We teach content. Can we teach “thinking”?
(Find that paper on “better to teach abstractions?!)
The conventional system assumes that the child’s mind will ‘self-organize’ its higher levels, without any external guidance.
Most everyone agrees that schools should prepare our children for fruitful careers as citizens of a peaceful, productive society. To accomplish this, most schools provide programs in which pupils spend their first few years at learning a modest amount about each of several subjects or fields; typically, these include some courses in language skills, social studies and history, and some glimpses of science and mathematics. This policy appears to be based on the belief that equipping children with ‘broad foundations’ will help them to later develop more specialized skills.
This kind of broad but shallow curriculum works well for some students—but this essay will argue that general education” (along with its frequent assignments and tests) fails to help most students develop the multi-leveled networks of knowledge and skills that one needs for solving hard problems. This results in what I see as an worldwide epidemic of mental shallowness: most adults don’t seem to think very well. And the remedy that I will propose is to encourage more projects and hobbies. (Of course, that doesn’t apply
Outline:
What’s involve in solving hard problems.
Then, what does one learn from this?
Credit Assignments. I don’t have room to explain this here, so look at Section 8-5 of The Emotion Machine. The essential point of efficient learning is that, after you have solved a problem, it is not enough just to remember the answer: you need to remember the strategies that you used to discover that answer. Allen Newell pointed this out in his seminal paper on how to make a smart chess-playing machine.
Allen Newell 1955: "It is extremely doubtful whether there is enough information in "win, lose or draw," when referred to the whole play of the game [so, for learning to be effective], each play of the game must yield much more information. … If a goal is achieved, its subgoals are reinforced; if not they are inhibited. … Every tactic that is created provides information about the success or failure of tactic search rules; every opponent's action provides information about success or failure of likelihood inferences and so on.”
I should note that we still don’t have learning programs that work this way, perhaps because most research on learning machines has emphasized statistical inference rather than reasoning. In any case, all this suggests that clock-based classes would not be good for those who can’t tolerate interruptions.
build taller “intellectual towers.” [Which leaves us in a dangerous world!]
Objections;
“Shallow in what sense? Wisdom of the crowd! Intellectuals don’t really do so well—and although they may be good in their specialties, they are often deficient in common sense.
Besides, it is widely agreed that it is in our nature to have a wide range of IQs. Whatever we do, half of the population will always be of ‘below average intelligence!”
In any case, this essay discusses some possible ways to teach “deeper thinking.” The main conjecture is that our best thinkers developed those skills through their ‘extra-curricular’ activities, and in particular, by intense pursuit of certain types of pastimes and hobbies.
[edit] Learning that most ‘facts’ or ‘generalization’ have exceptions. The importance of Negative Expertise. Knowing the most common kinds of mistakes. How to recognize xxx and bugs. Overcoming your many ways to get stuck. Especially, “reflective skills” with which you recognize, diagnose, etc., various ways in which you’re prone to make mistakes, go down wrong paths, waste time, hold on to dysfunctional ways to thik, etc.
For example, to solve a non-trivial problem, you first need to find some way to represent it—for example, as a verbal question, a pictorial diagram, or a list of constraints to be satisfied. Then you need to design a search for possible solutions, or a way to divide the problem into several smaller ones—and doing this may require you to invent some new ways to represent situations, goals, plans, ideas, and relationships.
Those skills also include ways to think about oneself—so that you can reflect on when and how you might need to change yourself. Then you may need to think about some of those conceptions themselves. Effective thinkers can do all these things unconsciously, and it all seems effortless to them, because those processes can work independently in multiple layers of their mental organizations. But how does a person acquire those abilities? This is a subject we rarely discuss. Instead, it seems to me, that we tacitly assume that this sort of synthesis will happen spontaneously: just expose a child to many subjects—and, somehow, then, it eventually will all be put together, or ‘integrated’ or ‘absorbed’, etc.
Is reflective thinking a subject that we can teach? Should we add “Theories of Thinking” to the elementary curriculum? I suspect that when children develop such “cognitive towers” at all, this happens mainly when they are involved in more intensely engaging activities—like those we often see when children pursue their favorite amusements and “hobbies”.
To remedy this, I will suggest that the curriculum should make room for one or more ‘hobbies’ or specialties for each child to work out in greater depth. For until they have had this kind of experience, those children won’t have good models of ways to organize more powerful, ‘vertical’ mental structures. [And as I noted in Memo 2, modern schools leave little time for such things.]
Our Thesis: Most of general education will be wasted unless a child already possesses some experience with what it is like to acquire and use some particular subject in great depth.
[This subject itself — about theories of thinking—is *not* part of the standard curriculum.
For once this has been accomplished, then, when a child starts to explore a new realm or domain, that child will already be equipped with one or more prototype models and strategies for building a new such intellectual structure, to represent the knowledge in that particular new realm.
