Methods used to investigate problems in the sciences include building-up strategies, insight, and change (or serendipitous discovery). Discusses appropriate learning experiences for the undergraduate science students so they are more likely to benefit from the second method of scientific discovery as they make a career in their chosen field. (JN)

Discusses the development and use of flowcharts to involve students in the major stages of experimental design and hypothesizing. The progress of stages attempts to simplify the complexity involved during problem-solving in science investigations. Several illustrative flowcharts are included. (JN)

This book presents first-person accounts of 20 young female inventors. Most have won prizes for their inventions; some have even obtained patents. Part 1 "Inventors and Their Inventions," focuses on the young inventors and their lives, how they came up with their ideas, who helped them, what problems they faced, and how they solved their problems.…

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)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)

A problem-solving approach is developed for secondary or college students to estimate the number of piano tuners in a large city. The answer and method are analyzed for appropriateness. Four similar problems are suggested. (DC)

A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

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)

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…

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)…

Discusses possible approaches to solving the problem of how many different triangles can be formed on an n x n geoboard and the different geometric concepts utilized to formulate a solution. Approaches include counting strategies, writing a computer program, and using difference equations. (MDH)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)