This book contains activities designed to help teachers enrich the mathematical experiences of all children and reach toward fulfillment of the National Council of Teachers of Mathematics (NCTM) Standards. Chapters include: (1) "Prenumber, Number, Non-Number"; (2) "Place Value"; (3) "Addition, Subtraction"; (4)…

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

A problem solving approach to the teaching of the Pythagorean Theorem is described. (SD)

An activity-based unit on congruence and similarity is described. The themes underlying the unit are the usefulness of analogy in determining mathematical principles, and the notion that the number of conditions imposed on figures affects the number of factors which must be specified to insure congruence or similarity. (SD)

A computer language that can be used by people of all ages, Logo allows children the freedom to direct their own learning. Integrating Logo into the curriculum provides students the opportunity to program a computer, to engage in logical, sequential thinking and planning, to solve problems, and to manipulate text, language, graphics, and music…

This document contains three modules. The first of these examines applications of algebra to geometry. It is designed to teach students how to algebraically characterize points which may be constructed with a compass and straight edge, and how to use this characterization to obtain classical geometric nonconstructibility results. The second unit…

This research involved the observation and audio-recording of 30 ninth-grade mathematics students recommended as being outstanding by their mathematics teachers. Each student was presented with five different problem situations for which he or she was to make mathematical conjectures. During the interview, the students thought aloud and all of…

The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…

This report presents a more detailed elaboration and discussion of the mathematical content of the central concepts which have been designated as the Mathematical Strands of the Mathematics Curriculum for grades K-8. In Part I of the report there is a discussion of the pedagogical philosophy which the committee felt was to have an importance equal…

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

Considers a trigonometric solution to a standard calculus minimization problem. Presents a geometric solution which can be used to solve other trigonometric or algebraic problems. (PK)

Provides domino geometry problems, problems with arithmetic progressions, and magic pentagram sums. (JM)

Presents a collection of problems focusing on: (1) squares in arithmetic and number theory; (2) squares in geometry; (3) topics blending arithmetic and geometric aspects of squares; and (4) squares and Logo. A sample student worksheet (with answers) is included. (JN)

Discusses the development of visual thinking in students. Also presents a strategy that incorporates visualization exercises within the framework of traditional mathematics. The technique appears successful for students studying geometry, fractions, and problem solving. Visualization abilities increase understanding and therefore give students…