Contrast this with what happens when one becomes an apprentice. Note: Not all hobbies lend themselves to building such towers. I don’t think that this comes with collecting baseball cards!
Of course, this demands more teacher versatility, etc.
Many children already have -- focus – in sports, etc..
Some new alternatives that now could be made available via the use of more modern technologies.
§§§§§
Or “higher” development, namely, what might be called “” skills that one needs to develop a many-level functional structure: (One answer to this is that our intentions about that won’t actually matter much because, in the end, the result will be a variety…). In any case our goals include:
— Knowing a little about lot, but failing to “put things together” enough
— —There are countless bugs one may encounter in this, which one may need to learn from a different kind of experience.
— —Too many connections cause floundering and traffic jams; too few lead to triviality, etc.)
A ‘Management” theory of the mind’.
HANDICAPS. We also want our systems to ameliorate major handicaps. In many institutions today this is extremely expensive, and [can become a serious economic drain on the system. [I expect AI to eventually change this.] In particular it can result in a conflict with a different goal: To provide additional help and encouragement for children who appear to have greater than normal potentials.
Mentors: OLPC could make this feasible, by linking children to appropriate mentors who can help them pursue their particular interests. The network- world is certain to grow much larger.
Conjecture: New goal: To become very competent in at least one specialty.
Children do acquire such organizations in other (non-educational contexts.) learning language, using bodies in the world, but not for ‘academic’ subjects, e.g., going between arithmetic and higher geometry, etc—wider range of ‘mathematical” concepts. MATH - a certain body of ideas and methods for doing things that involves deliberate construction of new representations and procedures for manipulating them.
In fact, here are some areas in which most pre-school children construct (by themselves) some quite advanced specialties. (Some of these closely correspond to Howard Gardner’s “kinds of intelligences.)
Language: words, sentences, paragraphs, stories. [Gardner’s Linguistic Intelligence]
Time: events and sequential relationships.
Space. View synthesis into sold model. Imagine different views. How things might fit together. Paths in space. Combining objects into architectural into structures, e.g., towers, arches, etc. [Gardner’s Spatial Intelligence]
Vision: features, objects, structures, scene-analysis, and especially, distinguishing animate and biological objects. [Gardner’s Naturalist Intelligence]
Athletics: postures, locomotion, paths, [Gardner’s Bodily-Kinesthetic Intelligence]
Sound. Recognitions. Auditory scene-analysis.
Social models. Personalities, relationships, [Gardner’s Interpersonal Intelligence ]
Psychological models of oneself. Reflective Thinking. [Gardner’s Intra-personal Intelligence]
Memory management: storage and retrieval
Audio-music, voice, [Gardner’s Musical Intelligence]
Reasoning. [Gardner’s Logical-Mathematical Intelligence]
Self-consciousness reflection, values, ethics. [Gardner’s Existential Intelligence ]
Some educators maintain that what is most vital is to find ways to help our children learn traditional "basic skills" such as reading and writing, arithmetic, geography, and other traditional subjects. Certainly these are necessary. But just as certainly, those skills are not sufficient for dealing with modern industrial life. In this essay, I will argue that it is even more important to help our children also to learn how to build their own mental management skills -- for the growth and expansion of their own minds. We usually think of education in terms of what children learn, but we rarely teach about learning itself - about how children might learn new ways to learn.
In general, we have to be concerned with education in two domains: for specialists, and in general. For training specialists, we should be concerned with how people learn to acquire special skills and knowledge. How does a person become an expert? Is this a special skill that we can teach? More generally, we want to improve public education in general. How do people acquire "general knowledge"? How, in fact, do we learn to learn? How do we acquire effective working habits? How do we learn to organize our memories? What is involved in our proficiency to solve problems? In short, what is the nature of our thinking skills, and how do we acquire them? To what extent are these qualities affected by our Self-images. To what extent is learning innate, and to what extent is it affected by what we learn about learning itself?
Distinguish between teaching known facts and theories about science and teaching how to think like a scientist! Example: Don’t try to prove a theory is right: better to see which of two theories fits more evidence—and then propose theories about the exceptions.
How does Science differ from religion? Religion encourages some collection of “faiths”—whereas the goal of most scientists is to discover here and why “established laws” may be wrong, and then to make new hypotheses. In other words, always keep testing one’s old ideas.
NOTE: computer science, beginning n the 1950s, provided a hugely important set of ways to represent complex processes. Perhaps this should be considered as ‘basic’ as those “R’s.” Computers changed everything. First ‘science’ of Complex processes. CS is a whole new world—much like mathematics, but also very different. A thousand new concepts!
Most adults are afraid to learn about computers. In fact, most adults don't even know how to set their wristwatches.
How to be "computer-literate." Literacy means both reading and writing. But most books and courses about computers only tell you about writing programs. Worse, they only tell about commands and instructions and programming-language grammar rules. But real languages are more than words and grammar rules. There's also literature -- what people use the language for. No one ever learns a language from being told its grammar rules. We always start with stories about things that interest us.
