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KNOWLEDGE AS

DESIGN

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KNOWLEDGE AS

DESIGN

D. N. Perkins

~ ~~o~~~;n~~~up NEW YORK AND LONDON

First Published by Lawrence Erlbaum Associates, Inc., Publishers 365 Broadway Hillsdale, New Jersey 07642

Transferred to Digital Printing 2009 by Routledge 270 Madison Ave, New York NY 10016 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN

Permission to reprint the following poems in Chapter 3 is gratefully acknowledged:

"The Span of Life" by Robert Frost, from The Poetry of Robert Frost, edited by Edward Connery Lathem. Copyright 1936 by Robert Frost. Copyright © 1964 by Lesley Frost Ballan- tine. Copyright © 1969 by Holt, Rinehart and Winston. Reprinted by permission of Henry Holt and Company, Inc.

"On the Vanity of Earthly Greatness" from Gaily the Troubadour by Arthur Guiterman, publisher E. P. Dutton, copyright 1936. Reprinted by permission of Lousie H. Sclove.

"My Papa's Waltz" by Theodore Roethke, from The Collected Poems of Theodore Roethke, copyright 1942 by Hearst Magazines, Inc., published by Doubleday & Company. Reprinted with permission of the publisher.

Illustrative completion of Theodore Roethke's "My Papa's Waltz" composed by John Ciardi, from How Does a Poem Mean? (Second Edition), p. 369, by John Ciardi and Miller Williams. Copyright © 1975 by Houghton Mifflin Company. Used by permission.

Copyright © 1986 by Lawrence Erlbaum Associates, Inc. All rights reserved. No part of this book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without the prior written permission of the publisher.

Library of Congress Cataloging in Publication Data

Perkins, D. N., 1942- Knowledge as design.

Bibliography: p. 1. Thought and thinking-Study and teaching.

2. Reasoning. 3. Knowledge, Theoryof. 4. Imagery (Psychology) 5. Pattern perception. 1. Title. LBI590.3.P47 1986 370.15'2 86-13596 ISBN 0-89859-839-7 ISBN 0-89859-863-X (pbk.)

Publisher's Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original may be apparent.

Fortunate in the teachers, formal and informal, that I have had, I dedicate this book to them

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Contents

ACKNOWLEDGMENTS xi

INTRODUCTION: THE GIVING AND GETTING OF KNOWLEDGE xiii

CHAPTER 1 KNOWLEDGE AS DESIGN

What is Design? 2 Knowledge as Information versus Knowledge as

Design 2 Four Design Questions 5 The Cutting Edge: An Example in Depth 9 The Theory of Natural Selection: A Second

Example in Depth 14 Knowledge as Design: The Arguments 18 Restoring Connections 21 What You Can Do 32

1

CHAPTER 2 DESIGN COLORED GLASSES 35

How to Recognize a Design 36 How to Deal with a NonDesign 39 How to Cope with an Abundance of Designs 40 How to Think about Everyday Inventions as

Designs 42 How to Cover Explanatory and Evaluative

Arguments 43 How to Think about Procedures as Designs 47 How to Think about a Formal Procedure 50 How to Think about Claims as Designs 53 How to Think about Families of Designs 55 How to Think About a Family of Procedures 57

vii

viii CONTENTS

How to Go Wildly Abstract 60 What You Can Do 62

CHAPTER 3 WORDS BY DESIGN

Reading by Design: Content 65 Reading by Design: Organization 71 Reading by Design: Critical Concepts 76 Writing by Design: Essay Themes 79 Writing by Design: Essay Organization 83 Writing by Design: Other than Essays 86 What You Can Do 90

64

CHAPTER 4 ACTS OF DESIGN 93

Invention and the Design Questions 94 Design in the School of Today 96 Opportunities for Design 98 Models of Modeling 107 Strategies of Design 114 Intrinsic Motivation 115 Problem Finding 119 What You Can Do 122

CHAPTER 5 INSIDE MODELS

What is a Model? 126 On the Omnipresence of Models 131 Mental Models 135 Mental Muddles 142 Teaching and Learning with Models Evidence for the Effectiveness of Models What You Can Do 153

CHAPTER 6 INSIDE ARGUMENT

147 150

124

155

Argument as Design 156 Sound Arguments 158 Justifying the Standards 162 Formal Patterns of Argument 164 Some Patterns of Informal Argument 168 Kinds of Argument 177 What You Can Do 182

CONTENTS ix

CHAPTER 7 THE ART OF ARGUMENT 183

A Study of Informal Reasoning 184 Improving Informal Argument 186 A Quick Argument for This Approach 190 Tie Breakers 192 The Challenge of Formal Argument 196 The Art of Mathematical Argument 198 Heuristic Power 204 What You Can Do 207

CHAPTER 8 SCHOOLING MINDS 210

What Holds Schools Back? 211 Bridging from Information to Design 213 Bridging from Teacher to Students 217 Bridging from Subject to Subject 221 Bridging from Context to Context 225 The Design that Designs Itself 230

Notes Sources

233 242

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Acknowledgments

Two friends and colleagues, Catalina Laserna and Omar Carrizales, contributed greatly to the initial development of the ideas explored in this book. Catalina Laserna, an anthropologist, worked with me in writing and testing the inventive thinking sequence for Project Intelligence, which produced the Odyssey thinking course. There we first recognized the importance of the concept of design. We jointly gave a workshop in Colombia, her native country, where the concep- tion moved significantly closer to its present form. Since that time, we have continued to collaborate. Omar Carrizales, a professor of mathematics at the Universidad Central in Caracas, Venezuela, spent a sabbatical year at the Harvard Graduate. School of Educa- tion, during which we had extended conversations about knowledge as design and the general problem of developing students' thinking. Many of the examples presented in this book directly reflect discus- sions with Catalina and Omar.

As already mentioned, the ideas in this book grew out of my work on Project Intelligence. Special thanks go to Jose Buscaglia for get- ting me involved and providing good counsel throughout, Mario Grignetti for his sensitive responses to the evolving inventive thinking lessons, Ray Nickerson, director of the project, for his provision of elbow room as well as good advice, and Margarita de Sanchez, for her astute practical perspective on thinking skills programs and their implementation.

xi

xii ACKNOWLEDGMENTS

Several individuals provided valuable responses to the draft of this book. Vernon Howard, Israel Scheffler, and associates of the Philos- phy of Education Research Center at the Harvard Graduate School of Education offered helpful feedback. Ken Hawes in particular sup- plied fine-grained reactions to a number of points. Howard Gardner, co-director with me of Harvard Project Zero and colleague of many years, mused over the first several chapters in helpful ways. Jonathan Baron of the University of Pennsylvania went over the manuscript, producing apt advice chapter by chapter. Inabeth Miller, then at the Harvard Graduate School of Education and now at the Boston Museum of Science, offered trenchant thoughts on the slant accessibilty of the book. Julia Hough, my editor at Lawrence Erlbaum Associates, supplied sensitive guidance chapter by chapter, section by section.

While this book is far from a direct report of research or curricu- lum development work, it has benefitted from knowledge I have gained through such activities. Consequently, I would like to ack- nowledge the government of Venezuela and Petroleos of Venezuela, which supported Project Intelligence, and the Spencer Foundation and the National Institute of Education, both of which supported a line of research into the development of informal reasoning espe- cially reflected in Chapters 6 and 7. My thinking also was informed through my work at the Educational Technology Center of the Har- vard Graduate School of Education, functioning with funding from the federal government.

Let me add the standard disclaimer that, of course, the ideas expressed here do not necessarily reflect the positions or policies of the supporting agencies.

Finally, my wife Ann, two sons Teddy and Tommy, and daughter Alice were willing respondents to trial balloons of many colors as these notions evolved. Warm thanks for their ready help and sup- port.

Introduction: The Giving and Getting of Knowledge

We wish for what comes hard. You can see that in our literature and religion, our myths and folktales. For instance, how many nov- els have you read or movies have you viewed about the joys of eat- ing? Not many, in part because this joy comes fairly easily for most of us. On the other hand, sex, money, and power remain staples of novelists, directors, and their audiences. Sex, money, and power do not come as easily, so people find the fantasy endlessly engaging.

This book concerns a rarer field for fantasy-the giving and get- ting of knowledge. We 'wish for knowledge too. I construe knowledge broadly, including facts, concepts, principles, skills, and their intelligent, insightful, and sensitive use. I have in mind active knowledge that one thinks critically and creatively about and with, not just passive knowledge that does little but await the final exam. Knowledge - especially active knowledge - counts among those things that do not come easily. So, although we may not cherish it quite as much as sex, money, and power, we have some literature and religion, myths and folktales about this hunger also.

