6OSME Origami Math Presentation by NBoakes

A 7 Year Study of Origami’s Impact on College Age Students6th International Conference on Origami in Science, Mathematics & Education August 2014Tokyo, Japan

Presented by:

Dr. Norma

Boakes

A little bit about where I’m from….

When I discovered Origami….0I was teaching high school geometry

but found students struggled visualizing and applying math in context

0I found myself as bored as the students. The “rote” method wasn’t working

0I sought out ways to make math fun and engaging I attended a workshop on Origami in the classroom at a math conference

The rest is history……..

Sources of inspiration

0 Books0 Unfolding Mathematics with Unit Origami by Betsy Franco0 Math in Motion- Origami in the Classroom by Barbara Pearl0 Paper square geometry: The mathematics of origami by

Youngs & Lomeli……0 Articles

0 “Turning Origami into the Language of Mathematics”0 “Origami: The Mathematician’s Art”0 “Origami: Paper folding the Algorithmic Way”…..

0 Origami USA & OSME Conferences

This lead to my doctoral studies…

0Origami was common practice but not something that was formally studied

0The result… My doctoral dissertation study

The effects of origami lessons on students’ spatial visualization skills and achievement levels in a seventh-grade mathematics classroom

Coining the phrase “Origami-Mathematics Lessons”

“…a mathematics lesson taught using an origami activity linking students’ mathematics knowledge and skill during the folding process and with the resultant Origami figure” (Boakes, 2006)

Step 1: Start white side up. Orient like a diamond. Bring the bottom corner up to the top corner and crease.

*We oriented this square as a diamond but has it changed? How are a square and a diamond similar? *Once you fold the corner up, what kind of triangle have you formed?

Sample questions I ask….

Step 2: Fold triangle in half by bringing left base angle to the right base angle of the triangle and creasing.

*What line did you form when you bring one base angle to the other? Do you still have the same kind of shape?

Reviewing Related Literature

Origami

Geometry & spatial

reasoning

Theoretical Framework

My studyPiaget- knowledge

H. Gardner- multiple intelligences

National Math Standards (NCTM)

Barbara PearlArnold

Tubis

Tom Hull

Betsy Franco

Bruner-learning modalities

Defining spatial ability

See Boakes, 2006

Focus of Research Conducted0Spatial Visualization- a person’s capacity to

perform a series of mental manipulations of an object in both two- and three-dimensional forms

0Spatial Ability- a more general term for a person’s ability to be able to perceive, recall, create, and arrange spatial images

Imagine rotating the image on the left.

Which one’s orientation changed by more than a rotation on the right?

Same (S)= rotation onlyDifferent (D)= reflection and rotation

Known as “Card Rotation Test”, tests 2-D visualization skills

Imagine the fold steps to the left then punching a hole through the sheets.

Which to the right is it unfolded?

Known as “Paper Folding Test”, tests more complex 2-D visualization skills

The 2-D net of a 3-D figure is shown on the left. On the right is the 3-D figure completed.

Can you match up corresponding edges?

From the Kit of Factor-Referenced Cognitive Tests

Known as “Surface Development” Test, test 2-D to 3-D visualization skills

Research I have completed to date…0 2006 study with middle school children (n= 56)

0 Origami infused into a geometry unit0 Quasi-experimental pre-post test design0 Results: Scores on post-tests improved for both groups though

no significant differences were foundPublished in Origami4

0 2008-2010 study with college-age students (n=75)0 Origami infused into a course called “Art & Math of Origami”0 Single group pre-post test design w/sorting factors (STEM &

existing spatial ability)0 Results:

0 Pre-post scores significantly increased for all participants0 Some significant differences found for STEM vs. non-STEM studentsPublished in Origami5

Design of Updated Study

0 Sample- Cluster sample of college population taking college course on Origami (7 semesters of students combined)

0 Treatment- Origami and origami-mathematics lessons infused in course

0 Length of study- one college semester 0 Instruments

0 Pre- to post-tests of spatial ability (3 total)0 Background survey

Treatment0 Course called GNM 2257- The Art & Math of Origami

0 4 college credit elective course open to ALL majors0 Categorized as a GNM (General Natural Science and

Mathematics)0 Counts as an “A” or art course, a required component of

all degree programs0 Counts as one out of 3 possible quantitative reasoning

courses students are required to take. 0 Known as a “Q2”, quantitative reasoning in context

course

Sample Population

0 Sample of all students taking course from 08-present (n=164)

0 Junior/senior level college-age students enrolled in college course0 Approximately 2/3 female0 77% caucasian

0 Areas of study0 STEM (math, science, technology…)- 42 students0 Non-STEM (literature, history, psyc,….)- 112

students0 Spatial experience

0 Low spatial experiences- 80 students0 Mid-to-high spatial experiences- 74 students

Course descriptor

This course is intended for all majors, and is designed to train students how to perform the ancient art of paper folding while exploring the art's connection to a variety of disciplines. Students will review and strengthen their mathematic knowledge through discussion and hands-on exploration. In addition, connections to culture and history, and art will be interwoven throughout coursework.