The importance of reflective thinking.
Naïve theories of memories—instead of explicit thinking about representation, etc.
Obsolete theories about reinforcement, rather than [conflict idea of xxx]
In the present-day educational industry, the most popular theories of learning emphasize the role of positive reinforcement -- of learning by being rewarded for success.
In the behavioristic classroom, such issues are simply never faced; instead, the pupil is presented with a sequence of exercises that are so carefully graded that no new problem will ever seem very difficult, because it is so little different from the previous ones.
This often appears to work in the classroom, but I doubt that it is good preparation for reality -- because it does not address the question of how our pupils get new ideas, or how they can better organize old ideas. I suspect that as we engage increasingly difficult problems, we learn more from failure than from successes -- because, in the course of solving hard problems, things often must get worse before they get better. [Negative Expertise]
Speed: the Evils of “Show your Work.” E.g., the distortions caused by grading, etc.
When that happens, it seems to me, a person must be able to switch to a different, non-reinforcement kind of learning. In the course of creative thinking, a person must be prepared to recognize temporary failures -- and to learn from them. Simple reward is not enough; one must actually learn to enjoy each momentary setback and transient discomfort. A creative thinker learns to relish (consciously or unconsciously) each moment of self-criticism, and each pang of distress, as a valuable moment of growth and development. For, in doing this, one comes better to understand the structure of the domain one is learning; we must learn the bad parts as well as the good, and know about the most likely bugs and mistakes we can make, as well as the easiest solutions. And I have the impression that the final result of the "positive reinforcement" approach can in the end be tragic; when such a child is confronted with a more novel situation, that child has virtually no recourse but to "try harder" or fail, because of not possessing suitably powerful strategies for how to organize and learn a new subject that has not been so carefully prepared in advance by a skillful teacher.
What are good ways to organize your time? How should you plan your activities? What should you do when a Plan goes wrong?
When some attempt fails, what should you change? When you succeed at some goal, then what should you learn? When many things happen, which ones should you remember— and how should you describe or represent them? More generally, when anything happens, what kinds of questions should you ask— and what are some good ways to answer them?
What kinds of situations do people face— and what are good ways to deal with them?
How should you manage your social relations? How should you choose which mentors to trust?
Main idea: General education vs. Expertise. The experience of learning a particular skill in substantial depth. What is it like to have a ‘deep understanding of something?
Our Thesis: Most of general education will be wasted unless a child already possesses at least one experience with understanding what it is like to acquire and use some particular subject in great depth. (One might suppose it would be even better to develop several of these—but confirming this would need some evidence, because there might be disadvantages to starting out with more than such model of expertise.)
I’ve never seen much discussion of this; instead, it seems to me, that we tacitly assume that this sort of synthesis will happen spontaneously: just expose a child to many subjects—and, somehow, then, it eventually will all be put together, or ‘integrated’ or ‘absorbed’, etc.
For once this has been accomplished, then, when a child starts to explore a new realm or domain, that child will already be equipped with one or more prototype models and strategies for building a new such intellectual structure, to represent the knowledge in that particular new realm.
Many little details, rules, reactions to deficiencies. Fixing bugs, without starting over. Multiple levels of tactics and strategies. Good collections of analogies. Knowing the most likely mistakes and causes of failure — and how to fix, repair, get-around them. Knowing which level to work on, and when? Knowing how to acquire more abilities at each level.
Children do this in their Hobbies and Sports — but not often in school. Why not?
"Learning to a test"—which forces teachers to spend too much time on indoctrinating very small fragments of knowledge or skill, because these are easy to “grade” or “rate”. Project-skills take time to produce, and are much harder to evaluate. So schools leave these out. Except in “extra-curricular activities.
Vertical Education.
In other words, I don’t like the image in which every child is made to spend almost of its time at learning some simple versions of history, literature, arithmetic, geography, etc.
Then what? I think that the critical thing is to learn about what it is like to understand something more deeply, or vertically, or – it needs a catchier name.
A common view is that our schools should aim toward providing each student with a “broad and general education.” Subject-based classes attempt to do by teaching each child about each of a set of separate subjects. To do this, conventional classrooms divide most of every pupil’s time into “hours,” each of which teaches some fragments of knowledge about some particular subject — such as history, language, or mathematics.
In contrast, in real–world activities, some problems take only a minute to solve, while some projects require hours or days. In those large-scale tasks, it can take some time for a person to “get back” to a previous state; this suggests having longer unbroken periods
Knowing a little about many different things. A general education can give you the resourcefulness to change your job. So its value is to keep you from getting stuck in a job you don’t like.
One goal of education is to discover one’s potential specialties.
Generally, my image of a good education is not to aim at a “general education.” That is, a broad but shallow curriculum in which the first few years are to learn a small amount about each of many different things. [All children will do that in any case.]