There was Moses, for example. Moses went up into the moun- tain, faced God, and brought back His word. The particular wis- dom of the ten commandments was a gift from God to Moses, and from Moses to us all. What a fine idea about something that does not come easily-knowledge as a gift. Jumping forward a few thousand years, there is Stanley Kubrick's classic 2001: A Space

xiii

xiv INTRODUCTION

Odyssey. Remember how, at the beginning, the godlike monolith stands on earth to impart intelligence to a tribe of simians. They sniff curiously about the base of this blank alien shape. Then it begins to sing a one note tune that hurts their ears, shocks their heads, crinkles their brains, wakes their minds up. Soon and for the first time, a bone is seen as a club. They have the gift of insight.

Both these narratives carry a moral about our hunger for knowledge and how to fulfill it. Real knowledge (wisdom, insight, and so on) is so difficult you cannot get it for yourself. You have to get it as a gift. Like many stories on many matters, such tales marry our fears to wishful thinking. In reality, knowledge does not come as easily as a gift. Learning is a sometimes inspiring but too often onerous challenge. In reality, teachers cannot give wisdom as handily as God gave it to Moses or the monolith to the simians. Teaching also is an occasionally smooth but often labored process. This book concerns ways to make more tractable the teaching and learning of knowledge and its critical and creative use.

Who should worry about all this and why? Well, who are the givers and getters of knowledge? We all are-you, I, your and my sons and daughters, parents and grandparents, nephews, nieces, aunts, uncles, enemies, friends, acquaintances, partners, school- mates, playmates, workmates, bedmates. Giving and getting knowledge is a core survival strategy of humankind. This is an old point. Take a couple in cashmere sweaters, put them out in the wilderness, and they probably will not make it for a month. They are far less well equipped with anatomy and instincts for survival than the ignorant buzzard whose shadow crosses them at noon. They are not even good enough at what humans are especially good at-learning-to get themselves out of the bind.

But give them a start, a minimal mass of knowledge, enough to survive, and they and their descendants will start to build it up and pass it along. Civilizations such as Egypt or Greece were made not out of pyramids or Parthenons but principally out of knowledge built up and passed along. The technological world today, on the surface a construction of microchips and prestressed concrete, is underneath an edifice of knowledge. To be sure, the talent for building up knowledge that has brought us this high in some ways threatens to tip us over the brink of disaster. Short of that disaster, we will never be done learning. Indeed, we hardly dare to be done, since now we need to learn our way out of messes we have learned our way into.

INTRODUCTION XV

So the travails of teaching and learning should be the concern of us all. In fact, they always have been to a significant extent. One way or another, any society makes serious provision for teaching and learning. In industrialized societies, this takes the form of schools that try to get across a body of scientific and humanistic knowledge. Unfortunately, we have had only middling success.

For instance, you may remember your own frustrations. Perhaps you recall crouching over a college desk, busily transcribing the professor's blackboard notes, bothered by the itch in the back of your mind that said you did not really understand. Later you worked it out-painfully. Or you may remember when you read an article on the binary number system that gives computers their basic operating language. Binary to decimal conversions were tract- able, but you never did get straight how to translate big decimal numbers into binary. Or you may bring to mind the poems by Emily Dickenson you read in ninth grade; you would have tried your hand at writing a couple in that spirit, but there was no dis- cussion about how to do such things nor any occasion to try. Or perhaps you recall wanting to get off your chest some of the incon- sistencies of English spelling; but the teacher was not ready to treat such anomalies as an interesting phenomenon worth discussing. Or perhaps you remember how you wondered why a minus times a minus number yields a plus number, or how the history course with the flood of facts scared you off at the end of the third week.

More frustration about middling success can be found in the spate of recent reports about precollege education in the United States. We hear the litany of ills repeated from perceptive voice after voice: Students cannot write. They can learn the number facts, but they cannot solve problems. They can read the words but they cannot think about the words analytically nor draw apt infer- ences from them. Some students do better, of course, but some of them do worse. Too many are getting passive knowledge instead of active knowledge, knowledge they store and retrieve but do not know how to use. In short, the learning of facts proceeds well enough but critical and creative thinking languish.

Sometimes in more acid moods, I like to put it this way. Educa- tion too often amounts to truth mongering. Truths are sold to learners as givens to be learned, without context, without critical perspective, without creative application. In gentler moments, I recognize the source of the problem: Education for genuine under-

xvi INTRODUCTION

standing and critical and creative thinking is a hard and in some ways technical enterprise, calling for theories and tools of teaching and learning suited to the challenge. Truth mongering is a rela- tively unsubtle and nontechnical endeavor, so naturally much of teaching and learning drifts into that pattern.

But in recognizing the trap, we need not be resigned to it. This book is impatient with truth mongering. It concerns the universal human enterprise of transmitting knowledge. It hopes that this enterprise can be much more immediate, penetrating, and empowering than the status quo suggests. It explores some notions about how to do the giving and getting of knowledge better, in schools and out of them, in homes and out of them, on the job and off it, wherever you happen to be, whatever you need to learn or teach.

1 Knowledge as Design

The classic British science fiction author H. G. Wells once wrote a story about a man who wishes the world would stop turning. Troubled and in need of time, the hero of his tale wants tomorrow to come a little later. The conceit of Wells' narrative is that the fel- low gets his wish, but from that moment on all consequences follow according to natural law. The Earth stops turning, but the atmo- sphere does not. Enormous winds sweep down forests and farms. The oceans also keep in motion, heaving up onto the land, demol- ishing homes and factories. Bridges and skyscrapers, not part of the Earth, retain momentum, toppling over of their own impetus.

This whimsey about the price of idle wishes invites a like parable about human invention. Suppose that, tired of TV commercials and trendy boutiques, someone wishes that there is no such thing as design. After all, for most of us, design is a rather special word- the enterprise of admen, architects, and fashion czars. But broadly construed, design refers to the human endeavor of shaping objects to purposes. Let us, like Wells, follow rigorously the consequences of this wish. The clothes vanish from our bodies, never having been invented. The floors and pavements on which we walk slip away into nothingness. We find no books, no artificial lighting, not even a primitive hearth. We wander around the wilderness, mouthing at one another. And perhaps, if language itself can be considered a design, we do not even understand what the mouthings mean.

1

2 1. KNOWLEDGE AS DESIGN

WHAT IS DESIGN?

This parable dramatizes how pervasive and important design is: Our sophisticated lives depend utterly upon it. If building up and passing along knowledge is one characteristic of the human way, another is embodying knowledge in the form of a tool to get some- thing done. A knife is a tool for cutting, a bed a tool for sleeping, a house a tool for sheltering, and so on.

In general, one might say that a design is a structure adapted to a purpose. Sometimes a single person conceives that structure and its purpose- Benjamin Franklin as the inventor of the lightning rod. Sometimes a structure gets shaped to a purpose gradually over time, through the ingenuity of many individuals-the ballpoint pen as a remote descendant of the quill pen. Sometimes a structure gets adapted by a relatively blind process of social evolution, as with customs and languages that reflect human psychological and cul- tural needs. But notice that in this book we do not use another sense of design: regular pattern that serves no particular purpose, as in ripples on sand dunes.

If knowledge and design both are so central to the human condi- tion, then a speculation looks tempting. The two themes might be fused, viewing knowledge itself as design. For instance, you could think of the theory of relativity as a sort of screwdriver. Both are human constructs. Both were devised to serve purposes - the screwdriver physically taking apart and putting together certain sorts of things, the theory of relativity conceptually taking apart and putting together certain sorts of phenomena. That seems promising; at least "knowledge as design" poses a provocative meta- phor. Indeed, perhaps knowledge is not just like design but is design in a quite straightforward and practical sense.

KNOWLEDGE AS INFORMATION VERSUS KNOWLEDGE AS DESIGN

What is knowledge? Fuzzy as it is, the question has some impor- tance. How we think of knowledge could influence considerably how we go about teaching and learning. A stolid formula tends to shape how we see knowledge and the giving and getting of it: knowledge as information. The theme of knowledge as design can

KNOWLEDGE AS INFORMATION VERSUS KNOWLEDGE AS DESIGN 3

break the familiar frame of reference, opening up neglected oppor- tunities for understanding and critical and creative thinking.

Through learning at home, at work, and in schools, we accumu- late a data base of information that we can then apply in various circumstances. For instance, you know a friend's phone number, the layout of your town or city, the rules of chess, your favorite foods, when Columbus discovered America, the Pythagorean theorem, the capital of Russia, Newton's laws. You have this infor- mation at your disposal and may call upon it for whatever you want to do with it.

