This presentation was an invited session of the MAA Association and held as part of the 2016 Joint Mathematical Meeting. My presentation focuses on the growing body of evidence of the value of Origami as a teaching tool in the K-12 math classroom.

1. My Origami Journey from Classroom
Teacher to University Professor
Presented by:
Dr.Norma Boakes
Associate Professor of Education
School of Education
Email:Norma.Boakes@stockton.edu
All work presented can be found at
https://www.researchgate.net/profile/Norma_Boakes

2. A little bit about where I’m from….

3. The journey….
And what I learned about Origami in the
classroom along the way…..

4. As a high school math teacher…
• Earned a BA & math secondary
certification
• Began teaching sophomore geometry
• Found the way I learned wasn’t working
for my students

5. Finding a way to make geometry active…..

6. The front should look like this.
The back should look like this.

7. Excerpt from Unfolding Math with Unit Origami

9. “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, p.32)

10. Link to the standards….
Common Core Math Standards
• Geometry- Gr.8- Understand congruence &
similarity using physical models
• HS- “Make formal geometric constructions with a
variety of tools and methods (compass &
straightedge, string, reflective devices, paper
folding, dynamic software, etc.)” p.76
• Math Practices- Make sense of problems…
“younger students might use concrete objects or
pictures to conceptualize and solve”

11. Progressions for the CCSS
Grade 1…..“Students can learn to use their
intuitive understandings of measurement,
congruence, and symmetry to guide their work
on tasks such as puzzles and making simple
origami construction.” p. 9
Grade 3…. “More advanced paper-folding
(origami) tasks afford the same mathematical
practices of seeing and using structure,
conjecturing and justifying conjectures.” p.13
Excerpts from the Progressions for the Common Core State Standards (2012)

12. Review of literature on the topic
• Publications at the time linking Origami and
mathematics
– 27 Origami books relating to mathematics as of
2004 (Tubis, 2004)
– Articles in popular mathematics education
magazines by NCTM
– International Conferences on Origami in
Education and Therapy (COET)
• Claimed Origami has potential as an
instructional tool

13. Prevalence of
topic has grown….

16. Mathematical skills related to Origami
• Spatial Visualization- a person’s capacity to perform
a series of mental manipulations of an object in
both two- and three-dimensional forms
• Spatial Ability- a more general term for a person’s
ability to be able to perceive, recall, create, and
arrange spatial images

17. In the MS Classroom

18. Research design
• Pre-test/post-test quasi-experimental design
– Spatial visualization
– Math achievement via NAEP
• 56 seventh-grade student participants
– Experimental group- 14 males, 11 females
– Control group- 11 males, 20 females
• 2x2 factorial analysis
– Independent variables- method of instruction and gender
– Dependent variables- mathematics achievement and
spatial visualization ability

19. Data Sources
• Mathematics Achievement Test- collection of 27
items from the NAEP geometry/spatial ability strand
• Spatial visualization instruments-
– Card Rotation Test
– Paper Folding Test
– Surface Development Test
– * All tests are from the Kit of Factor-Referenced Cognitive Tests
• Observation Instrument

20. Imagine rotating the image on the left.
Which one’s orientation changed by more than a rotation on the
right?
Same (S)= rotation only
Different (D)= reflection and rotation
Card Rotation Test
Tests 2-D visualization skills

21. Imagine the fold steps to the left then punching a
hole through the sheets.
Which to the right is it unfolded?
Paper Folding Test
Tests more complex 2-D visualization skills

22. 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
Surface Development Test
Tests 2-D to 3-D visualization skills

23. From:
Origami4, 2009
*Gains are seen
for both groups
*A bit more for
the experimental
group

24. What was learned from the research formally….
• Specialized training was no more beneficial than
traditional geometry instruction
• Males and females showed some differences among
the tests (*card rotation).
• Possible contributing factors:
– Social and cultural background
– Inappropriate assessment choice
– Amount of exposure time to training
– Content of traditional text
– Grouping and selection constraints

