dynamic visualization method for effective education in … · 2019-12-25 · learning, therefore,...

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ISSN 0386-1678

Report of the Research Institute of Industrial Technology, Nihon UniversityNumber 94, 2008

* Professor, University Research Center, Nihon University** Professor, School of Social Information Studies, Otsuma Women’s University

Dynamic Visualization Method for Effective Education in Management Engineering

Makoto SUDO* and Hiroto NAMIHIRA**

( Received July 14, 2008 )

Abstract

In engineering fields, the teaching method has been used to teach individual facts, theorems, theoretical equations, phenomena, and other subjects, all of which are organized/arranged in a consistent manner, focusing on logical development and including the description of application methods, while holding respect for universality.

This can be said to prove the fact that there has been no effective teaching method by which students can obtain an understanding quickly in a way that is easy and appealing to them.

This paper presents a “Dynamic Visualization Method” that can represent apparently complex logical developments and theoretical equations on a computer as two-dimensional or three-dimensional visual im-ages that can be easily understood. This means that processes of developing a logical or theoretical sequence are represented as momentary changes in a sequentially responsive way to ensure that the qualia of the learner can be directly stimulated. It is believed that learners can easily understand logical and theoretical developments by following sequences of visual images and can also acquire application capabilities in relatively short periods of time.

This “dynamic visualization method” is already used for education in statistics, probability theory, linear algebra, algorithms, complex analysis, and other fields. This paper discusses the application of the method to management engineering. The application of this method to management engineering is expected to ensure efficient education for production control, quality control, stock and procurement management, process management, and others and to cultivate learners’ further interest and deepen their understanding.

Keywords: Effective Education, Dynamic Visualization Method, Qualia, Management engineering

Makoto SUDO and Hiroto NAMIHIRA

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tion to be learned.(1) The teaching method is primarily intended to

communicate procedures for reaching solutions that are led by theoretical equations, not focusing on the communication of the essential mean-ing of the theoretical equations. In other words, education based on this teaching method is more like training.

The background of this teaching method can be presumed to come from a strong belief that educa-tion would be orthodox if it respects universality and reasonableness as in the case of the method-ology of general science and seeks comprehen-sion achieved though reasoning with the aid of mathematical equations or similar means.

(2) When a complex theory is explained, it is implic-itly assumed that the learners have basic knowl-edge. In most cases, however, this assumption does not hold true due to the tremendous changes in the educational environment.

(3) The procedure of teaching a complex theory consists of explaining each of the components that comprise the entire theory and then inte-grating the statement about each component to help comprehend the entirety. Unfortunately, if learners receive explanation about components without understanding the entirety, they can still be ignorant of the entire theory when they try to integrate the explanations of the components.

(4) In the high school and earlier school stages, the purpose of learning is to pass entrance ex-aminations. Learning, therefore, is the same as remembering.

(5) On the part of educators, efforts made to compen-sate for abstractiveness of theories are insufficient. Completed theories are the result of summarizing, closely examining, and formulating cores that are extracts from a large number of experiences. Therefore, theories are abstractive in essence. Anything abstractive is difficult to understand. Theories should be taught effectively by way of careful explanation that allows students to link the theory being taught to specific events or senses familiar to them.

The above issues are essential to the traditional education/teaching methods. It can be said that their

1. Introduction

Nobody would agree that today’s education method is satisfactory.

As far as engineering fields are concerned, nobody would object that efforts should be made for building an innovative-technology-oriented country in Japan where natural resources are insufficient. When envisioning the coming society, we can see days of more rigorous changes than ever and always encounter new phenom-ena that are based on structures different from those encountered in the past. When attempting to deal with these situations, people will notice that mere experi-ences and memories of theirs are of little use and that only the power of thinking by themselves is of help. When people are confronted with unfamiliar theoreti-cal equations or theoretical developments and want to find underlying problems or structures, they need to have the power of inferring “what might cause this” or presenting hypotheses, or creativity. This creativity requires “profound understanding” of things that are the starting point of thinking.

Especially, during the period from the end of the 20th century to the beginning of the 21st century, society has greatly demanded innovation in information technology and education. At present, global standardization has been accelerating. In this circumstance, the fostering of creative human resources who will be active in IT society is an urgent national project.

