Geometry Thinking Research Articles

Shaping the Standards: Geometry and Geometric Thinking

This article is the third in a series inviting discussion of, and reaction to, the draft of Principles and Standards for School Mathematics. This month's article focuses on geometry and geometric thinking. Your feedback will help the writers prepare the final version of the document next summer; the final version will be released in April 2000.

Call for Manuscripts for the February 19 99 Focus Issue: Geometry and Geometric Thinking

Call for Manuscripts for the February 19 99 Focus Issue: Geometry and Geometric Thinking

Call for Manuscripts for the February 1999 Focus Issue: Geometry and Geometric Thinking

Call for Manuscripts for the February 1999 Focus Issue: Geometry and Geometric Thinking

Call for Manuscripts for the February 1999 Focus Issue: Geometry and Geometric Thinking

Call for Manuscripts for the February 1999 Focus Issue: Geometry and Geometric Thinking

The Van Hiele Model of Thinking in Geometry among Adolescents

The Van Hiele Model of Thinking in Geometry among Adolescents

Using the Turtle Tot robot to enhance Logo for the hearing impaired.

This paper describes the Turtle Tot, a Logo powered robot that assists hearing-impaired students in making the transition from the concrete geometric movement of their bodies to the directed geometry of computer Logo. Also described is the process for leading students from describing the elements of their body movements to directing the Turtle Tot through computer Logo, to directing the on-screen turtle with Logo procedures. Through this process, students can explore directionality, basic geometry, language concepts, and logical thinking.

Van Hiele Levels of Thinking in Geometry

Van Hiele Levels of Thinking in Geometry

What's Going on…

Family math. The EQUALS staff at the Lawrence Hall of Science, University of California, Berkeley, has developed a program of classes to involve parents in their children's future schooling and jobs. Information about careers and the importance of mathematics to future jobs and schooling is woven throughout the classes. Mathematics topics are drawn from measurement, probability and statistics, patterns and functions, geometry, arithmetic, and logical thinking, and activities are designed to supplement the classroom curriculum. Classes are given for specific grade levels, spanning kindergarten through general mathematics. A hands-on approach, used with emphases on problem solving and the enjoyment of mathematics, includes instructions for use at home. FAMILY MATH is funded by the Fund for the Improvement of Postsecondary Education. A dissemination workshop will train new leaders in the fall of 1984. For further information contact Virginia Thompson and Ruth Cossey, c/o EQUALS, Lawrence Hall of Science, University of California, Berkeley, CA 94720.

The Present State of Evaluation of Critical Thinking in Algebra and Geometry

Very early in the history of people much attention was given to the study of mathematics; practical applications alone made study necessary, but mathematical investigations were carried on, too, for their own sake. The secret society of the Pythagoreans (about 500 B. C.) set up a training school for the instruction of new members. The curriculum consisted of four subjects:—geometry, arithmetic, astronomy, and music. It was Plato (about the fourth century B. C.) who hung over his academic door a sign that read, “Let no one who is unacquainted with geometry enter here.” The belief that a study of mathematics led to clear thinking and logical marshalling of ideas is evident from the titles of books popular in their day; there was Alcuin's (735-804) Problems for Quickening the Mind and Robert Recorde's (1510-1558) The Whetstone of Witte.

Functional Thinking in Geometry

Geometry has been questioned as a high school subject by the general educator. However, this criticism has not been due so much to the subject as to the manner of teaching.