SUGISAKAMASANORI

Journal of Robotics, Networking and Artificial Life
Vol. 10(3); December (2023), pp. 235–241
ISSN (Online): 2352-6386; ISSN (Print): 235-9021
https://alife-robotics.org/jrnal.html

Research Article

Proposal of Integrated Methodology for Creativity Oriented
STEM Education Using the View Point of ETT Theory
Tetsuo Hattori1, Toshihiro Hayashi1, Mai Hattori1, Yoshiro Imai1, Asako Ohno2, Takeshi Tanaka3
Kagawa University, 1-1 Saiwai-cho, Takamatsu, Kagawa 760-0016, Japan
Osaka Sangyo University, 3-1-1, Nakagaito, Daito-shi, Osaka 574-8530, Japan
3
Hiroshima Institute of Technology, Saeki-ku, Hiroshima 731-5143, Japan
1
2

ARTICLE INFO
Article History
Received 17 January 2024
Accepted 04 May 2024
Keywords
STEM education
Equivalent transformation thinking (ETT) theory
Identification of equivalence
3-Dimensional computer graphics (3DCG).

ABSTRACT

Recently, the necessity of integrated and comprehensive methodology for STEM (Science,
Technology, Engineering and Mathematics) education is growing. In this paper, we propose an
educational methodology utilizing the viewpoint of Equivalent Transformation Thinking (ETT)theory which has been proposed by Dr. Kikuya Ichikawa in 1955 as a principle of creativity.
Especially, we show that the viewpoint of ETT is very useful not only for new technology
invention but also for STEM Education in the sense that it deepens insights of the contents to belearned. Moreover, we suggest that the appropriate combination of the ETT viewpoint and thevisual presentation such as animation and simulation by 3-Dimensional Computer Graphics(3DCG) will be more effective in motivating students to study further.
© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

deeply understand the learning contents, to promote theirmotivation, and to stimulate their creativity ([9], [10],[11]).

1. Introduction
Recently, the necessity of integrated and comprehensive
methodology for Science, Technology, Engineering andMathematics (STEM) education seems to be growing [1],[2], because the content of the STEM field is becoming
increasingly sophisticated.
For the STEM education, we propose the methodology
based on the viewpoint of Equivalent Transformation
Thinking (ETT) theory which was advocated as aprinciple of creativity by Dr. Kikuya Ichikawa in 1955,
after his investigation and analysis of the past discoveries
and technological inventions.
In this paper, we briefly explain the ETT theory ([3], [4],[5], [6], [7], [8]) and describe that the viewpoint of ETT
is very useful not only for new technology invention but
also for STEM education. This is because the pastinventions, discoveries and academic developments in
STEM field can be explained according to the ETTtheory.
Also in this paper, we emphasize that the suitable
presentation of the ETT viewpoint using visualization
technology will be very effective for the students to

2.

ETT Theory

As aforementioned, the ETT theory has been proposed
as a principle of creativity by late Dr. Kikuya Ichikawa
in 1955, after his investigation of the past discoveries andoriginal inventions to analyze how creation was done.
And, he clarified the investigation results that newtechnology developments and creations were produced
along with the ETT process based on “AnalogicalThinking and its Abstraction”. Then he represented theETT process as a simple form of symbolic logicalexpression which is called “Equivalence Equation” asshown in Fig. 1.

Corresponding author E-mail: hattori@pe.kagawa-u.ac.jp

235

3. ETT Viewpoint for Education
3.1. From Construction Geometry to Analytical
Geometry by Cartesian Coordinate System
Looking back on history, we can find out many facts thatthe progress of research in the field of STEM has been
made due to the actions of ETT (or Identification ofEquivalence or Analogical Thinking and its Abstraction),and that the results have broadened our horizons anddeepened our knowledge. Then, we consider that clear
presentation and utilization of the viewpoint of ETT isalso effective for STEM education.
For an example, the “Cartesian coordinate system”
produced by René Descartes which gives a one-to-one
correspondence between a point P on a plane and a pairof two numbers (x,y), i.e., P ⇔ (x,y) where x and y arequantities based on the distances along to the direction of
two orthogonal axes (x-axis and y-axis), respectively.
As a result, taking a parabolic curve C for an example,
it can be simply represented by a set of coordinates andalgebra, without showing the procedure of geometricdrawing, such as
C= {P(x, y) | y =ax2, a: constant number}.
This is one of examples that ETT not only opens the
new field of mathematics such as Analytic Geometry andAlgebraic Geometry from Construction Geometry, butalso brings about the new concept such as “Field” into
physics.
So, we consider that it is worth to enhance the idea of
ETT, and that, in the education of the STEM subjects, toclearly show the viewpoint due to ETT when teaching
will be effective.

