Fostering Widespread Computer-Related Innovation

by Allen Klinger

Computer Science and Engineering

University of California Los Angeles

Los Angeles, California 90095-1596

310 825-7695

<klinger@cs.ucla.edu>

Overview

This paper concerns training a knowledgeable work force to ensure maximum economic benefit from computer and information technology. America's unique strength, readiness to accept non-traditional approaches to real problems, can be threatened by trends in computer technology and education. Governmental support for technology-training/support can preserve and advance our overall international competitiveness.

Computers and new information-handling modes are widespread factors for increased efficiency. These technologies support high productivity and world-market competitiveness. Yet there are major deficiencies in the computerization of key populations. Access to knowledge-centered employment is education-limited. And schools offer widely-different experiences to students depending on the computing and communications infrastructure present, and their teachers' level of familiarity with current information technology. Three concrete suggestions to deal with this appear in the section titled Conceptual Underpinnings.

The central issue for government research investment is where to place funding to have the greatest possible leverage. This paper asserts that the way to have major impact is to trade on two strengths: 1) the great willingness to accept technical gadgetry and the implicit acceptance of changes in ways to work present in most Americans; and, 2) the multiethnic nature of U.S. society. The U.S. entertainment industry is a model of both aspects: it also can be used as a driving force in establishing strong economic-incentive motivations for technology-dissemination. This industry has set standards and preserved a world-lead through use of high technology. Likewise it has pioneered in addressing the multi-ethnic nature of life in the U.S.A., as well as the world. Further, like other U.S.-industries, e.g., transportation, communication, it has led a process of world-wide-change that continues today.

The focus of this paper is on three main areas where government investment in technology research can have significant impact:

1. Realistic Technology Expectations for 2000 and Beyond

2. Future Federal Information and Communications Research and Development Applications

3. Strategic Focus Areas for Information and Communications

Technology Expectations and Possible Benefits

The theme of this section is that government can and should accelerate the positive economic impact from using computer technology. We believe this can occur by funding research and development modes to widen or deepen knowledge of computer information tools. This section addresses two main fronts in dealing with computer technology. Both involve the technical knowledge of our citizenry. The first is associated with the process of innovation. The second is directed to managing/applying new technical tools.

As computers move out into society their effective use becomes a necessary part of business success. They've changed communication style and substance, accelerating the reshaping of corporations, promoting unstructured in place of hierarchical organizational form. The positive aspect of this involves increased democratization. Information is widely available. More individuals can use it because of computer networks. Expecting the average employee to be information-knowledgeable or information-ready is not realistic today. Yet this is something that many organizations actively seek or promote by in-house training. We can ask the question differently: "What is it that Federal Information and Communication Research and Development should fund in order to make information technology easily absorbed either by new trainee employees or students in schools?"

Increasing the capability of those people lacking fundamental technical skill is a realistic technology objective for 2000 and beyond. Adapting to phone-answering, automatic teller, and video-cassette-recorder technologies has been a process of mutual accommodation. Analogously, future technology objectives should be to keep tools evolving in a direction that makes them easier to use with less prior technical training, a process already well underway in domains such as electronic mail and world-wide-web-browsing. There are many economic, political and social aspects of widening computer-mediated information-access. Hence it is essential that the government support research oriented to broadening the base of skilled users. The July 8, 1995 L.A. Times gives a very low estimate of the percentage of our population able to `surf the net' productively [1]. This activity already is, or soon is going to be, an aspect of literacy. Today we assume that most people can read (and write) but the skill was only possessed by kings and specialists a few hundred years ago [1]. Another aspect of this is the need to deepen search-results' quality. This is essential to obtain maximum benefit from interconnected computer knowledge and data base systems.

The varied ways this can be achieved include using mass media: information-ability driving game rewards, creation of something like a knowledge super bowl. Economic reward could also be placed behind efforts like tutorial book publishing: whenever a tool posted on the internet or world-wide-web reaches a certain level of acceptability (as indicated, e.g., by number of times individuals access a web page), it could be funded for refinement and improvement. Another approach could award a prize to the developer, upgrade a person's eligibility for a competition, or begin involvement in a desirable activity or membership. See the section on Conceptual Underpinnings for additional approaches.