But can we consider knowledge in a different light, as design rather than information? That would mean viewing pieces of knowledge as structures adapted to a purpose, just as a screwdriver or a sieve are structures adapted to a purpose. You know your friend's phone number-so you can call when you need to. More- over, your knowledge is well-adapted to the purpose; the number is only seven digits long and well-rehearsed, so you can remember it readily. You know the layout of your town or city-so you can get to work, to your home, to the airport, wherever you want to go. Again, your knowledge is well-adapted; if you have lived in a place a while, you probably have a rather comprehensive "mental map" of the area that you can apply not only in finding places you nor- mally go to but in navigating to new locations in the same area. Similar points can be made about knowing the rules of chess or your favorite foods.

For these examples of everyday practical knowledge, knowledge as design does make sense, but how about more academic knowledge? When you ask yourself what the purpose of a piece of knowledge like "Columbus discovered America in 1492" or the Pythagorean theorem is, you may not have a ready answer. Treating that sort of knowledge as a design - as a structure adapted to one or more purposes - does not come so easily.

The question is how to interpret the shortfall. Possibly knowledge as information is the right way to think about academic knowledge. On the other hand, perhaps academic knowledge can be thought of as design, but the "information attitude" toward knowledge that pervades teaching and learning in academic settings has let to our accumulating knowledge stripped of its design characteristics. In academic settings, we often treat knowledge as data devoid of pur- pose, rather than as design laden with purpose. To recall a theme

4 1. KNOWLEDGE AS DESIGN

from the introduction, much of the academic knowledge we hold shows a symptom of truth mongering-knowledge disconnected from the contexts of application and justification that make it meaningful.

If all this is so, by pushing the point one should be able to see academic knowledge as design after all. Indeed, sometimes the case that academic information has-or should have-a design character is easy to make. The theory of relativity was already mentioned. Consider its ancestor, Newton's laws. These have a fairly tran- sparent purpose: organizing a diverse set of observations in .order to explain phenomena of motion, anything from the trajectory of a baseball to the orbits of the planets. Also, the laws have a parsi- monious and powerful mathematical structure well-adapted to this purpose.

"Important facts" such as when Columbus discovered America pose a more difficult challenge. One might question whether the facts have that much importance after all. However, connected to significant purposes they at least take on somewhat more meaning. For .instance, milestone dates like 1492 are pegs for parallel histori- cal events. What was happening in Europe at about that time, or in the far East? For another, 1492 and other milestone dates in American history provide a kind of scaffolding for placing inter- mediate events. What happened in America between 1492 and the next milestone date? In such roles, a date functions not just as information but as implement, in particular a tool for grasping and holding information. What was mere data becomes design.

There is a tempting analogy here with Stanley Kubrick's 2001. What is an old bone-just an object in the environment, or a tool? Surely Kubrick's simians knew about bones long before the monol- ith, but not bones as clubs. Bones were simply objects lying around. But with the help of the monolith, the simians saw how a bone could be used as a weapon. Something like this applies to academic information also. To be sure, we have a fair amount of mere infor- mation sitting in our mind's attic that does little more than wait and weather there, like old bones. But when a piece of data gets connected to purposes, it becomes design-like. In this way, all information potentially is design. Of course.. not very datum we have functions as design or even can do so readily. All of us keep in storage a great deal of passive information, one might even say dead information. But that is part of the problem. There is little

FOUR DESIGN QUESTIONS 5

point In teaching and learning that provides primarily dead infor- mation.

In summary, knowledge as design makes sense. One can see both practical and academic knowledge through that lens. In various contexts and for various reasons, you might prefer one construal or the other for knowledge - information or design. In the context of teaching and learning, knowledge as design has much to offer. Knowledge as information purveys a passive view of knowledge, one that highlights knowledge in storage rather than knowledge as an implement of action. Knowledge as design might be our best bet for a first principle in building a theory of knowledge for teaching and learning.

FOUR DESIGN QUESTIONS

All this is okay as far as it goes, but a mere attitude will not carry us very far unless we can elaborate it into a method. "All right," a cautious voice complains. "You want to call the concept of ecology, Boyle's law, and the Bill of Rights designs. But that's pretty easy and only mildly illuminating. What do you do to follow up?"

What we need is a way to use the theme of design systematically as a tool for understanding knowledge. To put this another way, we need a theory of understanding reflecting the theme of design. And perhaps there is one. Here are four questions that help in prying open the nature of any design.

1. What is its purpose (or purposes)? 2. What is its structure? 3. What are model cases of it? 4. What are arguments that explain and evaluate it?

Consider, for instance, an ordinary screwdriver. Here you know the answers. You certainly know about purpose: It's for turning screws. Other purposes could be mentioned too; such as prying open paint cans, but we focus on the most common purpose here.

As to structure, you can give me a general description of it, out- lining its major parts and materials-the plastic or wooden handle, the metal shaft, the flat tip, and so on. In general, the term struc- ture is used loosely and broadly to mean whatever components,

6 1. KNOWLEDGE AS DESIGN

materials, properties, relations, and so on, characterize the object in question. As with purpose, there may be different ways of describing structure; we simply pick one that is natural and illuminating in the context.

As to models, you can show me or draw me examples of screwdrivers. You can demonstrate how to use one. In general, a model exemplifies in some concrete way the design or how it works.

As to arguments, you can explain why it should work. In partic- ular, the handle lets one grip and twist. The flat tip nests into the screw and allows one to turn it. You can also give some pros and cons about its design. For instance, sometimes an ordinary screwdriver does not provide enough leverage to turn screws in hardwood. Sometimes it slips and scars a wood surface. Note that under evaluation we include side effects pro or can, such as scar- ring wood, as well as effectiveness in the principle objective, turning screws. In summary, your understanding of the design of an ordi- nary screwdriver includes knowledge about purpose, structure, models, and argument.

Moreover, if you do not understand those four things about a design, you do not understand the design fully. For instance, con- sider the sample design in Figure 1.1. The pictured model lets you

FIG. 1.1. A mystery design

FOUR DESIGN QUESTIONS 7

see much of the structure of this design. Here is some further infor- mation about its structure: It is made entirely of steel and has a width of about six inches at the bottom.

Even with all this information, however, you probably do not feel that you understand the design, because you do not have answers to the questions about purpose or arguments. As to pur- pose, the gadget is a toaster, designed to hold toast over a gas burner. That much of a clue probably lets you figure out some arguments for yourself. Why should it work? The gas flame will toast the pieces of bread as they sit against the wires, supported by the bends near the bottom. With another moment of thought, you can begin to see some pros and cons. For instance, one has to turn the bread in order to toast both sides.

As in this example, so in general: It appears that understanding a design thoroughly and well means understanding answers to the four design questions. Note that there is nothing very novel or eso- teric about this notion. The four design questions simply articulate the sort of understanding we all achieve about such ordinary objects as scissors, thumbtacks, belts, shoes, and chairs. They also spell out points we commonly pay heed to when teaching and learning in many concrete contexts such as carpentry or motor repair. The four design questions offer a guide to doing more cons- ciously and carefully what we often do intuitively anyway.

But do the questions apply to a piece of knowledge as well as they apply to a screwdriver? The issue is crucial, since we need a theory of understanding that encompasses knowledge of all sorts, from the most concrete to the most abstract. Let us test the matter. For a first example, consider your knowledge of what a traffic light means. The knowledge has a purpose: to allow you to judge when it is safe and legal to proceed. It seems natural to interpret the structure of the knowledge as these constituent rules: Green means go; red means stop; yellow means proceed with caution. You can give models of the knowledge - a picture or a demonstration at the next traffic light. And, finally, you can give arguments for the util- ity of having such rules - the arguments of experience or a citation of the legal code, for two instances.

Perhaps the design questions suit such pragmatic knowledge as what to do at a traffic light but not more abstract knowledge. Consider Newton's laws again. One certainly can ask after purpose-to integrate and explain data about the motions of bodies

8 1. KNOWLEDGE AS DESIGN

from baseballs to planets. A useful rendering of structure would be the laws themselves, considered one by one. (Instead, you could take the component words of the laws as the elements of structure, but this would not be an illuminating choice; if you pick the indivi- dual laws as your elements of structure you can ponder under argu- ment how each law contributes to the ensemble, but if you pick each word you choose a grain too fine to allow an illuminating account of the whole). Model cases include the solar system and how the laws explain the orbits of the planets. Arguments include an explanation of how the laws work together to give a complete account of a range of dynamic phenomena and an evaluation of the evidence for and against Newtonian mechanics.

