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

A little bit about where I’m from….

The journey….

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

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

Finding a way to make geometry active…..

The front should look like this.

The back should look like this.

Excerpt from Unfolding Math with Unit Origami

“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)

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”

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)

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

Prevalence of topic has grown….

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

In the MS Classroom

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

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

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

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

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

From: Origami4, 2009

*Gains are seen for both groups *A bit more for the experimental group

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

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

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

Bringing Origami to the college level…

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

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)

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

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.

Sample Assignments &

Activities

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)

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)

And the results…. Spatial Abilities

• Every year showed a gain in scores for all tests.

• Gains were significant in most cases.

Results by Grouping Variable

• Gain in scores regardless of grouping (STEM vs Non)

• No significant differences in performance by grouping

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)

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.

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

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

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

Year 2- 2013 Training the

trainer

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

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

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….

The resulting guide for trainers….

And trainers with their pupils!

Responses to survey about the workshop…

Year 2 Year 3 Mea

n S.D.

Mean

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)

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 ….

Newest Project- Problem solving

• Held in Summer 2015 • Focus on problem solving in

math – Approaches – Perspectives – Challenges – Techniques

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

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