Ao: original system, Bτ: transformed (or arrival) system, Σa: a
set of special/peculiar properties and conditions that holds thesystem Ao, cε: core essence or essential meaning that reasons theequivalence under some conditions, Σb: a set of necessary
properties and conditions, vi: viewpoint at a certain meta level.

Fig. 1 Equivalence Equation of ETT Theory.
The description of “Equivalence Equation” means that,from a certain viewpoint vi, the original system Ao canbe transformed to the system Bτ according to theconditionalized essence cε, where some properties andconditions Σa in Ao are discarded, and new elements ofproperty and condition Σb are added to the system Bτ.
When Dr. Ichikawa presented “Equivalence Equation”,
he also showed the schematic flowchart of ETT. And heinsisted that, if we make effort to develop something to
be desired according to the ETT flowchart, creative
achievement will be possible more efficiently.
As for the ETT theory, he mainly published the papers
at the Creativity Research Workshop that was held by Dr.
Hideki Yukawa, the winner of 1949 Nobel Prize inPhysics. Dr. Yukawa called this Dr. Ichikawa’s theory as"Identification Theory" in his own words and highly
praised it [5].
For example of application of ETT theory, the newinvention process of basketball shoes which can stopsuddenly by Mr. Kihachiro Onitsuka can be explained
according to the theory [6]. Mr. Onitsuka got the ideafrom the octopus foot suckers when he looked at cooked
vinegared octopus as shown in Fig. 2.

3.2. Archimedes' Principle of Buoyancy
According to Archimedes' principle, floating power (orbuoyant force) that operates on a body immersed in a
fluid, is equal to the weight of the fluid in the same
volume as the volume of body in the fluid (Fig. 3).
As shown in Fig. 3. suppose that an object is quietly
floating on the water while the underwater volume area
V is receiving the floating power from surrounding water.
Then if we think of that the situation is equivalent toanother one where the water part in the same volume area
V is receiving the floating power from surrounding waterand quietly balanced (Fig. 3(c)), we understand thatArchimedes’ principle holds. This is also an example ofthe viewpoint of ETT.

Fig. 2 Example of invention of basketball shoes where
the inventing process can be explained by ETT Theory236

3.4. Explanation of Faraday’s World First Motor
Faraday's world first electromagnetic rotating device isshown in Fig. 5, where the current flows from top tobottom into the left and right mercury containers.

(a)

(b)

(a)

(c)

(b)

Fig. 3 Floating power (or buoyant force) that operates ona body immersed in a fluid (water). (a) An object isquietly floating on the water. (b) F1 is the power thatreceives at the underpart volume V of object. (c) The
situation where water in the same volume area V isquietly balanced.

(c)3.3. Mechanical Dynamic System (MDS) andElectric Circuit System (ECS)For taking the relation between MDS and ECS as an
example, we can deal with the equations of two systems(see Fig. 4) as equivalent equation from both meaning ofmathematics and physics. We consider that this kind ofclear presentation on what is equivalent in what meaning
is useful for integrated education for STEM.