Simple facts seem the hardest sorts of knowledge to view as design. Will the design questions serve there? Consider the fact that George Washington was the first president of the United States. This piece of knowledge could have various purposes, one of the most important being to give us an anchor point in history, as with Columbus's "1492" mentioned earlier. Classifying historical events by presidential administration is a neat way to organize the course of American history. As to structure, it may be useful to think of two components: "George Washington," which identifies a certain individual, and "first president of the United States," which identifies a role that individual played. Regarding models, one can find movies and books that dramatize the period and Washington's presidency. We also have complex mental models of what it is to be a president-the responsibilities, benefits, power, and so on. Regarding arguments, we have plentiful evidence that Washington was indeed the first president, and we can explain how this fact might help us to organize our historical knowledge by providing an anchor point.

Furthermore, as in the case of the screwdriver and the toaster, unless you understand answers to the four design questions, you do not really understand the fact that George Washington was the first president of the United States. If you lack the structure, you lack the fact itself and so of course do not understand it. If you see no purposes for this piece of knowledge, you also lack a kind of under- standing, the kind that sees what to do with things. If you lack models of it, including mental models, you will not be able to make the sorts of inferences that are a routine part of understand- ing something. Finally, if you lack arguments, you do not under- stand the grounds or motivation for the fact.

THE CUTTING EDGE: AN EXAMPLE IN DEPTH 9

To be sure, our understanding of a fact is often shaky in one or more of these respects. But this is only to say that we get along with partial understandings much of the time. The aim of the four design questions is to guide understanding by providing four sub- categories of .understanding that spell out what it means to under- stand a design comprehensively. The questions apply to almost any knowledge you might want to understand.

THE CUTTING EDGE: AN EXAMPLE IN DEPTH

The weather signs are encouraging. The design questions offer a guide to understanding designs in general and knowledge in partic- ular. Moreover, the examples already given suggest that often it is rather easy to answer the design questions. This has some impor- tance, because, to help with the giving and getting of knowledge, the design questions should be easy to use in most cases. To double check this point, imagine thinking through the four design ques- tions for such school topics as these:

The organization of the U. S. Senate. A deceptive practice in advertising. The organization of a paragraph. The form of an Italian sonnet. The rate X time = distance formula. The heart as a pump.

For most people with a bit of background knowledge, such topics yield up answers to the four design questions handily. In our teacher roles, we might teach such things by way of the four design questions; in our learner roles, we might work through the four questions for ourselves by gleaning information from texts and other sources and applying a little common sense.

There remains the matter of depth. Do the design questions offer a guide to understanding in situations of some subtlety and com- plexity? A lot hangs on the answer, because, although much that we teach and learn is relatively straightforward, a certain portion is not. Let us put the issue to a test.

Consider, for example, the cutting edge, a design so common and taken for granted that most of us never think about it. Can

10 1. KNOWLEDGE AS DESIGN

the design questions provide a framework for presenting the cutting edge in a way that makes the underlying principles clear?

What is the Purpose?

Any kitchen, workshop, barn, or armory presents a study in the diversity of the cutting edge - knives, axes, planes, lathes, chisels, cleavers, razors, sabers, bayonets. And it is not difficult to make the list longer. The cutting edge, with its generic purpose of cutting substances from butter to steel, is one of the basic human inven- tions. Most animals survive by adapting to their environments. But, to a remarkable extent, human beings survive by adapting their environments to themselves. The cutting edge is one of the basic tools for doing so.

What is the Structure?

Perhaps a knife provides the handiest example of a cutting edge. In an ordinary kitchen knife, one finds the basic structure of this ancient tool. There is not much to it - a chunk of metal smoothly tapered to a sharp edge. The cutting edge presents about as simple a structure as one finds anywhere.

What are some Models?

A visit to your kitchen should provide several.

What is the Argument?

The questions have been easy so far. Evaluative argument, too, would be fairly easy-the conveniences of cutting edges versus their dangers. It is when we turn to explanatory argument and seek the principles behind the cutting edge that the mystery emerges. Why does a cutting edge cut? "Because it's sharp," is the first answer to come to mind. But a little thought shows that this does not give much of an answer. It simply pushes the question one step further back: Why does sharpness foster cutting? In fact, the simple struc- ture of the cutting edge is a little misleading. At least three distinct principles conspire to help the cutting edge to do its job.

THE CUTTING EDGE: AN EXAMPLE IN DEPTH 11

The Principle of the Wedge. First of all, the tapered profile of a knife blade makes it a kind of wedge. A wedge is a way of ampli- fying muscle power. Anyone who has driven a nail or a stake with their wedge-like points has experienced the power amplification the wedge provides. Imagine what it would be like to drive a nail or a stake with a blunt tip.

A quick look at the mathematics of the wedge is worthwhile. Like the lever, another basic tool, the wedge purchases greater force at the price of distance. Figure 1.2 illustrates how this hap- pens. Suppose you push the wedge four inches to the right with a certain force. The wedge only spreads whatever it is separating one inch, because of the taper. But it accomplishes that one inch spread with four times the force. Notice that this amplification reflects directly the geometry of the wedge. As in the picture, a wedge four inches long and one inch wide at the base gives you a four to one power amplification.

What kind of power amplification do you get from the wedge shape of a typical knife? This is again just a matter of geometry. It is not even necessary to employ sophisticated measuring instruments like micrometers, since you can measure roughly the length and base of the wedge in a kitchen knife using a memo pad. A quick application to a small paring knife in my kitchen reveals a taper 47 sheets long and a thickness at the base of 8 sheets. The taper is about 6 times longer than the base, for a power amplification of 6.

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FIG. 1.2. Amplification of force by a wedge

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12 1. KNOWLEDGE AS DESIGN

That probably overestimates the amplification some, since it looks as though the taper is slightly more rapid toward the edge. But we have a rough estimate at any rate.

Concentration of Force. There is another kind of force amplification at work in the cutting edge, as you can illustrate with some ordinary household objects. Press the head of a large nail into your hand ·with moderate force. The pressure of the flat surface hurts very little. Now do the same with the head of a small nail. Here the pressure of the head may bother a little. Now do the same with the head of a pin. This easily can hurt quite a bit.

The difference cannot reflect the wedge effect, since in all cases you used the flat head rather than the pointed tip. Rather, as you move from large nail to small nail to the head of the pin, the same moderate force becomes applied over a smaller and smaller area- first the area of the large nail head, then the area of the small nail head, and finally the area of the pin head. One might say that the same force was condensed to become more and more intense.

As in the case of the wedge, the mathematics of this is a matter of ratios. This time it is ratios of areas. If the area of the head of the pin is one sixth the area of the nail head, the force will be six times as great throughout that area. Using this principle, you can calculate the amplification achieved by a sharp knife rather than, let us say, a knife with no sharpness at all, a knife as thick at the blade as at the back. The knife considered earlier was 8 sheets thick at the base. Suppose it was 300 sheets long (the length does not matter since it cancels out anyway). Then the area of the unsharpened blade is 300 X 8. The knife looks pretty sharp, so let us guess that the edge of the blade is in fact about 1/2 a sheet thick, for an area of 300 X 1/2. That is 1/16 the area for a power amplification of 16.

Those who have some background in physics will recognize that it is possible to talk about this more precisely. We have been lump- ing together force and pressure. The proper thing to say is that the force your hand applies to the knife results in a pressure between the cutting edge and the object, pressure measured in pounds per square inch or some other ratio of force per unit area. Naturally, the smaller the area receiving the same force-the sharper, that is, the cutting edge - the higher the pressure.

THE CUTTING EDGE: AN EXAMPLE IN DEPTH 13

Scratching. So far, two kinds of force amplification seem to serve the cutting edge - the wedge effect, which works to spread apart forcefully the substance being cut, and the concentration effect, which works to press the edge forcefully against the sub- stance being cut. But everyday experience with knives teaches that these two factors do not explain cutting completely. It is a com- monplace that if you simply press a knife against your hand without making any slicing motion, the knife will do no harm.

The missing principle is scratching. How scratching helps a seemingly smooth edge to cut can best be understood by consider- ing some related examples. First of all, imagine you are scratching a piece of wood with the tip of a nail. A groove in the surface of the wood results. Notice that the scratching effect depends on hav- ing a point and, to some extent, a wedge-shaped point. That is, it depends on the two force amplifiers discussed already. Now imagine how a saw cuts wood. To a first approximation, a saw is a row of nails, all scratching at the surface simultaneously. The saw cuts deeper because there are many points scratching at once.