Creating new forms of visual communication provides the most logical domain for exploiting information technology in a deepening sense (i.e., maintaining/advancing technical capability). In [2] there are examples of technology being redirected to meet the needs of individuals (Freestyle system for annotating digital files; Apple Corp. Newton handwriting recognition system). Both handwriting and the idea behind Intuit's Quicken checkbook- interface financial-software are essentially visual communication tools. Research should focus on visual communication since it is at the center of Manufacturing and Civil/Mechanical Engineering processes.

Future Applications

This section deals with governmental influence causing products to be created. We present two scenarios. In each, specific information and communication research applications can be caused to occur by funding research and development. If created these applications would enable new computer information tools to be in the hands of diverse communities of specialists. Further, the central issue faced here, the use of the visual capability in design and in reasoning, could lead to new fundamental knowledge and/or novel means for inter-language communication.

A very reasonable assumption is that in five or ten years new computer products will be based on solid-models displayed via high-resolution graphics. Such a universe of novel solid shapes could have extensive economic impact. Federal research and development funding could guide this in several ways. First, the fundamental link between visual imagination and product innovation, invention, and scientific abstraction [3] could be supported. Research support for computer-graphics, solid-models, and display concepts could focus on creating virtual reality design tools. This would have value as a new dynamic visual medium enabling designers to conceive of products. It also has product development potential in entertainment and in education. Finally, this conceivably could be the cornerstone of a new and potentially universal human language based on images.

Computer innovations and research and development steps toward products could support interdiction efforts in several domains. A few are anti-submarine warfare, counter-terrorism, medical intervention, and international contraband shipment including narcotics. Computer applications could simultaneously present multiple kinds of information. They could involve visual solid-displays. This might enable a human to get the sense of a general situation involving spatial or spatial-temporal information variation. Such tools would be highly valuable to photo-interpreters, forensic specialists, plastic surgeons, radiologists, and many other medical service-providers.

The underlying technology would be computer-assisted human visual capability. In teaching mathematics to the many, fundamental areas are generally ignored today: neither logarithms nor spherical geometry are new or in ... but they are a part of the underpinnings of many aspects of reasoning. Likewise they offer opportunity for gaining conceptual insight. Both are central to diverse domains. Logarithms apply to measures of audible sound (decibels) and earthquake intensities (Richter scale). Travel on the seas and in space involves non-planar geometry. Each of these practical areas is best approached through visual means based on mathematical knowledge. Yet today they both are arcane, not fundamental, in terms of the school curriculum and the general understanding of the U.S. population. Conceptually they are generally as ill-understood as the quadrature of the lune (area of the visible segment of a partially-obscured moon) and Isaac Newton's first step toward fame [4]. Both are past accomplishments that aren't understood by most people today. Likewise, both involve mathematical fundamentals generally ignored, that depend intrinsically on a visual idea. The same sort of thing is present in great depth in the collection of proofs without words [5]. There is a fundamental opportunity present in creating new visual tools and procedures since it is possible to state things that can be proven most easily by some form of visual reasoning. For two examples consider the request to assign all of nine whole apples to four baskets so that an odd number is in each, and how it is resolved by visual means in appendix Figure A. Another instance of visual reasoning depends on a general statement, taken from a computer science text: the Greeks knew that any cube can be decomposed into the sum of adjacent odd numbers. Appendix Figure B visually displays two examples, 8 = 5 + 3 and 27 = 11 + 9 + 7 . Without the visual clues it is difficult to understand which odd numbers add up to 125 or 729. However the two Figure B images quickly lead to a general rule indicating how to list the odd numerals comprising these cubes, or any number that is an integer to the third power.

The visual use of computers also has potential for creating novel means for inter-language communication. This is so because of the diversity of alphabets in the world, and the pictorial nature of written Chinese. Considering the size of the Chinese population a useful realistic computer product could be based on animating selected Chinese ideographs and then morphing them into alphabetic strings. Strange as that may seem, it is only a bit more venturesome than appendix Figure C about cancellation rules, and the number-spatial speculations of Albrecht Durer and Benjamin Franklin displayed in appendix Figure D. To see what can be done with widely-available computer tools, view the appendix Figure E.

Strategic Focus Areas

The three strategic focus areas I see are:

1. Information Access
2. Visual Models
3. Fundamental Knowledge and Technical Readiness

The information access area constitutes data bases, computer networks, encyclopedias, the world-wide-web, auditory/visual/text interactions, and the implications of hyper-text. Items in this domain are evolving rapidly and are essentially unbounded. They constitute a new formulation of all of human knowledge.