Unfortunately, it has always been pointed out in Japan that students are lower in academic performance than ever and are less interested in scholarship. It is very doubtful that the teaching method used so far can meet the demands of the coming days. It seems necessary to develop a new high-quality, elaborate teaching method that can encourage learners to further their interest and lead them to a deeper understanding.

2. Questions about traditional teaching methods

The teaching methods that are discussed here are lim-ited to those used to teach students theoretical content in engineering, science, mathematics, or other scholarship at universities or other educational institutions. The discussion focuses on issues involved in the traditional teaching method or in the communication of informa-


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combination represents the functional incompetence of the traditional education/teaching methods.

3. Consideration on understanding

What is considered here is “what is understanding,” which seems to be a trivial question.

When we “do not understand,” we well know what condition we are in. In contrast, it is extremely difficult to answer when directly asked what condition you are in when you “understand.”

Empirically, we feel that we “understand” when we receive an explanation that is composed of concepts comprehensible to us. That is to say, our understanding of a thing is the positioning of the thing in the coordinate system built around us. The meaning of an object is the value measured in the respective coordinate system. Therefore, “understanding” is considered as a subjective experience. From this viewpoint, communication is ef-fective if it directly appeals to “Qualia”. It is difficult to use verbal communication for qualia, such as “beautiful west sky aglow with the setting sun.” However, what a person actually senses is qualia that are only felt by that person, representing a meaning/understanding that belongs to him/her.

The traditional teaching method that is currently in use is to communicate knowledge by way of language, mathematical equations, theoretical formulas, logical

expressions, and other forms. It is considered that such formal communication is followed by the digesting of intake content into what belongs to the learner (subjec-tive understanding/meaning). It is presumed that a high barrier is involved in conversion from formal under-standing to subjective understanding (actual sense).

It is generally said that understanding advances in the direction from individual to universal notions. This means that it is reasonable to begin with understanding of individual notions with meanings specific to individ-ual people and proceed to understanding of abstractive universal notions. To seek effective information com-munication methods, therefore, we should recognize that the direction of traditional education method that respects universality and begins with formal knowledge is opposite to the desirable direction.

An example is used below for explanation.Fig. 1 is a visualized representation of a 2-dimen-

sional probability distribution. It shows how the output changes sequentially in response to input changes. If teaching only relies on explanation or discussion using the formal equation (1), it is very doubtful whether what is intended to be taught can be communicated in an effective, appealing way.

yyxx

yyxx

e

1

2221

1211

212/1

2221

1211

21

(1)

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Fig. 1 Visualization of 2 dimensional probability distribution


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4. Proposal of a teaching method focusing on communication of meaning

The reason why explanations using analogies are understandable is that the background context is com-prehensible to both the teacher and the learner. It should also be noted that the understanding of meanings, as it is noticed here, proceeds visually in the context.

When teaching one thing, it is therefore important to begin with sharing the meaning of the content (context) between the teacher and the learner. The sharing of the meaning of content can be considered as the formation of a field in which information will be communicated.

When we want to communicate a meaning efficiently in a short period of time, we can easily come up with use of the visual sense, which can deal with media with large amounts of information. Therefore, this chapter begins with considering the characteristics of the visual sense and proceeds to the proposal of building a new teaching method while looking into IT technologies, which are the infrastructure of modern society.

4.1 Characteristics of the visual sense

The visual sense handles and processes enormous amounts of information when compared with the other four senses. The characteristics of the visual sense are considered below.

The generally conceived characteristics of the visual sense are as follows:

(1) Detect unified patterns from different objects(2) Detect regularity, symmetry, and simple elements

from figures(3) Detect simplicity from complex objects(4) Sense the second derivatives of intensity and

strength functions in a way sensitive to changes (see Fig. 2).

The Kanizsa triangle shown in Fig. 2 is a famous optical illusion. The arrangement of notched circles (Pacman figures) produces visual extraction of contours, edges, and boundaries to the effect that a triangle that does not physically exists appears as if it had boundaries determined by a subjective contour (Mach band), with an illusionary brightness that is higher than the actual brightness.

The combination of these characteristics suggests

that visual processing works to help extract meanings from figures and pictures.

4.2 IT technologies

We are tempted to think that people think freely. Actually, people, when thinking, are strongly bound by the thinking frameworks that prevail in their age. These thinking frameworks depend on the latest technologies that are available in the age.

