Making Geometry Fun with Origami
Lucila Cardenas Vega
University of Texas at Brownsville
Introduction
Teachers must have an understanding of students’ mathematical thinking in order to create meaningful learning opportunities. This becomes more relevant when teaching subjects that not all students have an interest for, such as, geometry. Since geometry is the study of shapes and configurations, it is important to understand how a student thinks about the different properties in geometry including, symmetry, congruence, lines and angles.
Students remember a lesson better and the information becomes more significant when learning is accessed through hands on activities. (Pearl, 2008). Origami is the art of transforming a flat sheet of material into a finished sculpture through folding and sculpting techniques. The use of origami can be thought of as art; however, there are so many other benefits of incorporating origami in geometry lessons.
According to experts, origami teaches students how to follow directions, encourages cooperation among students, improves motor skills and it helps develop multi-cultural awareness (Weirhem, 2005). Origami activities used in geometry lessons reinforces vocabulary words, facilitates the identification of shapes and simplifies congruency and symmetry (Pearl, 2008). In origami, students take a flat piece of paper and create a figure that is three dimensional. The use of origami in geometry is not new. Friedrich Froebel, the founder of kindergarten, was the first to introduce Origami into formal education. (Tietze, 2008). Froebel recognized the value of children learning through enjoyment and discovery. He considered the use of paper as a means for children to discover for themselves the principles of math and geometry. (Tietze, 2008). Piaget, the well known child development psychologist, argues that motor activity through precise movement is important to the cognitive development of the brain (Pearl, 2008).
This case study, aside from looking into the way students think when trying to identify congruency, symmetry and shapes, is also intended to discover the benefits of the use of origami to help students realize their imagination while exploring important mathematical concepts. This study seeks to identify the benefits of using an innovative teaching tool, such as origami, in order to improve the scored of children who struggle with geometric concepts.
Method
In this study, I examined the benefits of using origami to teach geometry concepts to elementary students who have difficulty understanding geometric concepts. The purpose was to try to improve their interest in certain concepts by using an inventive instrument such as origami designs.
Participants
The participants were randomly selected at an elementary school in Port Isabel, Texas. They consisted of two boys and two girls. They are in the fourth grade and struggle with geometry concepts. They are of low socio-economic status.
Materials
The materials used in this case study were step by step instructions to specific origami designs, origami paper, scissors, pencils and vocabulary flash cards. The students were provided with paper pre-cut to the appropriate size for each origami design. A copy of the directions for the chosen origami designs for each student was provided. The classroom environment was set up so that the participants could work in a table space large enough for the individual space needed.
Procedure
First they were given a brief history on what origami is and where is originates from. Next, the participants were shown example of previously designed origami sculptures. The lesson was set-up by orally reviewing key geometry terms for example, symmetry, congruent, faces, edges, triangle, square, rhombus and rectangle. The origami paper was distributed and students were asked to work in pairs while the instructor guided them through their first origami design. The first design was a simple sculpture was of a boat. Students were taken step by step of each folding instruction. Instructor spoke slowly and emphasized vocabulary terms previously reviewed.
Instructor: Begin with a rectangular piece of paper. Fold in half as shown. Then partially fold it again, making a crease near the top.
Student: Like this?
Instructor: Exactly.
Instructor monitored constantly to ensure that all students comprehended.
Instructor: Ok, now follow the crease and line up the corners and fold down.
Instructor: Now fold each edge of the paper upwards as I’m demonstrating. Use your fingers and you will notice e that it looks like a hat! What else do you notice of the shape so far?
Student: I see a triangle.
Student: I see two triangles and a rectangle.
Student: Both sides are the same.
Instructor: awesome! It has symmetry.
Instructor: very good, now we will continue a few more steps until we make a boat. Bring the corners of the hat towards each other. The edges will be pushed outwards. It's kind of like you're "squashing" the hat into a square.
Now take one lower corner of the square and fold it upwards. Flip the piece over and do the same for the other corner.
You now have a folded triangle. Open up the folded triangle, bring the corners together and again, press the triangle into a square as I am showing you. Now pull the outer corners of the square, one in each hand. Keep pulling to unfold your boat. We like to turn the boat over and expand the hole in the bottom. This will help it balance and float better.
Instructor: Ok, now let’s talk about or boats. What geometric shapes or terms did you notice during the process?
Students: I noticed triangles, rectangles, squares, and the boat has symmetry.
As an assessment, the participants were asked to create and origami sculpture individually by following step by step instruction that were given to them. This sculpture was scored using a rubric. Participants were asked to explain the sequence of folding the sculpture and use geometry terms learned.
Results
The participants were able to recognize and use basic geometric properties of two and three dimensional figures. The participants used appropriate vocabulary to describe the two-dimensional figure. The participants will be able to use this information in order to recognize and determine patterns and simple geometrical relationships. Overall, the participants enjoyed this activity. Some expressed that it did not seem like a geometry assignment but rather art class. All improved in listening and following directions skills.
Discussion
In some instances, the participants would appear anxious and frustrated if the sculpture would not look as planned. The instructor would re-direct them if needed. The students’ strengths were their enthusiasm in trying this new approach. They were very good at following instruction when they had visuals and step by step instructions that were given at their pace. They were able to incorporate their newly learned vocabulary terms rather easily and seemed to have made those words part of their vocabulary.
Their weaknesses were that they required the steps at a very slow pace and required constant reassurance during the process. After a few guided sculptures, the students were able to work individually and create successful sculptures. Before using the origami technique, I considered the students to be at a 0 or 1 in the van Hiele level based on their lack of understanding of the basic geometric terms and concepts compared to other students. After using the origami technique over a period of several months, the students have made significant progress and could be considered to be at a solid 1 or 2.
Conclusion
The case study involved using an innovative tool to analyze how students think about a geometric concept. The innovative tool used in this case study was the use of origami to help the learners make a connection of the geometric concepts. The participants were introduced to origami. The geometry terms were reinforced during the lesson to ensure they made a connection. During the process, the students were able to recognize several shapes that were being used in the steps to creating sculptures. I learned that the students were very engaged during the lesson and seemed to enjoy the activities. The lesson encouraged the students to work cooperatively and required both hands which activates the whole brain. I would recommend that others introduce geometry by using origami in order to make it fun and interesting. Geometry can seem boring and tedious to some students but by incorporating this entertaining technique students will be initially intrigued and want to learn more.

References
Pearl, B. (2008). Math in Motion: Origami in the classroom K-8: Mathematics and Educational Techniques, 137-142.
Tietze, M. (1994). The use of Hands-on Activities in the Third Year of an Integrated Sequence: a Core Curriculum in Geometry, 300-303.

Veblen, O. (2008). The Modern Approach to Elementary Geometry: Geometrical Patterns and Designs, 98-104.

Weinheim, M. (2005). Origami as the Shape of Things to Come. Retrieved from

www.NewYorkTimes.com