Visual models are at the breakout stage. They are increasingly heavily used in entertainment and a solid tool for physical scientists. Yet their use by the general community and by some specialists who need them is just beginning.

Fundamental knowledge is at a stage of reformulation. Whether chaos, fractals, the nature of proof, string theory, the double-helix, science moves forward in novel and unpredictable ways. Models from the past are supplemented or replaced. Works such as [3-5] point to the importance of visual reasoning. Computers make it possible to generate synthetic landscapes by fractals; tools such as [6], and many graphing hand calculators, place powerful tools in the hands of almost anyone. Appendix Figure F shows a visual use of one computer tool.

All three areas are strongly changed by rapidly-evolving computer technology. Rethinking the educational curriculum of the mathematical field to support needed computer information skills is a fundamental issue. A reasonable goal could be to ensure access to mathematics to anyone with the general interest. If we created the infrastructure, e.g., by a CD-ROM library of self-paced learning, we could foster support for learning/adapting to computer technology. This is one realistic way to address ensuring that computerization has a positive effect on quality of life. Broad popular acceptance of computer technology needs to be supported with governmental investment to enable the widest possible use of the associated tools, and the growing and deepening appreciation of exactly what these systems can deliver.

Conceptual Underpinnings

Mathematics stands in a uniquely responsible position because it is a kind of educational pillar. It provides the language and the tools for many science and engineering topics. It also has evolved from the observations of artisans and ordinary people, and today stands as an entry point of sorts into computer technology. Overcoming and eliminating mathematical anxiety is in our overall national interest. This is especially critical with regard to central city, minority, or immigrant-dominated schools. Stress on strongly visual aspects of mathematics can make the subject an entry-point into educational accomplishment for those not speaking majority-American-English. However, this requires for support for reorienting the field of mathematics, at least in primary-school grades. This is something that can be done at lower cost because of computers. Widespread use of computer technology in the better-supported aspects of society provides an important reason to consider a national effort to handle mathematics-fear/anxiety, especially for groups that now have high school dropout rates, or in other ways show inability to join the information revolution.

Pervasive computing means much more than the widespread availability of digital technology. It signifies the presence of computing, specifically digital circuitry, within virtually every manufactured item, but especially automobiles, microwave ovens, clocks, and diverse communication devices. Clearly computers also support conveniences like word processors, spreadsheets, and communication services such as electronic mail. They're deeper familiarity needs an intellectual and sympathetic start. One possible place in the educational system to get such a start is provided by mathematics ... if it is taught connected to art; to artisan skills; and to history. This need not be difficult, e.g., our founding fathers include the first president, George Washington, who was a surveyor, but it cannot be done without explicitly addressing the fears of teachers, who usually are themselves uncomfortable with mathematical knowledge.

Many students have become mathematics-avoiders in grade school. Even technically-trained individuals may find some junior high school level mathematics concepts more than they want to handle. Still there is an easy way to reach these people. By combining games with concepts, entertainment can support education. Children exposed to an hierarchy of games, each based on a mathematics idea, will be able to use their positive play experience to stay committed to learning there and in computing. The depth of the mathematics-avoidance problem is displayed in appendix Figure G, based on a survey conducted by the author at UCLA among students not oriented to science, engineering nor mathematics, but in the upper eighth of all California high school graduates.

Although the material of mathematics is important, it is not all-important. Most computing technology is developed apart from the basic framework of mathematics or even of logic. The variety within any field, and certainly within mathematics, makes it reasonable to consider the opportunity within the information and communication area for making access to ideas more widely available. The information available on networked computers is already vast and diverse, yet there are several related issues that must be dealt with to derive substantial economic benefit from its existence. The key issue is extending its formal-availability so that it assists those with aversion to school-structured knowledge, particularly in fields such as mathematics. The key issues are: encouraging information use, assuring information validity, and measuring information-capability or fundamental knowledge acquired.

There is general awareness that some parts of mathematics have become more important and others have faded. Twice, first after Sputnik, mathematical school curricula revision took place. In both cases the effort expended was substantial ... and the results unsatisfying. In the latest effort the key document [7] presents suggestions for emphasis and de-emphasis, and samples of teaching models via problems students can address, for grades K-4, 5-8, and 9-12. Still computer information and communications technology offer a revolutionary new major revision in the approach, if we focus on the key issues and center the approach more closely on the students' achievements. Review of any part of [7] quickly reveals that there is a broad character to the material included. This suggests focus on authentication of student-learning.