Two kinds of knives obviously work like this - bread knives and steak knives. Both have visible teeth that scratch their way through substances. In reality, all knives operate this way. The seemingly smooth edge of an ordinary knife is far from smooth on a micro- scopic scale. Every irregular protrusion on its surface becomes a point that helps the knife to scratch through substance. You can have some confidence in this idea exactly because experience teaches that good cutting requires a slicing motion. There must be a physical reason why that slicing motion helps. The reason, apparently, is that it makes the knife work more like a saw.

Scratching also gives you more control over the knife, which in turn makes cutting easier. If the material is tough, you can press down only a little as you saw back and forth. This means that the microscopic irregularities dig only a little into the material, so the entire force of the back and forth motion of your arm gets concen- trated on the limited contact the irregularities make with the material. If the material is not so tough, you can press down more. The microscopic irregularities make much more contact with the material, distributing the force of your back and forth motion more widely and hence getting less force per irregularity; but since the material is not as strong, the less force is enough. You cannot

14 1. KNOWLEDGE AS DESIGN

make such adjustments while pushing down alone and not sawing back and forth; you make them by both pushing down with a cer- tain force and sawing back and forth with a certain force to suit the toughness of the material.

In summary, the cutting edge depends on three factors to do its job. (1) the force amplifiers of the wedge and concentration effects operate at the macro level of the knife's tapered sides and thin edge. (2) The same force amplifiers work at the level of the microscopic irregularities along the edge of the knife when a sawing motion is used. (3) The wielder's independent control of downward force and back and forth force allows cutting with little effort materials of very varied strength. This picture of the cutting edge reveals considerable complexity underlying the deceptive simplicity of a tapered shape that, recalling our first answer, "cuts because it's sharp."

It is worth noting that models playa helpful role throughout this account of the cutting edge. To be sure, there was a short separate section labelled models. However, all the informal mental and phy- sical experiments, drawings, and allusions to particular examples from common knowledge and experience involved models as well. Broadly speaking, a model is any example or other representation that makes a concept more accessible by rendering it concrete, per- ceptual and vivid. True, the most typical model is a model of struc- ture, an example that makes the structure vivid. But, as with the discussion of the cutting edge, one can have models that dramatize purpose or argument also.

THE THEORY OF NATURAL SELECTION: A SECOND EXAMPLE IN DEPTH

The example of the cutting edge tested an issue: Can the design questions help us to get clear about something of some subtlety and complexity? The results seem encouraging. Subtle features of the cutting edge were brought out but in a way that naturally involved principles of physics. Come to think of it, physics can be found at

THE THEORY OF NATURAL SELECTION: A SECOND EXAMPLE IN DEPTH 15

work constantly not just among atoms and planets, but in the everyday world about us, among the knives, tacks, jacks, pans, spoons, shovels, rakes, and chairs. As illustrated, we can easily carry analysis of the physics of ordinary objects to the level of mathematics. How motivating to see physics at work that close to one's hand!

But the analysis of the cutting edge started with a concrete design and worked toward more abstract knowledge by way of argument. Can the design questions help when we begin with a subtle abstraction? We have to test again. As urged already, any theory is a design. Consider Darwin's theory of natural selection. Most people might recall the general purpose of the theory, but the structure, good model cases, and the arguments all are likely to be vague. Perhaps the design questions can pry open this piece of knowledge for our understanding.

What is the Purpose?

Nature presents us with a bewildering variety of life forms ingeni- ously adapted to their ways of life. There are, for example, bird bills for spearing fish, for crushing seeds, or for sipping nectar from the hearts of flowers. There are spiders that spin webs, that stalk their prey like panthers, even one that casts a web like an entan- gling net. The problem for science is to offer a causal account of these marvels of adaptation. How did they come to be? Charles Darwin sought to do that job of explanation with his theory of natural selection. His theory, like any theory, is a tool for produc- ing explanations of a certain range of phenomena, and hence a design.

What is a Model Case?

Consider this model case, loosely adapted from an actual event in England. Many years ago, a species of white moths frequented a forested area made up of trees with whitish bark. The moths were not exactly the same color. Some were a little darker, some a little lighter. But no moth had a very dark color and most matched fairly well the color of the bark. Birds living in the forest fed upon the moths, albeit with some difficulty since they were nearly invisi- ble against the bark.

16 1. KNOWLEDGE AS DESIGN

The advent of the industrial revolution upset the situation. The soot from nearby factories began to coat the trees. What happened then will be clearer if we have numbers to stand for the darkness of moths. Let us say that I is white, 10 is black, and the numbers between measure increasing greyness.

In the first generation of the factories, the moths ranged in color from 1 to 3. But the tree bark had turned a little darker. The birds that fed upon the moths could see the lighter colored moths more easily against the darker bark, and so ate most of them. So the moths left to breed the next generation were mostly 3's.

You might think that the next generation would all be 3's, like their parents. However, there was a sprawl beyond the parental range. The next generation of moths showed greys 2, 3, and 4. The trees were still getting darker. The birds came and ate mostly the more visible moths of greys 2 and 3, leaving the 4's to breed the next generation.

Again the next generation showed a sprawl relative to the parents. Although most of the parents were 4's, the young moths ranged in color from 3 to 5. Again the birds came, eating mostly the 3's and 4's, and leaving the 5's to breed the next generation.

The pattern should be clear by now. Gradually, the moth popu- lation became darker and darker, as the birds gobbled up the lighter members of each generation while the darker members remained to breed the next generation. In the course of a few years, the forest was filled with dark moths-moths about the same color as the sooty trees-when originally there had been no dark moths at all.

What is the Structure?

This model case illustrates three key principles in the structure of the theory of natural selection. First of all, there is inheritance. The young moths have more or less the same greyness as their parents. Of course, the principle applies generally to all life: Offspring have more or less the same characteristics as their parents. Secondly, there is variation. The offspring of the moths do not always have exactly the same color as the parents, but range somewhat around the parents. In general, the offspring in any species display minor differences from the parents. Finally, there is selection. The birds select the lighter colored moths to eat, leaving

THE THEORY OF NATURAL SELECTION: A SECOND EXAMPLE IN DEPTH 17

the darker ones to breed the next generation. In general, it is com- monplace in nature that some factor in the environment - a preda- tor, availability of a certain sort of food, temperature, amount of water, and so on - makes a characteristic advantageous for survival and breeding.

What is the Argument?

As with many situations in science, the argument for the theory of natural selection has two sides. On the one hand, does the logic of the theory hold together? In particular, do the key features of inheritance, variation, and selection predict the result- gradual adaptation? On the other hand, does the empirical evidence sup- port the theory? Specifically, do the observations of biologists and paleontologists support the theory of natural selection? The latter calls for a long technical discussion out of place here. Perhaps it will be enough to illustrate knowledge as design if we look only at the former-the logic of Darwin's theory.

The points to be made are two. First, the features of inheritance, variation, and selection are sufficient to explain evolution. That is, taken together, they predict evolution. Second, the theory has no excess baggage: Each feature plays a necessary role in the explana- tion.

The argument for the first point amounts to a reprise at a gen- eral level of the story of the moths. Suppose we have variation of some characteristic. Also, suppose we have selection for more of this characteristic. Then the parents of the next generation will have more of that characteristic, because the other potential parents will not, by a large, survive and breed. Now suppose we have inheritance. Then the parents will pass more of that charac- teristic on to their offspring. But remember again that we have variation. The offspring will have the desireable characteristic in varying degrees, making way for another round of selection where those that have the characteristic to a lesser degree are less likely to survive and breed. Accordingly, over many generations, an accu- mulative effect will occur.

As to the lack of excess baggage, it is easy to see why each of the three principles is required. Taking the model case of the moths again, suppose inheritance did not occur. Then, in the first genera- tion, the birds would still eat the whiter moths, leaving the 3's to

18 1. KNOWLEDGE AS DESIGN

breed the next generation. However, no inheritance means that the characteristics of the offspring are not constrained by the parents. So the offspring of the 3's would not be mostly 3's, but instead would reflect the demographics of the original population -1 's, 2's, and 3's, with maybe a couple of 4's due to variation but no pro- gress toward a dark population. So inheritance is necessary.

Now suppose that selection did not occur-no birds. Then L's, 2's, and S's would all become parents of the next generation. Indeed, the 3's might produce a few 4's along with 2's and 3's as offspring, but again there would be no significant shift toward a dark population. So selection is a necessary part of the process.

Now suppose that variation did not occur. Then the birds would eat most of the L's and 2's and the darker 3's would breed the next generation. But, without variation, all the offspring would be 3's and their offspring in turn 3's. The population could never get any darker. So variation also is a necessary part of the process.

Quite apart from the empirical evidence for the theory of evolu- tion, these arguments highlight its logical elegance - the three ele- ments of inheritance, selection, and variation sufficient taken together to explain evolution, and each one of them necessary to make the theory work.