The present time is the age of exploding computer technology. Extensive efforts are being made for e-learning, which is an education/learning method that, using information and communication technologies, is offered by virtual universities built on the Internet. However, the use of IT technologies as an effective method for communicating information content is still insufficient. It is necessary to create a new commu-nication method that takes the greatest advantage of computers and to print human wisdom onto IT. This may lead to the possibility of a breakthrough.

4.3 Proposal of a new education method (Dynamic Visualization Method)

Based on the discussion above, the author proposes a new education/teaching method (dynamic visualiza-tion method) characterized by the following purpose, methodology, and functions:Purpose: Provide an education that allows the es-

sence of logical content to be communi-cated as images directly to the qualia of learners in a way to move the learners.

Fig. 2 Kanizsa triangle


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Methodology: Dynamically visualize logical content using computer technology. Logic is considered as a driving action to change a given initial status to a final status. That part of a logical status which rep-resents the meaning is expressed on the computer in a two-dimensional or three-dimensional way. Status changes that follow logical development are calcu-lated by the computer, the results being projected on the screen. This enables the learners to visually understand the logical development on the computer.

Functions: Momentary communication of meanings (sharing of concept prior to explana-tion).

Pseudo-experience (automatic genera-tion of this and that cases)

What-if support (possibility of support-ing creative development)

The above is illustrated as follows (See Fig. 3):The proposed methodology is explained below using

an example in which the methodology is applied to prin-cipal component analysis, which is a typical analysis technique in the field of multivariate analysis. Principal component analysis is a statistical structure analysis method by which given multivariate statistical data is analyzed to detect a structure (component) hidden in the data to ensure that the detected new structure will be used to re-interpret the entirety. The traditional sequence

in which this method is explained is as follows:(1) Formulation of the sum of the squares of distances

between multivariate data and a single straight line

(2) Deriving of the formula for obtaining the mini-mum of the sum of squares

(3) Calculation of the variance and covariance of multivariate data

(4) Explanation of eigenvalue problem with vari-ance-covariance matrix

(5) Explanation of eigenvalue solutions and engen-vectors

(6) Explanation of the contribution of the principal component using eigenvalues

The level of knowledge considered as prerequisite to understanding explanation in each stage is so high that it is not a practical precondition for most learners. Even though learners manage to understand the mathematical equations, it is doubtful that the underlying philosophy of principal component analysis can be correctly com-municated to learners.

The essence of principal component analysis lies in looking at multivariate data to find the direction in which the data is best organized and interpreting the meaning of the detected direction. Therefore, the projection of data that is seen from an arbitrary viewpoint is visualized to show how data variations relate to the direction of the chosen viewpoint. In the final stage, the direction in which the variation on the projection is the mini-mum is identified as the principal component direction

Automatic generation Logic: Drive ruleof initial status

Change Finalstatus

Visualizationof status

Initialstatus

Drive rule Drive rule

Computer

Visualizationof

initial status

Visualizationof

mid-way status

Visualizationof

final status

Visualizationof

initial status

Visualizationof

mid-way status

Visualizationof

final status

Fig. 3 Dynamic visualization of logic


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(eigenvector). This enables learners to understand the physical meaning of the principal component intuitively. Fig. 4 is a visualization of generated data. Fig. 5 shows the data and variance viewed in an arbitrary direction. Fig. 6 shows the variance of the data as viewed in the direction of the principal component. It helps learners understand that this variance is smaller than the variance of data viewed in any other direction. Fig. 7 shows data that is structured based on the principal component. These visualizations make it possible to communicate the essence of the principal component in multivariate data accurately in a short period of time without using mathematical equations. If the exact procedure is ex-

plained after the meaning of the entirety is successfully communicated, the learners can obtain a bird’s-eye view on how each part relates to the entirety. Very high educational effects are thus produced.

The proposed methodology has begun to be applied in various fields, including statistics, stochastic calculus, linear algebra, algorithms, and complex analysis and track records have begun to be collected.

5. Examples of application to management engineering and other various fields

Since management engineering deals with extremely diversified subjects, learners need to familiarize them-selves with a wide range of basic knowledge before entering the stage of learning expertise. This chapter presents examples of dynamic visualization as applied to probability theory, statistics, stochastic processes, multivariate analysis, linear algebra, algorithms, and others, followed by examples of dynamic visualization as applied to management engineering.

Fig. 8 is a visualization of the Poisson distribution represented by equation (2).