In other words, I don’t like the image in which every child is made to spend almost of its time at learning some simple versions of history, literature, arithmetic, geography, etc. Until they are older.
OUR BIG THESIS: A general education cannot work and very well unless and until one has been through the experience of understanding of some complex, deep structure.
Then what? I think that it would generally be better to try to learn to develop the skills involved in understanding a fewer subjects or topics more deeply, or vertically, or – it needs a catchier name: So we’ll contrast “Vertical vs. Horizontal Education.”
Then, one may be able to do apply these same skills, by analogy, the building representations and processes with which one can understand and manipulate other subjects. In other words, my conjecture is that the secret to “ general education close “ on “ might mean having had the experience of organizing a specific educational structure coax summation
(Is what can happen when a child develops a specific engagement or obsession with particular hobby or activity?
Thinking about how Thinking Works
Encouraging use of Multiple Methods
Mentally Practicing Physical Skills.
The “Adventure-Game” anecdote.
The vertical ones contain towers of structures, at multiple levels of abstraction, etc.
The horizontal ones are more-or-less level.
Other structure:
Tree-ontologies. In most, the layers are superficial
Trichotomy. Semantic networks have more kinds of connections: vertical and lateral. The side-links are important because they lead to useful analogies!
Curriculum vs. hobbies, etc.
Surely it is important to learn to make and use multi-layer skills!
In (some) hobbies. Math club. A business. Maybe some sports, but . . .
(In fact, for many children, is this their principal tower-experience?)
Clubs: it is likely that the organizer may be a good potential mentor! OR anyone who is advanced in that field.
The need to have cognitive maps for various subjects and specialties. The very concept of a field, subject, or realm of expertise.
== Writing a story: plots, characters, interactions, motives and subgoals, etc. (But the linear surface of language makes these hard to explicitly represent! E.g., see Tonfoni)
The real trouble with education is that so few students ever acquire much vertical mastery of any subject. It is easy to begin a subject, but if you don’t go on to develop powerful technical ideas the subject eventually stops making progress.
My theory of education is inverted. You should not start with a “general education.” I don't much sense in trying to make a survey span of subjects like history or literature, because I don’t think one can understand generalities until one knows the nature of some particular “vertical” specialty.
So I think we should first aim at developing a few vertical skills—that is, ones in which one operates at multiple levels of process and representations. Tower instead of Pancake! Thesis: Postpone ‘general education’ until the child knows how to develop a specialized, deep, and powerful skill.
“You don’t really begin to understand x until you understand it in several ways. What is it like to experience the sense of understanding something at many different levels—and possessing the skills to navigate a variety of different ways to represent—and to think about—the same subject in many different ways! Here is why I think that this should be at the very center of what we call Education:
What does it mean to understand something? Quotation about multiple ways. If you understand something in several ways, then you’re less likely to Get Stuck, because you can switch to another track. This should be our central Educational Goal! What is involved in understanding a ‘fact?” Needs links to analogies, Goals it can help with, Stories and anecdotes, etc. Learning particular facts and skills may be useless unless one links them to higher layers —or “Mental Critics”— that help you to decide when and how to use them.
"Never seek the "real meaning" of anything. A thing with only one meaning has scarcely any meaning at all. The best ideas are groups of thoughts where each lends meaning to the rest -- the way each strand of a rope or a cloth keeps the others from falling apart.
Whenever you make a theory, be sure also to make some alternatives. This way, you’ll ‘own’ many theories. You won’t feel ‘abandoned’ when one of them fails; instead you’ll be able to improve it.
What am I? How did I get there? What goals do I hold, and how did I get them? How do I manage my own ideas? How do I deal with new sets of Memes? How do things interact? How to make decisions. Balancing short- vs. long-term goals, predictions, etc.
What are theories? Summarize the basic idea in “Matter, Minds, and Models.”
Idea: a monitoring program that looks at each child (perhaps once per month) to detect an overall “deficiency in ability to think obsessively”!
{We recognize ADHD as a sort of disorder—but perhaps we should also consider some opposites!) Instead it may be an opportunity to help to develop a higher level of competence.
Development of new school materials. The idea of building one's own animal, with sensory, motor and behavioral systems. This educational conception could reconfiguration many ideas are usually treated separately in Biology, Mathematics, Physics, Social Studies, Psychology, and Economics - and, in many aspects, never discussed at all in School. The central subject is Behavior, oriented toward formulating interesting principles of behavior of individuals and organizations, and realizing them in working, experimental
Development of cognitive skills:
Problem Solving Strategies = Ways to Think. Learning their common bugs and limitations! “Critics and Selectors.”
Representations, data structures, retrieval methods, Inference mechanisms, Motivational systems, Learning useful models. Give people access to communication networks. Better graphical expression for computers. Interposing experienced human request translators.
