In learning geometry, children need to investigate, experiment and explore with everyday objects and other physical materials. Exercisesthat ask children to visualize draw, and compare shapes in various positions will help develop their spatial sense. Although a facilitywith the language of geometry is important, it should not be the focus of the geometry program but rather should grow naturally fromexploration and experience. Explorations can range from simple activities to challenging problem -solving situations that developuseful mathematical thinking skills. (NCTM K-4 Standards, p. 48)

Students discover relationships and develop spatial sense byconstructing, drawing, measuring, visualizing, comparing transformingand classifying geometric figures. Discussing ideas, conjecturing andtesting hypotheses precede the development of more formal summarystatements. (NCTM 5-8 Standards, p.112)

The purpose of teaching geometry in the elementary/middle school is tohelp children acquire abilities to be used in describing, comparing,representing and relating objects in the environment. The development ofsuch abilities relies heavily on the kinds of experiences children havewith real objects and on the ways which they respond to theseexperiences. Many geometry experiences should involve unstructured playactivities in which children are encourage to experiment, to find out,and tell "why and what".

    From ages 4 to 7.
    At this level activities should focus on the following skills:
    1. listing the attributes of geometric figures.
    2. comparing geometric figures to see how they are alike and how theyare different.
    3. identifying the results when geometric figures undergo change.
    4. identifying representations for geometric figures.
    5. describing relationships among geometric figures.
    From ages 7 to 9.
    At this level, children should engage in activities that willintroduce them to ideas related to the following:
    1. perpendicularity.
    2. parallelism.
    3. similarity.
    4. size.
    5. congruence.
    6. symmetry.

What we accomplish by using ORIGAMI is the planting and nourishing ofthe seeds of geometric thinking. Many geometric concepts are embedded inorigami. Understanding of the concepts involved and the way the childrenlearn allows the teacher to facilitate activities which are rich inexploration, application, representations, communication andmathematical reasoning. Origami provides a highly engaging andmotivating environment within which children extend their geometricexperiences and powers of spatial visualization. It gives a venue fortheir creative nature and invites play, problem solving and problemposing.

THE EXCERPT ABOVE FROM "Origami: Informal Geometry and a CulturalBridge"IS REPRINTED HERE with PERMISSION FROM THE AUTHORS, Fredrick L.SilvermanandNoel Nevada MANZANO, COLLEGE OF EDUCATION, University of NorthernColorado.THEY PRESENTED THIS PAPER AS PART OF A WORKSHOP FOR the NationalCouncil of Teachers of Mathematics (NCTM) Annual Conference, San Diego,1996.

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