# User:Georgejem/Origami in Mathematics Pedagogy/Origami and Teaching

“The use of [paper folding] not only affords interesting occupations to boys and girls, but also prepares their minds for the appreciation of science and art” ... “It would be perfectly legitimate to require pupils to fold the diagrams with paper. This would give them neat and accurate figures and impress the truth of the propositions forcibly on their minds. It would not be necessary to take any statement on trust, for what is now realised by the imagination and idealisation of clumsy figures can be seen in the concrete.”

These words by T. Sundara Rao are a fitting introduction to this chapter. They are taken from his book Geometric Exercises in Paper Folding published in Madras in 1901, one of the oldest known books on Origami and geometry, which explores the use of paper folding in teaching elementary geometry, ranging from constructing regular polygons to demonstrating proofs of geometrical constructions.

## Origami in Teaching Mathematics

It is apparent that origami has great mathematical potential when used in education, especially in geometry.Origami can provide a useful medium for the student to translate the two-dimensional information on a textbook page into the intended three-dimensional concept and as a context for developing mathematical ideas and insights and for posing mathematical questions. Students can explore such mathematical topics as combinations, permutations, angle measures, numerical and geometric patterns, perimeter, area, and volume relationships, the characteristics of polyhedra, symmetry, and possible map colourings.

The process of making origami models can aid the students’ learning in the following ways:

1. Visualize abstract concepts outside of the textbook: Students will encounter symmetry, angles, triangles, parallelograms, bisectors and many more in just one sequence of folds.
2. Expand and apply mathematical vocabulary: In the process of making an origami model, the students have a chance to use and improve their vocabulary of mathematical words to describe the folds. This familiarizes the students in speaking mathematics and opens a discussion of the concepts in the context of paper folding.
3. Recognize applications of mathematics: Origami can also be a way for the students to discover the application of mathematics in and around their environment.
4. Inexpensive and fun: Paper is an inexpensive, easily available resource and so the students can carry the learning beyond the classroom to their own homes and explore both the art and mathematics by themselves.

At the end of the lesson, the students have a tangible representation of the concepts in the form of the origami they create. It contributes to their sense of achievement, and the origami is a reward by itself.Objects made by the students themselves have great visual and personal appeal, which helps to sustain their interest in analysing mathematical characteristics.

## Effectiveness of Origami Instruction

The claims that origami-mathematics lessons blend a variety of approaches to instruction in a way that benefits the students mathematically is supported by researchers in mathematics as well as education. Research has shown that origami improves the spatial intelligence of the student and that students adapt and favour the method of origami instruction quickly.In a study conducted on the impact of origami as a teaching tool in the middle school classroom, it was found that origami lessons can contribute to geometry understanding and spatial skills and be a positive influence on the learning and understanding of concepts. The study also points out that when students were asked to write down one word to describe their experiences, students responded in an overwhelmingly positive manner with words like “fun,” “helpful,” “enjoyable,” and “awesome.” How often do students respond like this to math instruction? Thus, the students themselves felt that the origami lessons had helped them.

## Origametria

The Israeli Ministry of Education has introduced a program called ORIGAMETRIA in its public schools to teach curriculum geometry through origami. The name Origametria is made from the words “origami” and “geometry” and was created by the Israeli Origami Center (IOC) to describe its innovative program. In this program, each lesson involves making a simple origami model. During the folding process, the teacher leads a discussion on a relevant geometry topic, such as symmetry, angles, or area, depending on grade level.