EXPERTISE vs. Commonsense. Fixed script learner models. Menus adaptive interactive language. Models vs. realistic situations
Cognitive skills. (From Logo Introduction?] Some educators maintain that what is most vital is to find ways to help our children learn traditional "basic skills" such as reading and writing, arithmetic, geography, and other traditional subjects. Certainly these are necessary. But just as certainly, those skills are not sufficient for dealing with modern industrial life. In this essay, I will argue that it is even more important to help our children also to learn how to build their own mental management skills -- for the growth and expansion of their own minds. We usually think of education in terms of what children learn, but we rarely teach about learning itself - about how children might learn new ways to learn.
In general, we have to be concerned with education in two domains: for specialists, and in general. For training specialists, we should be concerned with how people learn to acquire special skills and knowledge. How does a person become an expert? Is this a special skill in itself? If so, how do we teach it? More generally, we want to improve public education in general. How do people acquire "general knowledge"? How, in fact, do we learn to learn? How do we acquire effective working habits? How do we learn to organize our memories? What is involved in our proficiency to solve problems? In short, what is the nature of our thinking skills, and how do we acquire them? To what extent are these qualities affected by our Self-images. To what extent is learning innate, and to what extent is it affected by what we learn about learning itself?
Computers today are not much like good tutors. They do not have much understanding or sympathy; they know little about the students' minds. Nor do they know much about the ordinary world, in which those students live. [Extract from Panalogy Proposal]
Don’t accept many popular myths. Don’t follow the majority. Avoid Fads Don’t believe that X can’t be done. Don’t believe that X is inexplicable. You simply don’t yet have the right theory. Challenge Impossibility “Proofs”
Develop a specialized, deep, and powerful skill. Postpone ‘general education’ until the child knows how to develop a powerful skill. Programming is a good one because it has endless levels of abstraction. So is Math.
Music. Try to make theories of what it does and how it works. Develop the theory of groups of the Circle of Fifths, and make a theory about how to modulate with diminished sevenths.
How would we like children to think about their bodies? Some might like to see a firmly mechanistic, "biological" view of the body as a system of organs interacting to produce behavior. Others might want to emphasize the adaptiveness of such systems. Some might want to emphasize their mysteries and complexities. Some want to emphasize the differences between man and animal and teach the wonder of being human, while others want to emphasize the continuity of evolution and our one-ness with animals and the rest of nature--and that evolution is still in progress.
The present school-education system supports none of these goals! When a child dissects a frog or a chicken is likely to conclude that bodies are messy, fragile, disorderly complexes of slimy stuff. Some might say, "that's how it is so we should accept it” But descriptions aren't true or false; they each serve different purposes. Confront that notion of "slimy" as possibly useful: examine the details of how visceral organs are supported inside the body, and recognize that elasticity will suffice in some situations, but that lubrication may be needed in others. The body has many jobs. To do them, we divide into subproblems. Respiration, Locomotion, Reproduction, and Nutrition each involve many subsystems. These systems interact in various ways. Thesis: much of our complexity is just to reduce interactive complexity itself! Thus, to achieve a locomotion goals, the body must be compact and graceful. Therefore the viscera must be packed compactly - but also supported so that motions do not strain them or their functional attachments. So organs need mechanical anchors and tree-like structures to distribute forces. Sometimes such supports must be confined, and interactions with other organs reduced. One way is just to lubricate their surfaces - and motivated observation shows why certain organs are so coated - and others not. Thus "sliminess" of viscera is not a mysterious, qualitative feature of a biological system, but a purposeful, specific design device for minimizing certain support interactions; in short, a definite "debugging" technique. Perhaps, then, we should first provide functional and behavioral models before dissection. The "discovery method" has pitfalls and one can't expect to discover much by manipulating dead animals without preparatory cognitive models.
Older generations still expect biology to be incomprehensible, and we still have unsound holistic principles and ideas in our language and school curricula. Instead of servile admiration of mystery, we might prefer an open-eyed desire to understand the design issues and solutions that are involved.
Another issue is to be concerned more with behavioral images than postural and digestive images! Traditional biology puts only token emphasis on behavior, learning, thinking, etc. and does not supply coherent alternative models for personal use. However, one can equip children to understand the behavior of feedback-directed goal-controlled systems, so that they can design and build or simulate the locomotion of an animal. This encourages thorough understanding of "first-order models" of such things, how well they work, how they fail, and what to do next.
Very little Science. And very little mechanics. Construction toys nearly disappeared. Plastic toys, cars you can't fix, appliances with "no user-serviceable parts". Children have no motive to understand things. LEGO developed robotics kits, following Papert's work in the 1980s. So did some other toy-makers. Some children learned a great deal from this.
SUPERSTITION. In the US, there developed a great tolerance for other people's cultures. Unfortunately, it was indiscriminate. Everyone accepted all sorts of astrology, occultism, mysticism, etc. All ideas were considered equally valid. Children how exhibited signs of critical thinking were considered intolerant and antisocial.