Fig. 5 Faraday’s World’s First Motor. (a) Documents left
at the Royal Institution. (b) Motion video made by 3DCG “Blender” ([9], [10]). (c) Explanation of each partand direction of electric current
Viewing from the above, when the current flows, bothof bar magnet and electrode (or conductor) rotate
clockwise. For the each of forces causing rotation, there
are different explanations (or lectures) in the left andright sides.
According to the general explanation, for the left side,
the electric current flowing through conductor makes
magnetic field according to Ampere's law, and the fieldrotates the movable bar magnet. On the contrary for theright side, the current in conductor of the movable
electrode receives Lorentz force from the magnetic field
caused by the fixed bar magnet.
On the other hand, we consider that there is a unified
explanation based on law of action and reaction. In theright side, like the left side, the current in conductor of
the movable electrode is making the magnetic fieldaccording to Ampere's law. And the current is going torotate the fixed bar magnet through the magnetic field
caused by the current. However, the bar magnet is fixed
and the conductor is floating, so the conductor rotates
while receiving the reaction force.

 d2x
dx x
dx
m
+r
+= F0 =(v)
 dt 2
dt k
dt

2
q
dq
 L d q + R dq +=
E0 =
( I
)
2

dt C
dt
 dt

Mass m ⇔Inductance L, Responsiveness r ⇔Resistance R,
Compliance k (the inverse of spring constant) ⇔Capacitance C

F0

(b)

(a)

(c)

Fig. 4 (a) Differential equations and their corresponding
elements in MDS and ECS. (b) Conceptual image of
MDS. (c) Conceptual image of ECS

237

This unified explanation will be further understandable
by presenting the 3-DCG video and illustrating that anelectric current generates a magnetic field around it andreceives a reaction force from the bar magnet via themagnetic field.
3.5. Recursive Programming Education
As for the education of programming, the recursive
programming tends to be difficult depending on the
problem to be solved.
Taking the programming of “Tower of Hanoi” for an
example of difficult problem (Fig. 6), the problem is tofind out the optimal procedure to move the tower of ndisks, from the place at pillar A (or start place) to thepillar C (or destination), using the pillar B (as work place),
under the constraints as below.
(i) Only one disk must be moved at a time, (ii) Do not go
outside the three pillar places of A, B, and C, (iii) Do not
put a disk over a smaller disk.

(a)

(b)

Fig. 6 The images of “Tower of Hanoi” problem that areparts of the motion video made by Blender. (a) Initialstate when the number of disks n=5. From the left end,
we call three pillar places as A, B, and C. (b) The smallest
disk at A is moved from A to C, and the next small disk
is on the way to move out from A

Fig.7 Equivalent moving pattern between the case of ndisks and the case of two disks in Tower of Hanoi
problem to optimally move n disks (n ≧3) from the place
A to C using the place B, where the set of n disks isdivided into two parts: upper part (n-1 disks) and thelowest part (the bottom largest disk). (a)Initial state. (b)and (c) The turning point when the upper part (a set of n1 disks) is moved from A to B, and then largest disk left
at A can be moved to C. (d) After the upper part is moved
from B to C, the problem is solved

For making the recursive program to solve the problem
in the general case of n disks, based on the ETTviewpoint, we note that there is a consistent pattern of
disk moving that appears clearly when the number ofdisks n=2.
That is, the moving pattern when the number of disks
n=2 is equivalent to that one in the case if we divide ndisks into two parts: upper part (n-1 disks) and the lowest
part (the bottom largest disk).

Then, if we let T(n, S, W, D) represent a procedure of
the “Tower of Hanoi” problem to move n disks from thestart place S to destination D using workplace W, we
obtain the following symbolic formulation as a recursive
procedure, based on the equivalent moving pattern.
T(n, S, W, D) =T(n-1, S, D, W) + Move the largest of ndisks from S to D+ T(n-1, W, S, D).
The procedure T(n, S, W, D) is concretely described as
Hanoi_Tower(n As Integer, S As String, W As String, D
As String) by Excel VBA. Fig. 8 shows the program andthe execution results, where the disks are numbered inascending order of diameter.

Suppose when the largest disk can be moved from A(start place) to C (destination) under the abovementioned
constraints (Fig. 7). Firstly, we must move the upper part(n-1 disks) from the place A to B (workplace).
Secondary, the largest disk (=lowest part) can be moved
from A to C. This movement is the most important
turning point. After that, we can move the upper part (n1 disks) from B to C.