For each of the key issues there is a starting-point concrete suggestion. For encouraging information use, already-successful volunteer-organization activities would give models of how to accomplish desired goals. In a phrase, the idea is that there should be an information- access merit-badge accomplishment-validation mechanism. Perhaps individuals who achieve special knowledge could be made eligible for internships or shorter visits at national laboratories where their ability could be used and enhanced. Even though the idea is related to the Boy Scouts of America system, the greatest value would be derived from linking this to the business world, not the volunteer-organizations. Individuals could be encouraged to provide prospective employers with lists of their validated information accomplishments.

Measuring capability in the information area could be an activity thrown open to professional societies or panels convened for the purpose of establishing national standards. The federal investment could be limited to establishing prizes for knowledge in key disciplines, such as mathematics, biology, computer science, physics, and history. Other disciplines could be added under regularly-held referenda, or via petitions from states or several professional societies. Attracting individuals to participate in the professional society or panel definition of the knowledge capability levels could be via making those who volunteer eligible for moderate-cost government sponsored programs, such as funding for research travel, sabbatical activity, etc.

Ensuring information validity is an activity analogous to professional journal peer review. It would be in our national interest if individuals interested in listing a body of information needed to have that material assessed by experts. The model of publication review would function equally well for validation and for tutorial merit. The regular academic faculty in institutions of higher learning should be encouraged to be part of a reviewing system for reorganizing knowledge. That is a valuable academic activity, and should be an essential part of the career of all educational professionals, even those in the elementary and secondary schools.

Conclusions

Access to information is economically important. Visual information offers practical applications and potential for refinement. Education in information should be at the center of strategies for dealing with disadvantaged communities. The nation needs all its diverse communities to be able to use information technology. New systems and lowered costs create an opportunity to provide computer and communications tools and knowledge more widely. We seek new solutions to address needs of rural, urban inner-city, immigrant, historically- under-represented-minority, elderly, and physically-challenged individuals.

Two primary barriers inhibit access to information technology and bear strongly on these groups of citizens. First, many people have no access to computer and communications hardware. Second, there is no means for providing people access to individuals with computer knowledge. Strategies to overcome these barriers need to include creation of a technology-access federal seed-money fund.

Existing community efforts can be coupled into the information and communication area. Encouraging philanthropic giving and parent-group financial participation is one possibility, while another involves sharing commonly-acquired technical resources. One approach to overcoming the lack of access to computer-skilled people could be to develop a tutorial service program. It could include stipends for college students enrolling as tutors, rewards to student-tutors for bringing individuals to pre-defined competence levels, and a greater pay- level for advanced work with people learning information skills.

The knowledge and trained people are available to meet the need for the scientific, engineering and mathematics communities to design an information-resource training program. One approach to such a program could be to use applied information-seeking as a basic module. Another could describe the fundamental knowledge in high-technology fields to define a basic set of standards in school subjects. Yet any such program must 1) stress rebuilding the prior connection to the artisan-discovers of much of the underlying knowledge; and, 2) ensure that amateurs are easily involved in information and communication.

Finally, there is a clear need for national leadership to create standards, foster creation of new educational material, and measure and validate achievement.

References

[1] Los Angeles Times, July 8, 1995, p. F-10: ... posted through the Internet on the World Wide Web (address: http://www.lacma.org/), which is used by less than 3% of the American population ... ; and, Clark, Kenneth, Civilisation: A Personal View, New York, Harper & Row , 1970, 1969, p.

[2] Klinger, Allen (ed.), Human-Machine Interactive Systems, New York: Plenum, 1991.

[3] Adams, James L., Conceptual Blockbusting, San Francisco : San Francisco Book Co., 1976; also, San Francisco, W. H. Freeman, 1974.

[4] Dunham, William, Journey Through Genius, The Great Theorems of Mathematics, NY: Wiley & Sons, 1990.

[5] Nelsen, Roger B., Proofs Without Words: Exercises in Visual Thinking, Washington, D. C.: Mathematical Association of America, 1993.