KNOWLEDGE AS DESIGN: THE ARGUMENTS

Have you notices that knowledge as design has been used to present itself? In the introduction, the purpose was addressed: teaching and learning for better understanding and critical and creative think- ing. Then in this chapter the structure was outlined: the notion of knowledge as design and the design questions about purpose, struc- ture, models, and argument. Numerous model cases have appeared, including the two extended ones about the cutting edge and natural selection. Some arguments for knowledge as design have been mentioned along the way but now a focus on argument is timely. Why specifically should this simple theory of knowledge promote understanding and critical and creative thinking in teach- ing and learning contexts?

Many reasons come straight out of the discussion so far. Treating knowledge as design treats it as active, to be used, rather than passive, to be stored. Grasp of purpose, structure, model

KNOWLEDGE AS DESIGN: THE ARGUMENTS 19

cases, and explanatory and evaluative arguments figures in under- standing anything thoroughly by definition. Lacking a sense of these, we do not really and comprehensively understand the thing in question. Moreover, attention to argument can help to identify uncertainty and weed out falsity. In this age of information glut, attention to purpose can help to decide what to learn and what not to learn, what to teach and what not to teach. Knowledge acquired with understanding equips learners to use it more flexibly, modify- ing it to suit novel applications; knowing a formula without under- standing inevitably limits its application to the rituals learned with it.

Knowledge as design and the four design questions highlight the critical and creative thinking behind knowledge, emphasizing knowledge as constructed by human inquiry rather than knowledge as "just there." Moreover, the four design questions provide a framework for teachers and learners doing their own critical think- ing about knowledge and creative thinking in making knowledge and products of mind generally. In particular, all four questions and the argument question especially offer a framework that teach- ers and learners can use for critical analysis. Examples in later chapters show how the design questions can be used as a guide to writing poems, writing essays, designing experiments, and other sorts of creative endeavors. Also, knowledge as design reveals provo- cative connections between different disciplines by making salient commonalities and contrasts in the kinds of purposes, structures, model cases, and arguments employed.

What about the psychological foundations of knowledge as design? The notion of knowledge as design and the design questions incorporate a number of principles, concepts, and concerns that have emerged in the contemporary psychology of mind. They need to, in order to guide the giving and getting of knowledge. For example, one current theme in the writing of some psychologists is the problem of "inert knowledge" -knowledge at the opposite pole from knowledge creatively applied. Research shows that learners commonly acquire a store of knowledge they can retrieve in quiz situations, but which they do not bring to bear in situations calling for active problem solving. This is a serious problem in medical education, for example, where volumes of anatomy and physiology absorbed by medical students lie inert when they face actual prob- lems of diagnosis and treatment. The emphasis on purpose is just

20 1. KNOWLEDGE AS DESIGN

one among several features of knowledge as design that should combat the problem of inert knowledge and foster its creative use.

More generally, the importance of purpose to understanding finds support in studies where understanding hangs on appreciating what something is for and also in the general importance of means-end analysis in human thought, where, for example, a chess player or a solver of problems in mathematics reasons out an approach by considering what moves might serve the goal at hand. As for structure, any number of psychological inquiries have exam- ined the learning of structures in various senses and highlighted their importance. The emphasis on models echoes studies showing that overt models can mediate understanding and that mental models-ways of envisioning a particular concept or situation-play a crucial role in human understanding. As to arguments, a body of psychological research on formal and informal reasoning and its hazards informs the better practice of critical thinking.

For yet another link with psychology, the design questions should abet even the most trivial side of learning, sheer memory. Research on memory has demonstrated repeatedly that organization, imagery, and meaningfulness foster memory. The four design ques- tions provide an organized approach to understanding any design, one that vests the design with meaning through emphasis on its purpose, structure, models, and argument. Models offer visualiza- tions and dramatizations, both providing imagery. While not dwel- ling on the psychological literature, from time to time in the com- ing chapters I make reference to it in connection with these themes.

Further argument for knowledge as design turns to education itself and its frustrations. One way to look at the problem focuses on practical and professional knowledge versus school knowledge. From early times, practical knowledge had a design character- purposeful knowledge about what sorts of stones made good cutting edges, what sorts of branches made fine clubs, where water could be found, what seeds would grow, what to make an oar or a sail of, how to build an arch. Today at both everyday and technical levels the same can be said. For the professional mathematician, an esta- blished theorem is a tool of inquiry. For the professional scientist, a theory is a tool of explanation. For the professional historian, an historical generalization is a tool for organizing historical events. Of course, the design perspective is largely tacit and unarticulated, an

RESTORING CONNECTIONS 21

automatic part of how the professional uses technical knowledge and how all of us use our everyday knowledge.

A time arrived in human history when specialized knowledge about nuclear physics, the sonnets of Shakespeare, or ancient Greece was to be given over to nonspecialists, as part of a general education. A problem of packaging occurred: What should the nonspecialist be told? The simplest thing was done - as used to be said on Dragnet, "Just the facts, M'am ," By and large, knowledge came to be presented as received or given, not much supported by arguments or linked to its purposeful role as an implement of inquiry or other sorts of creative and critical action.

How can we characterize this shortfall more sharply? One might say that our learning often suffers from disconnected knowledge- knowledge disconnected from purposes, models, structure, or argu- ment. That is, most learning situations neglect one or another of the design questions. In consequence, we emerge from those situa- tions without a full understanding of the knowledge we have encountered. The perspective of knowledge as design nudges us all, in our varied roles as teachers and learners, to remedy that neglect.

RESTORING CONNECTIONS

Conventional schooling suffers from numerous problems of discon- nected knowledge, but it need not. Although conventional school- ing only constitutes a part of learning, we do well to consider this special case both because it plays a central role in most people's learning and because its chronic problems of disconnection cry for repair. A number of examples follow.

Connecting to Purpose

Let us look more closely at a piece of information we touched on before: Columbus discovered America in 1492. We all dutifully learn that fact early in our educations. What most of us do not learn are purposes for knowing this and like facts. To put it another way, we learn dates and events as information, but not as design. Too much of instruction in history comes disconnected from the purposes that give history significance as a discipline.

22 1. KNOWLEDGE AS DESIGN

"Purpose" should be taken broadly here to include significance, import, role in integrative theorizing, and the like. A purpose for dates was mentioned earlier: The dates of milestone events in history serve as an organizing framework. What about Columbus's voyage as an event? It can be invested with import in a number of ways, through a number of questions for students to ponder. For example, was Columbus's voyage pivotal historically, or interesting only because it was "the first?" What analogies appear between voy- ages of discovery then and now? Do we still have voyages of discovery? Are there any besides space exploration? How are they different from Columbus's venture, and why? If straightforward physical exploration has fallen prey to an over-explored world, have other forms of exploration-say scientific inquiry-come to take the place of such adventures? And do they really?

Voyages of exploration, seeds of war, the rise and fall of civiliza- tions' key technological innovations, the fate of dynasties, how geography shapes politics, and endless other pages from history and histories are natural food for question-raising, analogy-making, theorizing, and other sorts of venturesome thinking. Lacking this link to inquiry, historical facts become threads without a tapestry. They stand disconnected from the contexts that make them mean- ingful. Some history instructors and history books take this problem to heart and try to deal with it. But many do not.

Oddly enough, mathematics, the most logical of disciplines, falls prey to problems of disconnection from purpose quite as much as history, the most empirical. Consider, for example, the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. Mathematics instruction routinely presents and proves this theorem. But that same instruction typically leaves the theorem disconnected from its import.

In fact, the Pythagorean theorem is a key design for much of mathematics. To name some connections, without really explaining them, in trigonometry, the theorem underlies crucial trigonometric identities-for example the identity saying that the square of sine X plus the square of cosine X equals one. In analytic geometry, the theorem becomes the basis for defining distance in a two- dimensional Cartesian coordinate system. The distance from point A to point B is the square root of the sums of the squares of the differences In the coordinates of A and B - because those

RESTORING CONNECTIONS 23

differences form two sides of a right triangle. A generalization of the formula applies when we have not two, but three or more dimensions. Indeed, the n-dimensional formula can be demon- strated by repeated applications of the Pythagorean theorem. All of this in turn contributes to other developments: the vector cross and dot products, for example, the correlation coefficient from statistics, or, from calculus, the formula for integrating to determine the length of a curve.

Of course, mentioning these connections in passing will not make them clear to a person unfamiliar with the mathematics. The prob- lem is to explain in advance the import of the Pythagorean theorem. Because mathematics builds complex edifices out of not so simple bricks, it is a challenge to forecast for learners the edifices the bricks will yield before the bricks themselves are thoroughly familiar. Because this is hard, usually no such effort is made. Abstractions are introduced, the purposes of which only become plain as those abstractions get built into a system they themselves help to define.