TOLERANCE. In the U.S., we wanted two things: good science education and respect for other persons' ideas. But how can we ask people to think in scientific, critical, skeptical, ways while, at the same time, accepting all those popular prejudices and superstitions. This put an impossible strain on the teachers.
ENTERTAINMENT. How marvelous that a human being, with that massive intelligence and unbelievable abilities - can watch sports games for hours. What a phenomenon. It is hard to predict what people will do in the future, because it is hard to explain what they do the present; they don't seem to like using their minds very much. Will they use them at all, in the future, when it becomes even less necessary?
TEACHING MACHINES. "Computer Aided Instruction". Good Machine-Teachers must "know" what the student is thinking.
PERSONAL COMPUTERS. Typical 10-year lag between advanced supercomputers and personal desktop equivalents. The child of 2003 has the equivalent of a Cray-2 or a CM-2. Is there educational improvement - or marching morons? The computer is largely brain-controlled by various kinds of interfaces: eye and face tracking, hand signals, etc. When is it feasible to use brain waves?
Why would one want to accumulate knowledge? Because one needs it to solve problems, achieve goals, cope with complicated situations, etc.
However, to make knowledge useful one will need good ways to choose which facts to retrieve—and this means that one’s fragments of knowledge must be interconnected in several ways (list analogy, similarity, relations to goals, etc.0.
One must develop skills so that, when needed facts are not available, one may be able to induce them from other things one already knows! In other words the nature and structure of the ways that one represents a new knowledge must be shaped in relation to the skills that one is likely to use in the future.
What kinds of educational situations could lead to constructing resourceful networks?
Thesis: this is best done by accomplishing projects—rather than learning many separate fragments.
So we have to think of sequences of appropriate projects— and the selection of these should involve both the interested the student and the preparation of the student.
Programming is a good one because it has endless levels of abstraction. So is Math. Even Music can be seen in such ways: if one is presented with theories of what it does and how it works. Develop the theory of groups of the Circle of Fifths, and make a theory about how to modulate with diminished sevenths.
“Natural and Function blocks of time, instead of arbitrary 50-minute “hours.
(We need to shape the networks so that kids don’t get addicted to games that don’t lead to useful skills.)
(For example, ArmadilloRun helps children learn a lot of ‘qualitative physics.” Controlling rocket ships. Finding ways to brace flimsy structures, etc.
In a typical math curriculum, you learn to add and multiply—but you don’t learn very much high-level knowledge about when such skills are appropriate. We don’t do well at teaching kinds to take on hard projects all by themselves.
We expect our schools to help with these. But most of the acquaintances that I consider to be successful are ones who, in their early years, pursued various hobbies and interests in ways that schools did not facilitate.
Not all hobbies lend themselves to constructing extensive vertical skills—that is, ones that are needed to deal with a problem that has many levels of complexity, abstraction, organization, etc I don’t think that this comes with collecting baseball cards!
I see this as more constructive than what usually comes from such hobbies as collecting stamps baseball cards, or stamps, etc. These begin with collections of objects all of the same character. What then? Well, it is possible that one can go on to develop ideas about the origins of those objects and some of the relationships between the events that they represent. However, that rarely leads anything much more to more than shallow networks of information—although it can occasionally lead to deeper ideas about the social and political organizations that produced them.
Contrast this with hobbies like learning mathematics, which can eventually lead to towering structures of increasingly abstract and powerful ideas; it can begin with geometric concepts and symmetries, and go on to ideas about groups of transformations, and mappings and homomorphisms; Eventually this can lead back to understanding arithmetic, and why (for example) there is only a single way to factor an integer as a product of primes: in the realm of topology, this can be seen as an instance the wonderful Jordan-Holder theorem that applies to all commutative groups of transformations.
[Sub-essay on this as one of the ways to understand the world we’re in; today, only a minuscule fraction of the population ever seen even a glimpse of this, because it is not often taught until one is a graduate student in mathematics or physics. An example of our failure to provide our students with any substantial “cognitive map” of the kind I mentioned in Memo–1.
In other words, a person who digs into modern mathematics (which very few people ever do) finds a new mental world in which one learns to see the same thing from perhaps a dozen successively higher levels of abstraction; an experience that could be compared to climbing an intellectual mountain—rather than aimlessly wandering around a conventional intellectual desert.
To do this, of course, one needs the kind of guidance that comes apprenticeship or mentorship; otherwise one is too likely to get stuck at some fixed horizontal level.
This is what often happens when a child develops what we call a hobby: an activity in which one spends a substantial amount of self-directed time at acquiring a substantial skill or body of knowledge—for example, in the course of trying to build a model car or airplane. T
In memo 2 “Most children have individual interests—hobbies, pastimes, and even obsessions—which may not be seen by their teachers as unrelated to the standard curriculum. Yet each person will eventually, need to find some profession or job in society—and while most people do find useful roles, quite a few end up with nothing to do, and this can be tragic or dangerous.” This suggests that we should take care not to classify a child’s ‘peculiar special interest‘ as being an eccentricity that interferes with that child’s “normal” progression toward a “general education. Instead, in many instances, it might be better to recognize and encourage those individualistic preoccupations. I’ll return to this in a later memo on “project-based” learning and education.”