　

eX

Px

!)X(

(2)

This figure visually shows that a Poisson distribution is closely linked with randomness. Learners can have

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Fig. 4 Visualization of data

Fig. 5 Visualization of data and variance viewed in an arbitrary direction


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�

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Fig. 8 Visualization of the Poisson distribution

Fig. 7 Structured dataFig. 6 Variance as viewed in the principal component direction


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pseudo-experience in comparing the theoretical prob-ability and actual frequency of a specified event.

Fig. 9 is a visualization of the binary distribution represented by equation (3).

pqqpxnx

nqpxn

xP xnxxnx

1,)!(!

!)( )(

(3)

The essence of a binary distribution generated is repre-sented by moving balls. A successful try moves the ball

down, whereas a failed try moves the ball right down. Therefore, the occurrence count is represented by the amount of right movement.

Fig. 10 is a visualization of the chi-square distribu-tion represented by equation (4).

(4)

2/12/22/

2 2

)()2/(2

1)(

e

nf n

nn

)1,0(222

21

2 Nxxxx in

��

� � � � � � ��

��

��

��

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��

Fig. 10 Visualization of the chi-square distribution

Fig. 9 Visualization of the binary distribution


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Fig. 12 Visualization of the random walk

Fig. 11 Visualization of the test theory

A chi-square distribution indicates how the variance calculated from n variables is accurate. This distribu-tion is included in the fundamentals of small-sample statistics. The figure shows the theoretical distribution for a given n, the confidence interval, and the result from a 1000-try experiment.

Fig. 11 is a visualization of the test theory repre-sented by equation (5).

(5)

1{

}/

{

H

thenn

xif

is given significance level of α％｝

This figure visually shows the rejection region and test

result for given arbitrary data and test conditions as well as a given significance level.

Fig. 12 is a visualization of the random walk theory represented by equation (6).

4/)}1,()1,(),1(),1({),( jixjixyixyixjix

(6)

The left figure shows a random walk process that begins with the origin. The move shown here appears incomprehensible. The right figure shows a plot of the final result from 1000 steps. It suggests a normal dis-tribution about the origin, visually showing the essence of a random walk.


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Fig. 15 Visualization of the vector projection in linear algebra

Fig. 14 Visualization of a branching process

Fig. 13 Visualization of the probability integral

Fig. 13 is a visualization of the probability integral represented by equation (7). g (x) is a given arbitrary function and B(x) is a Wiener process.

(7))]

21()

2()[

2(lim

)()()(

2

1

0

tkBtkBtkg

xdBxggI

nnk

nn

t

n

Fig. 14 is a visualization of a branching process. A branching process is a process in which how the offspring will increase is determined stochastically.

Fig. 15 is a visualization of the vector projection in linear algebra represented by equation (8).

210 xxbcbcba

(8)

This figure visually shows how an arbitrary vector is decomposed into specified components.

Fig. 16 is a visualization of the quadratic form rep-resented by equation (9).

(9)

yx

aaaa

yxz2221

1211)(


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Quadratic forms are important forms used when handling maxima/minima of functions. Whether or not the quadratic form is always positive determines the nature of the maximum/minimum.

It can be demonstrated that these visualizations enable learners to learn momentarily what could not be communicated without difficulty if the traditional teaching method were used. A quantitative assessment

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Fig. 16 Quadratic form

of the educational effects has revealed that twice the number of items that could be taught in a given period of time with the traditional method can be taught with the new teaching method.

Presented below are examples of application to cer-tain aspects of management engineering. Fig. 17 is a visualization of a periodic replenishment system used for inventory management. It is possible to specify a de-

Fig. 17 Periodic replenishment system


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mand distribution, a replenish cycle, a delivery period, and a service rate arbitrarily. The demand distribution over the pertinent lead time and the standard stock that should be held are displayed.

Fig. 18 is a visualization of a PERT chart. When the numbers of vertical and horizontal nodes are specified, a weighted graph is automatically created. This is fol-lowed by the visualization of the process for calculating

the earliest and latest dates and the critical path.Fig. 19 is a visualization of the multiple regression

analysis represented by equation (10).

YXXX tt 1)(ˆ

(10)

The data is automatically generated and the appropriate corresponding regression plane is displayed. When an (x, y) value is specified with a click at the pertinent

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Fig. 19 Visualization of the multiple analysis

Fig. 18 Visualization of PERT chart


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point on the plane, the corresponding predicted value is displayed.