238

‘************************************Sub main_Tower_of_Hanoi()
Dim n As Integer, Input_n As String
Input_n = InputBox("The number of disks ?")n = Val(Input_n) '数字文字列を数値に変換
Call Hanoi_Tower(n, "A", "B", "C")End Sub=b( n)b(n) b(n -1) b(3) b(2)
⋅
⋅⋅⋅
⋅
=
⋅ b(1) 2nb(n -1) b(n - 2) b(2) b(1)Therefore, a(n)=b(n)-1=2n-1.
Then when n=4 and n=5, the numbers of steps are 15,
and 31, respectively.
The program that outputs the step number at each step
can be obtained by modifying the program in Fig. 8, asshown in Fig. 9.

‘***********************************Sub Hanoi_Tower(n As Integer, S As String, W As
String, D As String)'/*Move n-1 disks from "S" to "W" via "D."*/If n >= 2 Then
Call Hanoi_Tower(n - 1, S, D, W)
End IfDebug.Print "Move the top disk No. " & n & " : " & S& "→" & D & "."'/*Move n-1 disks from "W" to "D" via "S."*/
If n >= 2 Then
Call Hanoi_Tower(n - 1, W, S, D)
End IfEnd Sub‘*****************************(a)‘****************************************Sub modified_Tower_of_Hanoi()
Dim n As Integer, Input_n As String, step As Integer
step = 0
Input_n = InputBox("The number of disks ?")n = Val(Input_n)Call Hanoi_Tower_m(n, "A", "B", "C", step)
End Sub‘****************************************Sub Hanoi_Tower_m(n As Integer, S As String, W As String,
D As String, step As Integer)'Move n-1 disks from "S" to "W" via "D."If n >= 2 Then
Call Hanoi_Tower_m(n - 1, S, D, W, step)
End Ifstep = step + 1
Debug.Print " Step " & step & " Move the top disk No. " & n& " : " & S & "→" & D & "."'Move n-1 disks from "W" to "D" via "S."If n >= 2 Then
Call Hanoi_Tower_m(n - 1, W, S, D, step)
End IfEnd Sub‘****************************************
(a)

(b)

(c)

Fig. 8 Excel VBA program and its execution results for
the Tower of Hanoi. (a) The program lists. (b) Inputbox
where n=4 is input. (c) The output at immediate window
in the case n=4(b)

Fig.9. Modified Excel VBA program and its execution
results for Tower of Hanoi problem. (a) The modified
program lists. (b) The output at immediate window in thecase n=4.

The number of necessary steps a(n) to move n disks is
decided from the above algorithm in the followings.
a(n)=a(n-1) +1+a(n-1) =2a(n-1) +1 (n≧2), (a (1) =1).
Let b(n)=a(n)+1, then b(1) =2 and b(n)=2b(n-1). Then,
239

4.

Conference of Electronics, Information and Systems
Society, IEE of Japan, GS3-6, pp.1058-1062 (2022) (inJapanese)

Conclusion

In this paper, we have proposed a methodology for
integrated and comprehensive STEM education, basedon the viewpoint of ETT. Moreover, we have presented
some application examples of teaching way from theETT viewpoint, in order to show the usefulness.
We consider that the suitably combined presentation of
ETT viewpoint and visualization such as 3-DCG will be
more effective in the STEM education.

Authors Introduction
Dr. Tetsuo Hattori

He received the B.E. and M.E. degrees
in Electrical Engineering from
Doshisha University, Japan, and the
Ph.D. degree in Electronics &Information Engineering from Osaka
University, Japan. After he worked for
Toshiba Eng. Co. Ltd., he had beenwith Kagawa University from 1988 to2015. Currently, he is a Professor
Emeritus there. Member of IEEJ and IEEE.