Recognizing the reality of the dilemma, however, does not require giving up on it. On the contrary, the premise of the design perspective on knowledge is that mathematics instruction must strive ingeniously, by way of models and analogies perhaps, to anti- cipate the applications of concepts and theorems. Not to do that leaves too much of mathematical machinery unmotivated for the learner.

Connecting to Models

The laws of Newton provide a classic example of disconnection from models. Contemporary psychological and educational research has shown that even students taking college physics courses main- tain entrenched misconceptions about the motion of bodies in space. They have an intuitive physics that mismatches the correct Newtonian one.

Here, for example, is a simple thought problem that gives many people trouble.

A rocket glides along in free fall at several hundred miles per hour. Wanting to head off in another direction, the pilot rotates the rocket so that it points at right angles to its direction of motion and fires. In what direction will the rocket travel? (See Figure 1.3.)

24 1. KNOWLEDGE AS DESIGN

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FIG. 1.3. Trajectory of rocket upon firing at right angles to direction of motion?

Many people expect that the rocket will start off at right angles to its original direction of motion, rather like a car turning a corner. But this answer neglects the behavior of objects in free fall. The newly fired rocket indeed accumulates motion at right angles to the original direction. But the original motion is still there too. Where, after all, would it go? The resultant net motion amounts to a compromise between the original direction and a right turn. The rocket goes off at an angle between the two, an angle depending on the intensity and duration of the blast. (See Figure 1.4.)

The answer conflicts with the intuitive physics of many people. The problem lies in part in our ordinary experience of the world. In most motion that we see, frictional forces dominate. For exam-

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RESTORING CONNECTIONS 25

FIG. 1.4. Trajectory rocket will follow.

ple, an object certainly does not keep moving in the same direction with the same velocity, as Newton's laws prescribe; because of fric- tion, it simply stops in a few seconds. Velocity "wears out" quickly, so to speak. A life filled with such experiences makes a right angle turn a reasonable prediction, a prediction backed by years of per- ception. After all, if space were full of friction, the forward motion of the rocket would quickly "wear out," and a blast at right angles would indeed take the rocket off at a right angle, unmodified by the original motion.

26 1. KNOWLEDGE AS DESIGN

Since life misleads us, education must do better. For example, computers 'can generate better models, an approach that some edu- cators have explored. The students encounter, on the display of a computer, a frictionless world of objects that behave as Newton's laws dictate. The students can try the experiment mentioned ear- lier, among- others. They can turn a rocket at right angles to its path of motion, blast away, and see what happens. One can also present displays where the learner can vary the degree of friction, to see how objects behave differently when friction dominates and when friction plays little or no role. After some experiences with such model cases, the students presumably develop a much better sense of what Newton's laws really imply.

We can also look harder for better models in everyday experi- ence. In sports there are situations aplenty where objects behave in a rather Newtonian way. Suppose, for example, that you are tack- ling a football player from the side. In what direction will the colli- sion send you and him? If you imagine your way through the event, your experience will answer: off at a diagonal- a compro- mise between the direction of your tackle, and the direction of his run. Or imagine you are playing basketball. Someone on the oppos- ing team takes a shot at the basket, and you swat the ball from the side. Does the ball fly off perpendicular to your hand? Of course not. It caroms off at an angle.

As here, so in general we can try harder to mine the ordinary world of experience for appropriate models. Whether by rummag- ing in everyday experience or constructing novel models, the aim is the same: to connect abstract physical principles to concrete experi- enced manifestations of them, so that the import of the principles will be understood in an intuitive way.

Connecting to Structure

Of the four design questions, the one about structure receives the most attention in conventional schooling. Usually, a teacher of English, mathematics, history, or physics takes some pains to lay out explicitly the concepts being taught. However, there is a situa - tion both within and outside of school where structure often gets neglected: when the teacher provides a model by demonstrating his or her own skill. For instance, artists sometimes teach students by modeling for them the process of painting, sculpting, or throwing a pot. A coach may demonstrate how to work on a trampoline or

RESTORING CONNECTIONS 27

shoot foul shots. Within the academic disciplines, a math teacher may sometimes demonstrate how to think through a math problem, the English teacher how to think in planning an essay.

Providing demonstrations is a case of modeling, and a powerful instructional move. But sometimes such models come without a concomitant laying out of structure. There is a deep problem of communication here: Many models are ambiguous. When you see them, it is not entirely clear what features of them count the most, unless an accompanying explanation of structure highlights those features. Recall, for instance, the model of the moths, the birds, and the factories for natural selection. Imagine that the descrip- tion had not singled out and emphasized the principles of selection, inheritance, and variation. The import and generality of the model would have been much less clear.

When models come disconnected from structure, this may signal simple neglect. But it often reflects a genuine difficulty in knowing what structure to present. You can model bicycle riding for your son or daughter, but what do you tell them to make clear the structure of what they should do? Similar problems arise no matter whether the demonstration concerns solving math problems, paint- ing a picture, or some other skilled performance: Often demonstra- tors do not have good descriptions of performances they can easily display. Their very status as experts aggravates the problem. So far are they from the experience of learners that they often have for- gotten which aspects are obvious, which obscure. Moreover, much of their own skill has become automatized so they do not know how they go about the activity in question as well as they did when they were learners.

So the learner gets a model without a good structural descrip- tion, which may help some, but not as much as a model with struc- ture. To connect to structure, the teacher has to strive toward a simple and telling description of the modeled activity, however little the teacher's own need for such a description.

Connecting to Argument

History as normally taught presents problems not only of disconnection from purpose, but disconnection from argument. How do we know that "Columbus sailed the ocean blue in fourteen hundred ninety two?" Because we have been so informed, but not

28 1. KNOWLEDGE AS DESIGN

because we have any better grounds for belief than the authority of the textbooks.

The risk is not that the textbooks might be wildly wrong. I sup- pose that most of the time they are right. Unfortunately, students learn history while not learning much historical reasoning-the pat- terns of inquiry that historians use to establish what happened and its import. Often an historian must labor mightily through circui- tous means to confirm an historical fact, not to mention an histori- cal generalization. Yet the usual way of presenting history conceals the mindwork behind it.

Some might say that there is a good excuse. Perhaps history is too specialized an area of inquiry for students. After all, most stu- dents can hardly hope for access to original materials regarding the French revolution or the early development of the steam engine.

However, This doubt identifies history with previous decades and centuries. Suppose instead that a group of students set out to recon- struct what happened at a town meeting two months ago. All the features of historical reasoning come at once to the fore. There is the quest for sources-newspaper accounts, witnesses to the event, perhaps a tape recording or even a videotape of the proceedings, official records, and so on. There is the quest for objectivity. Most witnesses were participants, perhaps participants with axes to grind. What axes? Do the witnesses agree? Do their disagreements follow fault lines of political difference? Then there is the quest for significance. Amidst a maze of minor issues addressed at this town meeting, what ones stand out as important? What general style or bias dominated the meeting? How did the meeting match or mismath the style or bias of past meetings? Do we see innovation, stagnation, retrenchment?

These questions pose challenges ranging from straightforward to very difficult. That, of course, is the point. Relatively recent events provide plentiful opportunities to do history. Obviously, none of this means that we should discard traditional history for the sake of historical reasoning, shifting our attention entirely to recent town meetings and neglecting the French revolution. But, for the moment at least, the risk surely lies in the other direction - not making enough of historical reasoning, rather than making too much of it.

Biology is another discipline where argument deserves more attention. Students learn that the blood circulates, but not how this

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became known, in one of the classic breakthrough episodes of med- ical inquiry. Students learn that genes encode the structure of living organisms, but little about the evidence for this bizarre claim that the complexity of a human body and brain lies dormant in a spiral structure of microscopic size.

Yet there is no need to neglect argument. Evidence for phenomena like the circulation of the blood can easily be given. Moreover, it is relatively easy to engage students in biological rea- soning. For instance, ecology offers a rich range of occasions for reasoning about the adaptation of organisms.

Here, for example, are three "think" questions in ecology.

1. Why do we find sessile animals (animals that stay attached to surfaces, like mussels or barnacles) in the water, but not on land?

2. Why do terrestrial animals lay far fewer eggs than aquatic animals?

3. With question 2 in mind, consider the case of terrestrial insects: They lay a great many eggs and hence seem an excep- tion to the usual terrestrial strategy. Why?