25. What I found informally…..
• Gains shown for
both groups
despite taking 12
hours away of
teaching from a
geometry unit
• Students liked
learning this way…
It was fun learning
how to do it.
I thought….it was such a great
and fun way of learning.
Bringing all math topics into
paper folding should be an
actual activity in everyday
math.
I thought it was fun
and at the same
time I was learning.
Quotes from article in Mathitudes, 2008

26. Working with
other K-12 grades
& subjects
• STEM programs- seeking to build math knowledge &
interest in technology design related to science
• Math classrooms- teaching math through Origami
models based on grade level
• Interdiscipinary lessons
– English
– Culture & history

27. Bringing Origami to the college level…

28. GNM 2257 - THE ART AND MATH OF ORIGAMI
Arts course (A).
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. Faculty: N. BOAKES
4.000 Credit hours
4.000 Lecture hours
Levels: Undergraduate
Schedule Types: Lecture
General Studies Division
General Studies Department
Course Attributes:
Arts -A
My course

29. Topics I cover
• Language and terminology of Origami
• Basic bases and folds*
• Traditional Origami*
• Modular Origami*
• Unique Material Origami
• Origami as an art form
• Kirigami*
*Mathematics explored (20% total of course)

30. Some specifics of
the course
• Students fold at every session
• The instructor teaches in the beginning the slowly
allows the students to work independently
• Students are often placed in pre-set teams to aid in
learning process, especially with mathematical exercises
• Students get “Free folding” days to work on their art
• All assignment link to Origami in some way
• Goal is to have students see Origami as form of
expression and work independently on art

31. One unit of cube
Fold pattern when a unit is unfolded
Math is explored in
the folding process
and with the final
model itself as part of
the course.

32. Sample
Assignments &
Activities

35. Continuing my research….
• Longitudinal study over 7+ times offered
• Quasi-experimental one group pre-post test
design
• Data sources
– Spatial visualization tests
– Pre-post survey
• Exposure to spatial tasks
• Area of study (STEM vs. non-STEM)

36. Participant snapshot through 2014…
• 154 college students as of 2014
• More non-STEM than STEM majors (73%)
• Balance of abilities coming in (low vs high
spatial)
From Symmetry: Culture and Science journal article (2015)

37. And the results…. Spatial Abilities
• Every year showed a gain in scores for all tests.
• Gains were significant in most cases.

38. Results by Grouping Variable
• Gain in scores regardless of grouping (STEM vs Non)
• No significant differences in performance by grouping

39. How students described the course when asked to
share three adjectives about their experiences….
REWARDING (4), RELAXING (4), BEAUTIFUL (3), COMPLEX (3) AND MATHEMATICAL (3)

40. Recent updates to my work….
A control group was added
for comparison purposes
Test Pre Post Post
Adj
F Sig
Card Rotation Exp 111.85 126.54 124.44 .15 .698
Control 103.07 117.58 122.13
Paper Folding Exp 13.04 14.62 14.13 .23 .64
Control 11.43 12.75 13.80
Surface Development* Exp 35.08 44.04 42.22 4.44 .007*
Control 30.07 32.17 36.11
Exp N=26, Control N=12
The test related to associated 2-D to 3-D shows significance between groups.

41. Bringing Origami
to Lesotho
• Traveled to Africa & Lesotho for last
4 years
• 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

42. English is the medium of instruction by 5th year of primary school.
Math is taught in English & is compulsory through 8th grade.

43. Year 1- 2012
• 2 day workshop on hands-on
instruction including Origami
• 40 high school mathematics
& science teachers from 21
schools (public and catholic)
• 27 males & 8 females
• All but 1 African American
trained in Lesotho

44. Year 2- 2013
Training the
trainer

45. Year 2
specifics….
3 workshops total over a one-week period
• Secondary teacher workshop- 16 African American
teachers including 5 females & 11 males
– 7 to 16 had some experience folding before
– This group included teachers I taught in year 1. They will
become “turn-key” trainers for other schools.
• Primary teacher workshop- 28 African American
teachers including 16 females & 12 male
• “Bonus”workshop- Visit to 70 primary teachers in
nearby schools

46. Year 3- Developing
curricular materials
• 25 teachers and 5
MOET (national
ed. dept)
• Aligned work to
national standards
• Developed a set of
lessons to be
shared with
Maseru schools