Are there kids who don’t have hobbies? Why did this happen? What happens to those kids—and should this condition suggest intervention? To what extent do sports serve this function?
How many children don’t have any hobbies, how does this happen, and what its consequences?
[Thesis about specialization, etc. Children should first become experts, then generalists! Hobbies, etc. The trouble with modern school classes, etc.] Develop a specialized, deep, and powerful skill. Postpone ‘general education’ until the child knows how to develop a powerful skill. Programming is a good one because it has endless levels of abstraction. So is Math.
BUILDING A TABLE: Lego, Tinkertoy, Wood and nails, etc. Simplified models, etc.
Example of a Productive Hobby: Model airplane.
Repeat: A common view is that our schools should aim toward providing each student with a “broad and general education.” Subject-based classes attempt to do by teaching each child about each of a set of separate subjects. To do this, conventional classrooms divide most of every pupil’s time into “hours,” each of which teaches some fragments of knowledge about some particular subject — such as history, language, or mathematics.
Contrast this with what happens when you want to solve a certain hard problem, or to develop a substantial project. Some problems take only a minute to solve, while other projects require hours or day. In such cases, you’ll want to divide up your time in ways that depend on what you want to accomplish. For example, in the course of trying to build a model car or airplane, one needs to acquire some substantial skills or bodies of knowledge, such as:
How to shape materials? Knife, saw, chisel, file. Melt, mold, press, bend.
How to fasten them together? When is it best to use nails or glues? Solder, weld? Nuts and bolts?
How to use and maintain tools: sharpening a drill or a knife, etc. How does one minimize friction?
How to increase a structure’s strength? How to make it more rigid or more flexible?
How to make parts that move properly; how do axles and bearing work?
What are good ways to store enough energy? How can one minimize friction?
More generally, how to plan an overall design?
For example, consider a project like building and flying a model airplane. In the course of pursuing this kind of hobby, one learns about different materials, ways to form and modify them, some of their various properties, ways to combine them into more complex forms, etc. Then some ideas about how the wings work, and why the forces involved require the wing to be stronger near the body than near the tips, etc., and why some parts will therefore need struts and braces, and stronger adhesives, etc.
How can a child organize such a diverse body of knowledge? [Collection of examples, stories, etc. Ways to make analogies. Build towers of increasing abstraction (instead of Pancakes of unstructured data).] To organize this, one needs to develop a Tower of “vertical” skills—composed of multiple levels of processes and representations.
A simpler job: how to make a book, attach or “bind” the pages, etc. Examples of projects: Build a model automobile, airplane, robot, etc. Each of these involves such sub-skills as Mechanical structures, electrical controls, computer programs, user interfaces, and the arts of design, etc.
Projects and Hobbies
What’s in a hobby? Whole projects!
Music: fingering. Harmony. Rhythm. Expression. Story-telling, etc.
Writing. See Poe’s essay on The Raven. Plots, characters, expressions, styles, etc.
Sports. Tactics, strategy, bodybuilding, health, resource management. Models of particular opponents (specific problems to solve.) See 4-minute-mile book!!! Anecdote. Camping. Bicycle-racing. Etc.
Asking questions and answering them. What is the Main Problem, Obstacle, or Opportunity?
What differences does one want to Make or Remove?
How to organize? Dividing the problem into parts. Making a list, or tree, of more complex diagram.
The joke about “Goals and Objectives”! This limits the planner to a 2-level plan!!!
How do you interrupt and resume a project? How do you return to a previous mental state? How do you store the ‘context’?
(On computer, you could assign a programmable key!)
What are examples of productive large projects?
Organizing large programs, Build a steam engine.
A tower theory in mathematics. Group theory: so much from so few axioms.
Organizing a business. Synthesizing a chemical. Building a Robot. Can be good because needs to debug a complex system. Mechanical project is OK, but the software also in important—and best done with a simulation!
Some day, kids could do AI projects—but not until someone provides an adequate shell—such as a usable Critic-Selector model.
Produce a Movie or Play. Writing a story. Mechanics: TinkerToy.
Electronics. The oscilloscope became your electronic eyes! Heathkit, etc.
Mathematics. Your mind was your eye
Chemistry. Sets not good. Inadequate equipment. Still---
How can we learn a skill that has no use at the present time, but might help us accomplish future goals?
Technical education: Why do so many people become afraid of technicalities? -- Of mathematics and science in general?
Knowledge vs. Skill Children must learn how to become experts. This innovative goal is shared by projects like Apple's Vivarium and MIT's Logo-LEGO, which are trying to provide children with facilities for building artificial animals with artificial minds.
Children need hobbies.