The Math of GNM 22570 We explore the mathematics

inherent inside the origami model through fold patterns like this one.

0 We look at the mathematics of the model itself.

Polygons & attributes

Congruence and similarity

Fractions and ratio

Angles

Polyhedra…….

Some specifics of the course

0 Students fold at every session 0 The instructor teaches in the beginning the slowly

allows the students to work independently0 Students are often placed in pre-set teams to aid in

learning process, especially with mathematical exercises

0 Students get “Free folding” days to work on their art0 All assignment link to Origami in some way

Topics I cover0 Language and terminology of Origami0 Basic bases and folds*0 Traditional Origami*0 Modular Origami*0 Unique Material Origami0 Origami as an art form0 Kirigami*

*Mathematics explored (20% total of course)

Sample Assignments &

ActivitiesMath Explorations

Quizzes

Written Assignments

http://www.origamitube.com/play.php?vid=472

https://www.youtube.com/watch?v=fgrBuq_q1No&feature=youtu.be

Instructional Origami Videos*highlights mathematics & origami knowledge

Origami Collection

Origami Showcase

Instruments0 Kit of Factor-Referenced Tests- categorized for link to

spatial visualization (field tested and validated)0 Card-Rotation0 Paper Folding0 Surface Development

0 Background Survey 0 STEM versus non-STEM0 Spatial experience

Curious what I learned from the 7 years of data combined

from this course?

Pre- to Post-test Results

Test nPre-test

mean (SD)Post-test

mean (SD)Gain Significance

Card Rotation 164110.73 (26.88)

126.85 (25.441)

16.12 p<.0005

Paper Folding 164 11.92 (3.34) 13.58 (3.31) 1.66 p<.0005

Surface Development

164 38.71 (14.19) 46.01 (12.61) 7.30 p<.0005

Table 1. Paired Sample T-test Results on Spatial Abilities.

ANCOVA Analysis(Factoring in existing skills)

Results

0 Students performed significantly better on all three tests given

0 Exposure to activities or college major (field of study) did not influence results significantly

0 Informal feedback gathered from the course offers support that the Origami can be beneficial in other ways…. Creativity, patience, focus…..

0 This course made me believe in my abilities more0 It gave me more patience.0 I feel like I have changed in the way I address

mathematics in this course. I have always been relatively terrified of mathematics, but I think that learning origami in a fun way distracted me from my fear of math, and helped me to become more mathematically competent.

0 I have changed in my appreciation of the difficulty of Origami. I suppose I've become more artistic, whereas I've gained a new art form and method.

0 Creativeness- Origami has showed me to step outside the box and be a little creative

Name three ways you feel you have changed as a result of this course. (This can be anything so long as you can describe why you feel that way.)

Bringing Origami to Africa & Lesotho

• Traveled to Africa & Lesotho for last 3 summers

• Train K-12 teachers on how to use Origami math in their classrooms

• To date, I have worked with over 250 teachers including “turn-key” trainers

NEW!

It started with teaching teachers how to use

Origami to teach math…

It grew to training “turn-key” trainers the following summer.

Receiving certificate of completion for training

Now, turn key trainers hold a workshops at local schools.

Coming soon….. Origami-mathematics lessons written and aligned to the national curriculum written by turn-key trainers. These lessons will be disseminated among schools throughout the country of Lesotho

References0 N. Boakes. “The Effects of Origami Lessons on Students' Spatial

Visualization Skills and Achievement Levels in a Seventh-Grade Mathematics Classroom.” EdD dissertation, Temple University, 2006.

0 N. Boakes. “The Impact of Origami-Mathematics Lessons on Achievement and Spatial Ability of Middle-School Students.” In Origami4, edited by R. Lang, pp.471-481. Natick, MA: AK Peters, Ltd., 2009.

0 N. Boakes. “Origami Instruction in the Middle School Mathematics Classroom: Its Impact on Spatial Visualization and Geometry Knowledge of Students.” Research in Middle Level Education Online 32:7 (2009), 1-12.

0 N. Boakes. “Origami and Spatial Thinking of College-Age Students”. In Origami 5, edited by Wang-Iverson, P., Lang, R., & Yim, M., pp.173-188. Boca Raton, Fl: Taylor and Francis Group, 2011.

0 R. Ekstrom, J. French, H. Harman, & D. Derman. Kit of Factor-Referenced Cognitive Tests. Princeton, NJ: Educational Testing Service (1976).

For more information about my research or to share your ideas…..

Norma Boakes, Ed.D.Associate Prof. of Education

Richard Stockton College of NJNorma.Boakes@stockton.edu

ありがとうございますThank you!