...students use paper folding to perform their initial investigations of symmetry and congruence in geometry (NCTM, 2000). Since prospective elementary school teachers need solid foundation in the mathematical basis of these reform initiatives, textbooks for these future teachers should contain paper-folding applications.

Although origami spans academic disciplines, paper folding has increasingly been applied to mathematical systems and structures (Hull, 1996; Auckly and Cleveland, 1995). Moreover, origami is a unique mathematical activity because one can take a sheet of paper and transform it into a three-dimensional object. This concrete experience in spatial reasoning can then be transformed into a lesson on symmetry or graph theory (Peterson, 1995). Educators have also applied paper folding to such diverse mathematical objects as logical structures (Cipra, 1998), axiomatic systems (Alperin, 2000), and tessellations with geometrical figures (Stewart, 1999).

Clements and Battista (1992) defined school geometry as the study of spatial objects, relationships, and transformations that have been formalized. As students participate in the physical opportunities afforded by origami and other manipulations with paper, they gain a foundation from which to build the formalizations needed in school geometry. Particularly, students benefit from experimenting and exploring with physical materials and models, and learning opportunities that require students to visualize, draw, and compare figures in various configurations help to develop spatial sense. Since geometry at the elementary and intermediate school levels aims to help students describe, relate, and represent objects in the environment, students can benefit from activities involving paper cutting, folding and tearing.

Put another way, transforming a flat piece of paper into a three-dimensional object is essentially a manifestation of spatial reasoning, a key component of geometrical learning. Thus, origami along with paper cutting and tearing can allow students to create, modify, and investigate specific geometric shapes such as polygons and polyhedra.

The use of origami in school programs is also one of the notable differences between American and Asian educational systems. Given the better performance of Asian children in international comparisons in mathematics, it may be worthwhile to give attention to the potential impacts origami can have on the development of US students' mathematical thinking. Rooted in Asia, origami reflects the creativity and aesthetics of those cultures. By taking part in origami and other paper manipulation activities, American students can gain an appreciation of Oferent cultures and alternate ways of observing and studying geometric figures. Cooney (2001) points out, that in our internal, national zeal to improve mathematics education in the US, we should not overlook the attributes and approaches of other cultures that have demonstrated high student achievement in mathematics. Clearly, Asian societies and their contributions to origami and other manipulations with paper are a case in point.

Silverman and Manzano (1996) further noted that what is accomplished by using origami is no less than the planting and nourishing of the seeds of geometric thinking. Among the geometric concepts that are embedded in origami are similarity, congruence, measurement, and construction. Understanding these and other basic concepts and the developmental ways that children learn allows the teacher to facilitate activities which are rich in exploration, application, representations, communications and mathematical reasoning. Silverman and Manzano conclude that paper folding provides a highly engaging and motivating environment within which children extend their geometric experiences and powers of spatial visualization. In short, well-planned activities involving paper can give a venue for students' creative nature and invite play, problem solving, and problem posing.

Arcidiacono (1992) in his geometry work at the Math Learning Center at Portland State University further noted that paper folding activities can cause students to reflect about the relationships among specialized polygons such as isosceles triangles, rhombi, and kites. However, the endorsement of paper folding extends back even further western education. Friedrich Froebel, a German founder of the Kindergarten Movement, introduced paper folding into nineteenth century kindergartens, and this introduction was further developed and carried on by later reformers (Lister, 2002). Through paper folding, children use...

NOTE: All illustrations and photos have been removed from this article.



Looking for additional articles?
Search our database of over 3 million articles.

Looking for more in-depth information on this industry?
Search our complete database of Industry & Market reports by text, subject, publication name or publication date.

About Goliath
Whether you're looking for sales prospects, competitive information, company analysis or best practices in managing your organization, Goliath can help you meet your business needs.

Our extensive business information databases empower business professionals with both the breadth and depth of credible, authoritative information they need to support their business goals. Whether it be strategic planning, sales prospecting, company research or defining management best practices - Goliath is your leading source for accurate information.