How to develop "tower skills?" Learn how to become experts. Teach specialty first -- or at lest, early.
Children should be encouraged to specialize. Teaching (encouraging) children to invent their own theories.
Peculiarly important because: Foundation of many sciences, engineering, etc. [Sub-essay on mathematics as one of the ways to understand the world we’re in; today, only a minuscule fraction of the population ever seen even a glimpse of this, because it is not often taught until one is a graduate student in mathematics or physics. An example of our failure to provide our students with any substantial “cognitive map” of the kind I mentioned in Memo–1.
In other words, a person who digs into modern mathematics (which very few people ever do) finds a new mental world in which one learns to see the same thing from perhaps a dozen successively higher levels of abstraction; an experience that could be compared to climbing an intellectual mountain—rather than aimlessly wandering around a conventional intellectual desert.
To do this, of course, one needs the kind of guidance that comes apprenticeship or mentorship; otherwise one is too likely to get stuck at some fixed horizontal level. Find reference to mathematics unique transfer-ability!
People often try to explain computers the same ways they explain ordinary things -- the way they teach arithmetic by making you learn "tables" for adding and multiplying. So they start explaining computers by telling you how to make them add two numbers. Then they tell you how to make the computer add up a lot of numbers. The trouble is, that's boring. For one thing, most of us already hate adding up numbers. Besides, it's not a very interesting story. You can't blame teachers for trying to make numbers interesting. But -- let's face it -- numbers by themselves don't have much character. In fact, that's the main reason why mathematicians like them! They find something magical in things that have no interesting qualities at all. That sounds like a paradox. Yet, when you think about it, that's exactly why we can use numbers so many different ways! Why is it that we get the same kind of result when we count different kinds of things -- whether we're counting flowers or trees or cars or dinosaurs? Why do we always end up the same -- with a number? That's the magic of arithmetic. It wipes away all fine details. It strips things of their character. The qualities of what you count just disappear without a trace.
Thesis: it is Important for a child to get attached to someone who shows that it is exciting to learn new things.
Self-respect: don’t waste yourself. Don’t let your ‘culture’ persuade and reward you to become almost the same as all the others. Instead, find a special, distinguished mentor—to help you find ways to learn things that others don't! [Re: advice to students.]
Idea: a monitoring program that looks at each child (perhaps once per month) to detect an overall “deficiency in ability to think obsessively”!
We recognize ADHD as a sort of disorder—but perhaps we should also consider some opposites!) Instead it may be an opportunity to help to develop a higher level of competence.
Outlining a proposal. Mental or document. Function, Implementation, Application Debugging, Marketing,
Finding collaborators and critics, etc. Finding a Mentor with relevant experience with similar problems. (What problems are similar, etc.?) Find testers or beta-users, etc.
Essay on taking things apart. developed by dissecting and understanding complete systems. Sure, we were always reading books about science, and we often were building simple things. But what a rank beginner could do was limited. Yes, you could buy a big kit of parts from Knight, or Heathkit, or later, Radio Shack, and build yourself a complicated radio set. But then you were unlikely to understand it or fix it if you'd made any mistake.
In many ways, the basic sciences are more destructive than constructive. You analyze more than synthesize. Break apart, not put together. You must know how the parts work, first, before you can figure out how to assemble them. For us the greatest school was the surplus store. My pediatrician, Dr. Michael Karsh: whenever I had some complex object, he would let me fluoroscope it.
Of course we want to improve schools, and get better teachers and so forth. But perhaps another of our goals should be developing ways for children to escape into better intellectual communities, where they can work on more substantial projects and develop deeper skills. Also, perhaps not everyone would agree about all the goals that we want our schools to achieve. To what extent do we want our future citizens to be cooperative and compliant—versus independent and critical thinking? To … share the same collections of beliefs?
From: cmbecker@space.mit.edu (Christopher M. Becker): If an engineer doesn't take any philosophy or literature, people label him a geek, nerd, or other term that indicates that his/her education is too focused on engineering courses. Is there a corresponding attitude towards students who have tunnel vision directed at humanities, political science, or other non-technical fields? In my experience the answer is no. The result may be dangerous. "Trillion dollar deficit" doesn't sound that scary unless you can comprehend large numbers. Million, Billion, Trillion sound alike and for a lot of people that's where the understanding stops.
Some talk about allowing children to make choices about what they should learn. I think that’s too simplistic, simply because they don’t know enough to make good such choices by themselves. However, I do prefer flexibility — and see the best way is to try to make sure that every child can derive enough wisdom from enough mentors. That is, individuals who know that kid and can help to guess what might be good to develop their interest in.
How many hobbies? Is it better to develop several of these? Research question: there might be disadvantages to starting out with more than model of expertise.)
Problems with peers who insult ‘nerds’. The problem of bullies and other aspects of social atmosphere. Too much concern with what others think!
Importance of learning that Most Statements have some Exceptions! Most processes have obscure bugs! The importance of negative expertise!