47. Sample Origami Lesson (in guide)
Name of Lesson: Origami Shuriken (Ninja Star)
Grade: 4
Learning Outcome from Syllabus: #7 Draw vertical, horizontal & diagonal
lines; #8 Identify regular and irregular polygons: pentagon and hexagon; #9
Identify and use symmetry of objects; # 10 & 11 find perimeter & area of
shapes
Materials needed: 2 square sheets of paper
Estimated time to fold model: 20 minutes (not including explorations)
Math Concepts and Vocabulary
Identify 2-D shapes (triangle, rectangle, square, parallelogram, hexagon,
octagon)
Types of lines- vertical, horizontal, diagonal
Properties of shapes (by angle and side length)
Line and rotational symmetry
Area and perimeter
Polygon types- regular and irregular
Some of the connections will
come as you write teacher
questions in next part….

50. The resulting guide for trainers….
And trainers with
their pupils!

51. Responses to survey about the workshop…
Year 2 Year 3
Mea
n
S.D.
Mea
n
S.D.
Useful tool 4.81 0.40 4.88 0.34
Can be applied to math I teach
4.60 0.51 4.61 0.50
Students would enjoy 4.60 0.51 4.81 0.40
Students like hands-on 4.56 0.51 4.78 0.42
Will try to use what I learned 4.36 0.63 4.69 0.47
Share what I learned 4.56 0.51 4.71 0.46
Learn more 4.81 .54 4.81 0.40
Overall response of participant 4.62 0.74 4.76 0.43
Scale: 1 (Strongly Disagree) to 5 (Strongly Agree)

52. It has been a great moment for the past three
years of my learning in origami. My narrow
vision has been opened up as a result. I have a
totally different approach to mathematics
either learning or teaching. Keep/continue
doing this great you are doing for Africa with
your help we have and see the light at the end
of the tunnel.
Public secondary teacher of Maseru
The training has been very useful not only me but to my learners and other
teachers at my school. We are now able to construct our own teaching aids in
different topics. I have also been able to train not only my teachers/colleagues
but other teachers from different neighboring schools. I wish it could be
included in our education system as a country. It can be very useful.
Public primary teacher of Maseru
What
trainers
had to
say ….

53. Newest Project- Problem solving
• Held in Summer 2015
• Focus on problem solving in
math
– Approaches
– Perspectives
– Challenges
– Techniques

55. Overall lessons learned….
• Origami is a beneficial tool for teaching and
exploring math concepts
• Origami has expanded beyond a craft and into an
art respected for many applications including
math
• The simplicity of Origami (paper) makes it a great
tool for other countries with similar needs in K-12
• Data over time offers some quantitative proof to
Origami’s impact on math skills, but much more
formal study is needed

56. Scholarly works
Peer-reviewed Journal Articles
• Boakes, N. (2015). Researching the intersection of origami, mathematics, education and art.
Symmetry: Culture & Art, 26(2), p.227-242.
• Boakes, N. (2014). Preparing competent, caring, and qualified teacher: A New Jersey
perspective on teacher preparation. Journal of Education Science, 16 (2014, 05), 15-30.
• Boakes, N. (2009). Origami instruction in the middle school math classroom: Its impact on
spatial visualization and geometry knowledge of students. Research in Middle Level
Education, 32(7), p.1-12.
• Boakes, N. (2008). Origami-math lessons: Paper folding as a teaching tool. Mathitudes, 1(1),
1-9.
Peer-reviewed Book Chapter
• Boakes, N. (2011). Origami and spatial thinking of college-age students. In Lang, R. (Ed.)
Origami5: Fifth International Meeting of Origami Science, Mathematics, and Education.
London, England: AK Peters, LTD.
• Boakes, N. (2009). The impact of Origami-mathematics lessons on achievement and spatial
ability of middle school students. In Lang, R. (Ed.) Origami4: Fourth International Meeting of
Origami Science, Mathematics, and Education. London, England: AK Peters, LTD.
For more information email me at Norma.Boakes@stockton.edu or
Go to https://www.researchgate.net/profile/Norma_Boakes