Fig. 20 is a visualization of a Buffon’s needle simula-tion.

The purpose of the methodology discussed above is to communicate the meaning of a piece of content in a simple way. People can easily feel that the effects of the methodology are significant. However, there is another problem that numerical assessment of communication of meanings is extremely difficult.

6. Conclusion

This paper has proposed an effective teaching method that, unlike traditional teaching methods which respect formal knowledge, begins with communicating what is meant as an imagination by stimulating the qualia of

the learner with the target of learning in a short period of time in a way that is appealing to the learner. This method has been implemented as dynamic visualization using computer technology. The paper also includes examples of application to education in typical basic scientific fields as well as the management engineering field.

This methodology can be applied to any level of learners, including students of all schools, from el-ementary school to graduate school, and workers. Since this method and its ripple effect make it possible to quickly teach what could not be communicated with traditional methods, it is expected to help solve the cur-rent problems in science and technology education, such as students’ reluctance to study science and technology and deterioration of thinking and creative power.

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Fig. 20 Visualization of Buffon’s needle simulation


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References

1) Hiroto Namihira: “Introduction to Use of Dynamic Visualization for Statistics,” JUSE Press. Ltd. 2005.2

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動的視覚化法（Dynamic Visualization Method）によるマネジメント工学の効果的教育

須藤　　誠，浪平　博人

概　　要

工学的専門分野における現在の教育法は，個々の事実，定理，理論式，現象などを統一的に整理し，論理的展開による解説や応用の方法などについて，普遍性をもって教えてきたといえる。しかしながら，それらを学生に効率よく，解り易く，印象的に，短時間の内に理解させさせるには，特効的な教授法が無かった，といっても過言で無い。　本論文は，一見複雑な論理展開や理論式を『動的視覚化技法：Dynamic Visualization Method』を取り入れることによって，コンピュータ上に，２次元或は３次元的に視覚的イメージとして，解り易く表現するものである。即ち，論理や理論式の展開過程を瞬間的変化として，逐次応答的に表現し，学生の『クオリア＝生の感覚』へと直接伝達できる教授手法を論文としたものである。従って，学ぶものにとっては，論理や理論式の展開が視覚的イメージを通して容易く理解でき，応用力も比較的早く身に付くと思われる。この『動的視覚化法』について，統計学，確率論，線形代数，アルゴリズム，複素関数論などに活用範囲を展開しているが，本論文はマネジメント工学への応用を述べるものである。この手法をマネジメント工学に応用することによって，例えば，生産管理，品質管理，在庫・調達管理，工程管理などへの効率的な教授法が期待でき，“学ぶものの興味を引き出し，深い理解に導く”ことができると思われる。

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Biographical Sketches of the Authors

Makoto SUDO is professor of University Research Center, Nihon University. He was born in Tokyo on 1945. He received his degrees of B. Eng. in 1967, M. Eng. in 1969 and Dr Eng. in 2002 from Nihon University. He has the titles of two Professional engineers, two APEC engineers, Architect and so on. He has published more than 70 practical and academic papers on the most leading design and construction technologies in the field of civil engineering. He was senior engineer and board member of Japanese consultant companies, engineering maker, and joint concerns with France, Korea, Taiwan and China.

He is a member of JSEE, JSCE, IPEJ, JFoA, IDIJ and so on. His specialty is civil engineering and architect engineering of PC structures and overseas plant constructions, project management of engineering and dynamic visualization method of logic.

Hiroto NAMIHIRA is professor of Faculty of Social Information of Otsuma Women’s University. He was born in 1942. He graduated from Department of Engineering, Yamaguchi University, 1964. He was engaged in development of software on system of manufacturing for technical calculation, production, selling and stock in Bridgestone Tire Co., Ltd., during 1964 to1985. Since then, he was professor of Junior College, The SANNO Institute of Management, during 1985 to 1998. He received his degrees of Dr. Eng. in 2002 from Tokai University. He has the titles of Professional engineer on information processing. He has published 10 practical and academic books on algorithm, C++, technology of information on expression and so on.

He is a member of JSEE, JIMA, ORSJ and IPSJ. His specialty is industrial engineering and management, development of software and programming languages, and dynamic visualization method of logic.

dynamic visualization method for effective education in … · 2019-12-25 · learning, therefore,...

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