References
1. Yeping Li, Ke Wang, Yu Xiao & Jeffrey E. Froyd,Research and trends in STEM education: a systematic
review of journal publications, International Journal of
STEM Education, Springer Open, Vol.7, No.11,
https://doi.org/10.1186/s40594-020-00207-6G (2020)
2. Fitzgerald, M. S., & Palincsar, A. S., Teaching practices
that support student sensemaking across grades anddisciplines: A conceptual review, Review of Research in
Education, Vol.43, pp.227–248(2019)
3. Kikuya Ichikawa, Science of Creativity, NHK Publishing(1970) (in Japanese)
4. Kikuya Ichikawa, Creative Engineering, Lattice Co., Ltd.
(1977) (in Japanese)
5. Hideki Yukawa, Leap to Creation, Kodansha (1968) (inJapanese)
6. Equivalent Transformation Creativity Society ed.,Equivalent transformation theory that can be understoodgraphically, NIKKAN KOGYO SHINBUNSHA (2005)(in Japanese)
7. Hikaru Matsuki, Hideaki Ogawa, Yasuaki Kajisha, A New
Movement on the Theory of Equivalent Transformal
Thinking, The Japanese Society for Artificial Intelligence,
Vol.22, No.3, pp.392-398 (2007) (in Japanese).
8. Takeo HARUYAM, A Study on the Technology and Skill
Transfer from the Creative Engineering Point of View,
Journal of Japan Society for Production Management,
Vol.15, No.1, pp.1-6 (2008) (in Japanese)
9. Tetsuo Hattori, Rikiya Masuda, Yoshio Moritoh, Yoshiro
Imai, Yusuke Kawakami, Takeshi Tanaka, Utilization ofBoth Free 3DCG Software “Blender” and 3D Printing for
Early STEM Education, Proc. of IEEE TALE2020 (AnInternational Conference on Engineering, Technology and
Education), ISBN 978-1-7281-6942-2, pp.971-974 (2020)
10. Tetsuo Hattori, Rikiya Masuda, Toshihiro Hayashi,
Yoshiro Imai, Yoshio Moritoh, Yusuke Kawakami,
Takeshi Tanaka, A STEM Education Method Utilizing
3DCG Software Blender, Proc. of the Sixth International
Conference on Electronics and Software Science(ICESS2020), ISBN978-1-941968-62-8, The Society of
Digital Information and Wireless Communications(SDIWC), pp.38-43 (2020)
11. Tetsuo Hattori, Asako Ohno, Yoshiro Imai, Yusuke
Kawakami, Katsunori Shimohara, Takeshi Tanaka:“Creativity Oriented STEM Education Utilizing
Equivalent Transformation Thinking Theory and Dynamic
Visualization Technology”, Proc. on 2022 Annual

Dr. Toshihiro Hayashi
He received the B.E., M.E., and Ph.D.
degrees in Information and System
Engineeringfrom
Tokushima
University, Japan, in 1989, 1991, and1994, respectively. Since July 2004, hehas been with Kagawa University, after
he worked at Saga University from April
1994 to June 2004. Currently, he is a
Professor at Kagawa University as the director of Integrated
Center for Informatics there.
Dr. Mai Hattori

Dr. Yoshiro Imai

She received the Ph.D. degree in
Medicine from Kagawa University,
Japan, in 2023. She is currently
engaged in the study on Education ofLife Science and Nutrition utilizingasaInformation
Technology
researcher of Integrated Center for
Informatics at Kagawa University.

He received the B.E. degree inInformation Engineering from Kyoto
University, Japan, in 1980, and Ph.D.
from Tokyo University of Agriculture
and Technology, Japan, in 2008. He had
been a professor at Kagawa University
until the end of March, 2021. Now he is
a Professor Emeritus there. His researchinterests include Computer Architecture and e-Learning
system Design, etc.

240Dr. Asako Ohno

She received the B.S. from Osaka
University of Foreign Studies in 2001.
She also received the M.S. and Ph.D.
degrees in Human Science from Kobe
University, in 2006 and 2009,
respectively. Currently, she is an
Associate Professor at Osaka Sangyo
University. Her research interests
include Intelligent Learning System, Learner Behavior
Analysis, Elementary Programming Education, etc.
Dr. Takeshi Tanaka
He received the B.E., M.E., and Ph.D.
degrees in Electrical and Material
Engineering from Hiroshima University,
Japan, in 1982, 1984, and 1990,
respectively. Currently, he is a Professor
at the Department of Electronics andComputer Engineering in Hiroshima
Institute of Technology. His researchinterests include Integrated Circuit Manufacturing,
Applications, and Education on Semiconductor, etc.

241