solvers outside of school by training in school and that they can be given the skills necessary for efficient discovery learning. The subjects were 116…

The article discusses the concept of inspiration as a component of creativity, including environmental influences, affective self-awareness, effective verbal communication to preserve inspired experiences, and the role of humor. The creative problem-solving process is also addressed, with attention to divergent thinking strategies and the practice…

In order to investigate the relationship between mental imagery and creative problem solving, a study of 44 separate accounts reporting mental imagery experiences associated with creative discoveries were examined. The data included 29 different scientists, among them Albert Einstein and Stephen Hawking, and 9 artists, musicians, and writers,…

Reports on the winning tool creations by 1,300 fourth-, fifth-, and sixth-grade students in the 1997 Craftsman/NSTA Young Inventors Awards Program. Students had to use mechanical and science process skills to design and build tools to meet their needs in solving a problem. The winning entry was a calibrated angle and depth scissors. (AIM)

The discovery of penicillin is cited in a discussion of the role of serendipity as it relates to scientific discovery. The importance of sagacity as a personality trait is noted. Successful researchers have questioning minds, are willing to view data from several perspectives, and recognize and appreciate the unexpected. (JW)

Pullout pages provide suggestions for teaching elementary students at all levels about the wonders of human ingenuity. The suggestions help students see that great ideas come from the need to solve real-life problems and that one great idea leads to another, so current inventions help predict future inventions. (SM)

The book "Productive Thinking", by Gestalt psychologist Max Wertheimer, was published over 50 years ago, yet it continues to wield influence. The book's argument on productive thinking, and why it is still relevant today, are the focus of this paper. Productive thinking involves going from a situation of bewilderment or confusion about some issue…

Based on a study dealing with problem-finding behavior of artists as the first step in the creative process (Getzels and Czikszentmihalyi), this study on the empirical nature of problem-finding included middle school students from a suburban-rural area in Western Pennsylvania. Eight students identified through three measures as creative were…

Describes grade-appropriate weekly activities designed to appeal directly to students by giving them open-ended questions. Activities may be worked on individually, in pairs, or in small groups. This particular set of activities focuses on stories from literature involving measurement, earning money, marketing a product, and setting up a…

This document reports on two 3-day workshops designed to train three vocational education instructors or curriculum developers from every Wisconsin school district in specific critical thinking skills strategies that they could implement in their districts. The document includes a three-page narrative description of the workshops that includes…

The Invent America program addresses the need to provide K-8 students with opportunities to learn critical and creative thinking skills through the process of inventing. Students apply problem-solving skills as they turn their own creative ideas into inventions. It is an effort to integrate the curriculum, help students synthesize knowledge, and…

The Invent America program addresses the need to provide K-8 students with opportunities to learn critical and creative thinking skills through the process of inventing. Students apply problem-solving skills as they turn their own creative ideas into inventions. It is an effort to integrate the curriculum, help students synthesize knowledge, and…

The Invent America program addresses the need to provide K-8 students with opportunities to learn critical and creative thinking skills through the process of inventing. Students apply problem-solving skills as they turn their own creative ideas into inventions. It is an effort to integrate the curriculum, help students synthesize knowledge, and…

The Invent America program addresses the need to provide K-8 students with opportunities to learn critical and creative thinking skills through the process of inventing. Students apply problem-solving skills as they turn their own creative ideas into inventions. It is an effort to integrate the curriculum, help students synthesize knowledge, and…