A one-page summary of the article

A one-page summary of the article  + some Question as summary that  I will Discussed with the teacher. 

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

1

0016
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 2

1

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.

F

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

?

•• ?

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-

*

?
?

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

RESTORING CONNECTIONS 29

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

30 1. KNOWLEDGE AS DESIGN

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

RESTORING CONNECTIONS 31

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

32 1. KNOWLEDGE AS DESIGN

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.

34 1. KNOWLEDGE AS DESIGN

• 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.

Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents

Acknowledgments

• Introduction: The Giving and Getting of Knowledge
• Chapter 1. Knowledge as Design