The method used at airports in determining the cloud height at night is presented. Several problems, the equation used, and a simple design of an alidade (an instrument that shows cloud heights directly) are also included. (MP)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

Discusses making tessellations by using a polyomino. Illustrates the various ways for various shapes of polyomino. Provides several diagrams and instructional guides. (YP)

This report attempts to discover how students think about and use mathematics in open-ended questions. Part I, "Open-ended Questions in Mathematics," describes the rationale for adding open-ended questions to the grade 12 mathematics test of the California Assessment Program (CAP). Part II describes the findings from students' responses…

This introductory book of a two-part publication, designed as an in-service tool for teachers of grades K-9, is based on the postulate that a teacher should become a better problem solver in order to teach problem solving more effectively to students. This booklet provides an overview of problem solving as a process used daily by all individuals…

Presented are the results of an investigation of stimulus integration capabilities of three- and four-year-old children in judgments of small and large numbers. There is much evidence that suggested young children have a concept of number for small numbers, but not for large ones. A concept of number was hypothesized by Piaget to rest on the…

Outlines the development of a lesson structured around four stages of problem-solving. Provides five problems and questions for understanding, getting started, and for extension in each of the problems. (YP)

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course that requires some previous knowledge of algebra and the ability to work at a rapid pace. Topics include the basic operations with signed integers; fractions; decimals; literal expressions; algebraic fractions; radicals;…

Describes a mathematical investigation of gold--how it is weighed, stored, used, and valued. For grades 3-4, children estimate the value of treasure chests filled with gold coins and explore the size and weight of gold bars. Children in grades 5-6 explore how gold is mined and used, and how the value of gold changes over time. (PVD)

This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This is designed as the second of a two-semester sequence. Topics include performing operations with radicals and exponents; learning to solve equations;…

This document contains the course syllabus and 12 independent practice modules for a college pre-calculus designed as the first course in a two-semester sequence for students in a Bachelor of Technology program. The course emphasizes engineering technology applications and verbal problems. Topics include a review of elementary algebra; factoring…

The use of calculators and computers in the schools is promoted. It is stated that calculators should be used in the mathematics classroom as soon as basic operations are understood. A point is made that calculators are no greater a threat to "learning the fundamentals" than slide rules, which have been available for over 350 years. It is…

Offers examples of non-standard mathematical application problems. The applications come from a variety of areas including industry and other cultures. (PK)