I will always remember how one individual in a workshop reacted to these questions. As here, the questions were presented as a way to promote reasoning: The participants were asked to think out answers. This particular fellow complained, "But we don't know anything about sessile animals! How can we possibly deal with such a question?"

His reaction illustrates a fundamental problem in educational practice. Most educators will agree that sooner or later in the course of instruction students need to learn to reason with what they know. But the usual conception, if anyone would dare to state it baldly, runs like this: "First you learn the facts. Then you learn to reason with them." In contrast, knowledge as design says, "Don't just learn the facts as data. Learn the facts as you learn to reason with them." Reasoning is not so locked into prior knowledge of the official facts that one cannot develop both at the same time. The ecology questions demonstrate this point. Everyone brings to such questions considerable general knowledge and common sense.

Take the first question, for example. Why should sessile animals occur in the sea, but not on land? Well, what difficulties would a

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land animal rooted to the spot encounter? It could not hunt or forage for food. It could only wait. Why should waiting for your dinner be a viable strategy in the sea but not on land? Does your dinner come to you any more readily in one place than the other? Perhaps so. In water, the currents constantly bring food past sessile animals. The buoyancy of water allows water to carry a far greater cargo of food than air does. With door to door delivery of gro- ceries, staying in one place makes sense, so the opportunity arises for some species to enjoy various advantages linked to staying in one place-for instance, heavy protective shells that would not be mobile anyway, or maintaining position in the nourishing soup of tidal areas or silty currents.

These reflections of the lifestyle of sessile animals grow not from any special biological knowledge, but from common sense and com- mon experience. We all know that creatures must eat. We all have some familiarity with the basic properties of a liquid medium. To be sure, a more technical knowledge base would allow deeper and more subtle reasoning. But a good start can be made at one.

A Report Card

As the above examples make plain, the design questions provide a guide to connected knowledge. They remind us to attend to all of the four aspects-purpose, structure, models, and argument-one or more of which we might otherwise omit. This can happen in any context of giving and getting knowledge, formal or informal, private or public. It certainly happens in formal education. Let me underscore this point by presenting a brief report card on the typi- cal handling of a few subject matters in elementary and secondary school- and all too often even at the university level.

Mathematics. Often strong on argument, presuming the argu- ments are understood. Falters frequently for lack of vivid models. Very explicit on the structure of the content, but often neglects the structure of how to do things-the problem solving process. In seri- ous trouble with purpose, because of a genuine, but partially sur- mountable, difficulty of describing the later role -of concepts and results just being introduced.

History. Often strong on models-specific examples of historical events. Structure is explicitly laid out; often, in fact, there is too

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much of it to keep track of; it is not organized enough. Weak on connection to purpose. How do various historical events and trends connect to others; what to they imply for modern times? Weak on argument. Students learn little about the justifications for impor- tant historical claims and get hardly any practice with historical reasonIng.

Biology. Structure is laid out explicitly. Often strong on models, through diagrams, dissections, and so on. Often strong on purpose, through discussion of the functions of various parts and processes. But weak on argument.

Physics. General purpose should be clear - to explain physical phenomena. However, the phenomena to be explained may seem minor matters rather irrelevant to life; students need to feel more vividly how infused life is with the laws of physics. Often strong on structure and argument, through mathematical derivations and the discussion of key experiments. Often weak on models, especially when our intuitive understanding of physical events conflicts with theory. Vivid models are needed to displace our naive concepts.

Literature and Art. Strong on models; students spend most of the time reading or looking at particular worthwhile examples. Mixed on purpose. Sometimes the role of the arts in society and in the lives of individuals is sensitively addressed, sometimes not. Mixed on structure, because of the descriptive and interpretive difficulties works of art often pose. Poor on evaluative argument. Although students encounter critical opinion, they often embrace the position that critical judgment solely reflects idiosyncratic taste. They receive virtually no exposure to the special ins and outs of aesthetic argument.

If your most or least favorite subject matter was left out, it is only because these examples should suffice to make the general point. Report cards like this are earned by nearly any subject one might name. Most subjects as normally taught suffer from significant problems of disconnection within themselves. In addi- tion, instruction rarely deals in connections between the subject matters by way of commonalities or contrasts in purpose, structure, models, or arguments. Consequently, subject matter knowledge

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means somewhat less than it might and sticks in learners' minds as indifferently as it does.

WHAT YOU CAN DO

Perhaps there is something new in speaking of knowledge as design. But there is nothing new about the four design questions taken separately. Consider purpose, for instance. Many a good teacher takes care to clarify the purpose of a piece of knowledge, and many a learner asks, although not always receiving an answer, "What's it good for?" In our teacher roles we routinely provide structure and often models or arguments. And if we do not, learners often call for them.

The potential of knowledge as design and the design questions comes not from any new slant on knowledge they introduce but by making explicit an old intuitive time-tested slant. While as teachers and learners we sometimes spontaneously treat knowledge as a pur- poseful structure and pay heed to models and arguments, all too often we do not. Knowledge as design crystallizes our best impulses into explicit method.

What, then, can you do in your role as a teacher or learner? Every chapter of this book addresses that question, so a full answer certainly cannot surface here in the first chapter. However, already the following practices should make sense.

As a learner in a formal or informal setting, you can:

• Watch out for the problem of disconnected knowledge. You can test your own understanding of concepts, principles, and so on, with the four design questions. Can you answer them all for the piece of knowledge in question? Moreover, can you think of new model cases, to be sure you are not just function- ing by rote?

• Guide your study of a particular piece of knowledge by the design questions, searching out answers to each one. Some- times you may discover that your source of knowledge-for instance, a textbook-neglects one or more of them. In that case, you may find answers in other sources or devise your own answers; at worst, you will know where the gaps in your understanding lie.

WHAT YOU CAN DO 33

• Look to the lessons of ordinary objects, thinking about the arguments that explain how their structure serves their pur- pose according to principles of physics, economics, or other disciplines, as in the case of the cutting edge.

• Ask yourself to be critical and creative about knowledge, analyzing pieces of knowledge with the design questions, con- structing new model cases, and even improving or creating knowledge, guided by the design questions.

In your teacher roles, you can:

• Watch out for the problem of disconnected knowledge. You can check your own understanding of what you are teaching by answering the four design questions yourself. You can ensure that your instruction deals with all four.

• Follow the design questions in presenting a topic, as was done for the cutting edge and Darwin's theory of natural selection. You can teach whatever you were going to teach anyway, using the framework of the design questions. (By the way, in presenting a piece of knowledge, purpose should come first to establish a frame of reference. Structure or models comes next - whichever seems to serve the need for clarity best in the particular case. Arguments appear either at the end or in alternation with points about structure, because arguments explain and evaluate the structure in relation to its purpose.)

• Use the design questions with learners of any age down to around four or five. Of course for young learners you would choose simpler things or concepts, use simpler and shorter explanations, and avoid vocabulary problems. For instance, instead of "purpose," you might say "What's it for?"; instead of "structure," "What's it like-parts, what it's made of, and so on?"; instead of "models," "What's an example?"; instead of "argument," "How is it supposed to work?" and "Does it do a good job?"

Use the design questions with learners of almost any ability level. Knowledge as design is not only or even especially for bright students. It is for anyone in a learning situation.

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• Take advantage of everyday designs to disclose deep principles at work. The discussion of the cutting edge is an example.

• Engage your students in design analysis, asking for purpose, structure, model cases, and explanatory and evaluative argu- ments. You can pose fairly accessible questions-the analysis of a chair, for example - or more challenging ones - why sessile animals are found in the sea but not on land, for instance.

• Teach your students the notion of knowledge as design and the design questions, to equzp them with this tool of thinking and learning. The same applies to any other strategies you want to convey. There have been experiments comparing direct instruction in thinking strategies with instruction in which teachers simply tried without comment to model the desired thinking strategies by their own actions and through examples. The first style of instruction gets much better results.

As teacher or learner you can remember this:

• Apply knowledge as design and the design questions flexibly. Does a particular- point fall under purpose or argument? Sometimes this is ambiguous, so place the point by whim. How do you analyze the structure of a beachball or a referendum? You invent a breakdown into parts or aspects that proves illuminating in the context. Knowledge as design invites gen- erative application, not rigid formulaic use. Accept the invita- tion!

The examples in this chapter give the flavor of the quest, but each teacher and learner must be his or her own cook. More exploration of the opportunities follows in the chapters to come, along with ways to apply knowledge as design to reading, writing, argument, and other mindful activities. To be sure, a seasoning of realism is crucial. No art of teaching and learning, including knowledge as design, will make the giving and getting of hard knowledge quick and easy. But knowledge as design should make the enterprise more mindful, manageable, and motivating.