[6] [Computer program systems for Mathematics.] THEORIST 2, Maple V R3, Waterloo Maple Software, Waterloo, Ontario, Canada (E-Mail: info@maplesoft.com, World Wide Web: http//:www.maplesoft.com); Mathematica 2.2, Wolfram Research, Champaign, Illinois (E-Mail: info@wri.com, World Wide Web: http://www.wri.com); MATLAB, The MATH WORKS Inc., Natick, Mass. (E-Mail: info@mathworks.com).

[7] Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia, National Council of Teachers of Mathematics, 1989, 1992.

Appendix

This appendix is to present some supporting images. These are examples of items that can be used to explain the mathematics process, not the details. Reliance on visual reasoning and examples and connections with historical people can lead individuals to appreciation of mathematics and to receptivity to computer information-handling. Reliance on visual forms supports creating conceptual understanding. That is an essential aspect of enabling more individuals in our society to attempt computer-related innovation.

An extensive list of references presenting mathematics to a general non-science-oriented person, other books conveying the general historic, cultural and anthropological links involving the subject, and specialist items regarding visual proofs can be obtained by writing or sending email to the author of this paper at the address on the first page. Motivation for the figures and credit for portions of the visuals depends on the following two references, in addition to those already cited.

[A.1] Stark, Harold M., An Introduction to Number Theory, Cambridge, MA.: MIT Press, 1978, 1970.

[A.2] Andrews, William S., Magic Squares and Cubes, NY: Dover Publications, Inc., 1960, replica of Open Court Publishing Company, Second Edition, 1917.

1. Even and Odd

Example (Reasoning, Problem-Solving):

You are given nine apples and can't cut any. Put an odd number of apples in each of four baskets.

|_________|

|_________________________|

|_________________________|

|_________________________|

Figure A. A Solution Using Sets of Baskets - Grouping Is Allowed

Example (Reasoning, Visualizing):

Why can every cube be represented as a sum of consecutive odd numbers?

Figure B. Decomposing Two Cubes Into Sums of Consecutive Odd Numbers

2. Arithmetic Operations

Example (Reasoning, Problem-Solving): What numbers under a hundred satisfy strange cancellation? [One case is 19/95 = 1/5. In strange cancellation eliminate any digits that appear in both the numerator and the denominator.]

Figure C. Strange Cancellation (Karplus, informal communication.)

3. Graphical Reasoning

Example (Visualization, Problem-Solving With Computers): Display a fourteen-sided solid that has an equilateral triangle at its north pole, an opposite-pointing congruent equilateral triangle at its south pole, and a hexagonal perimeter at its equator.

Figure D. Tabular and Graphical Display (Mathematica)

Figure E. Two Views of a Tetradecahedron (Mathematica) Example (Reasoning, Problem-Solving): Construct a magic square with five rows and five columns.

Benjamin Franklin's Magic Square Construction Method

Classroom Experiment - Finite Mathematics Math 2 Winter 1995 - Allen Klinger, UCLA

General Students

UC admission criteria - all of top 1/8 of California high school graduates. Annually 1000 black students are UC-eligible in entire State of California.

Survey conducted 13 January 1995, administered to 47 students. Concerned their high-school-mathematics learning, used five questions.

Five Questions

1. a > b with each involving powers of 10,
2. 2 simultaneous equations in 2 unknowns,
3. a quadratic equation,
4. log to base 10, and
5. permuting 5 objects.

Result
Range between high 91 % and low 31 % with mean 69 % and standard deviation 16 %. Mean score would get an objective letter grade of D+ (at best C-) for knowledge.

On average two responses per person said I know nothing about this question. Students response Not in my high school! to Questions were just high school mathematics.

Over 4 % of responders said I know nothing to at least 4/5 of the questions. In other words, more than 1 in 25 knows essentially nothing about the questions.

Conclusion

High schools do not adequately cover key computer-related mathematics. Non-science-oriented portion of top 1/8 CA h.s. grads. know nothing about 2/5 of the questions.

Specifics

Math material coverage no longer includes logarithms due to hand calculators. Students fear calculator-use yet their arithmetic errors prevent gaining positive reinforcement.
Standard math. visual aides aren't effectively communicated to learners.
Cartesian coordinate x- and y-axis line intercepts.
Students had difficulty with 2 by 2 arrays' determinants.

Text and lecture stop short of the abstract idea. Book conveys excessive operation detail.

Figure F. Assessment of High-School-Level Mathematics Knowledge