It is better
to solve one problem five different ways, than to
solve five different problems one way. — George Pólya:
Some parents want their schools to prepare their children for future jobs and careers. Other parents want schools to teach specific sets of ideals and beliefs. Some parents even want their young to learn to develop their own, independent ideas. But regardless of those different goals, most schools assign most of their pupils’ time to learning scattered fragments of knowledge about some so-called “basic” subjects—like reading, writing, arithmetic, science, and tidbits of cultural history—and then consume the rest of those children’s time with incessant tests and homework assignments.
Surely, that kind of “broad education” helps many children to comprehend many aspects of the worlds they’re in. However, I question how well it prepares them to deal with more complex real-world problems—because it is hard to exploit separate fragments of knowledge until one acquires the mental skills that one needs for retrieving and using the relevant ones.
Nevertheless, although we rarely teach children about how minds work, quite a few of them do become experts—in what we call their amusements and hobbies—as when they play computer games, or refine their athletic skills, or build structures with construction sets.
§2.6 of The Emotion Machine: The “playfulness” of childhood is the most demanding teacher that one could have; it makes us explore our world to see what's there, to try to explain what all those structures are, and to imagine what else could possibly be. Exploring, explaining and learning must be among a child’s most obstinate drives—and never again in those children’s lives will anything push them to work so hard. 
Indeed, some children focus so much on their hobbies that their parents fear that this will conflict with their education—and try to find ways to discourage them. However, this essay will propose, instead, to postpone “broad” education until each child has had some experience at becoming an expert in some specialty.
Critic: Do you really believe that that’s feasible? How could a six-year-old child become an expert? Surely one first needs to crawl and then walk before one can begin to run? And surely a child must start with concrete examples before dealing with more abstract descriptions.
On the contrary, some recent experiments weigh against that popular belief:
Jennifer Kaminski et al: “Transfer of conceptual knowledge is more likely to occur after learning a generic instantiation than after learning a concrete one. … Knowledge acquired through a generic instantiation can be transferred to a novel isomorph, while knowledge of a relevantly concrete instantiation does not transfer spontaneously. For relevantly concrete instantiations, the structural knowledge appears to be bound to the learning domain so that it cannot be easily recognized elsewhere.” 
So here we’ll propose to re-aim our schools toward encouraging children to pursue more focused hobbies and specialties—to provide them with more time for (and earlier experience with) developing more powerful sets of mental skills, which they later can extend to more academic activities. These issues are important because our children today are growing up in increasingly complex and dangerous worlds—while our institutions are failing to teach correspondingly better ways to think. The result has been a global pandemic of adults who lack effective ways to deal with increasingly challenging situations.
The Emotion Machine starts with the idea that every brain contains many “resources,” some of which recognize various patterns, and others can supervise various actions; yet other resources form goals or plans, and some contain large bodies of knowledge. Then we envision a mind as composed of a multi-level “cognitive tower,” whose lowest levels are mainly assembled genetically—whereas the higher-level processes grow in ways that depend less on inherited genes, and more on their interactions with the activities in the levels below them.
Values, Censors, Ideals, Taboos
Self-Reflective Thinking à Constructing Self-Models
Reflective Thinking à Planning and Self-Criticism
Deliberative Thinking à Reason, Search, Compare, etc.
Learned Reactions à Representing one’s Experience
Instinctive Reactions à Instinctive Urges and Drives
The Emotion Machine suggests that building such towers is the source of the unique resourcefulness that distinguishes us from other animals. If so, this suggest that a child’s first such constructions will have a large effect of the quality of that child’s later development.
Conjecture: once a child builds a cognitive tower that works well in some particular realm, that child will thereafter be better equipped to develop proficiencies that can be used in other domains.
The idea is that it seems plausible that the first few such developments could have a major effect on the qualities of that child’s future ones—because those will the child’s first experiments with organizing such ‘vertical’ structures. If so, then this would imply that our children’s early education should focus on activities, hobbies, and specialties that have the ‘desirable’ kinds of such qualities. Of course, this also implies that we’ll need good theories of which such qualities would be desirable’and what kinds of curriculums could help to promote them.
In particular, Chapter 7.5 of The Emotion Machine suggests that, at each of those multiple cognitive levels, certain important resources called Critics observe some events in the levels below them—and react by selecting which sets of resources would be useful to activate next; this reorganizes the person’s mind to use a different “way to think,” of the sorts we mentioned in Memo 3. For example, whenever some mental process gets stuck, one Critic could suggest a way to split the problem into smaller parts; another Critic might recollect how a similar problem was solved in the past—and yet another Critic might suggest a different way to represent the situation.
If a problem seems familiar, try reasoning by
If it seems unfamiliar, change your way to represent it.
If problem seems too hard, divide it into smaller parts.
If it still seems too hard, try a simpler version of it, etc.
What happens when several such critics are aroused at once? This won’t cause much conflict if each of those Critics arouses a different set of resources because, in such a case, a person can “think several ways at once.” For example, most of us simultaneously entertain processes involved with social, linguistic, visual, logical, and other kinds of mental processes—e.g., all of the kinds of thinking described in Howard Gardner’s view of the mind.
But what if your Critics’ suggestions conflict—for example, when multiple Critics try to control some of the same mental resources? (What happens when you try to think two tunes at once?) Then you’re likely to “get confused”—and if you can’t find some compromise works, our theory suggests that this condition itself should turn on a higher level Critic—namely, one that can detect this particular kind of confusion, and suggest an appropriate remedy. Then, of course, the quality of your hierarchy of critics will be a major influence on your competence and resourcefulness—especially if, when you’re confused, your Critics can diagnose why you’re confused.
Suppose you get stuck at achieving some goal. This could lead you to conclude that you’re simply not suited for that kind of job—perhaps because you lack the right kinds of ‘talents, ’ or just don’t have enough ‘intelligence.’ However, if you can recognize how you got stuck, this may suggest more constructive alternatives: perhaps you did not activate the right kinds of resources—or need to acquire some new ones, etc.
Seymour Papert: “Most children seem to have: and extensively use, an elaborate classification of mental abilities: "he's a brain," "he's a retard,” "he's dumb,” "I'm not mathematical-minded". The disastrous consequence is the habit of reacting to failure by classifying the problem as too hard, or oneself as 'not having the required aptitude, rather than by diagnosing the specific deficiency of knowledge or skill.”
What makes some folks more inventive than others? Why do some outshine others at solving hard problems? Why do some people less often get stuck? The most popular answers to questions like these assume that each person possesses a different amount of some faculty called ‘Intelligence.’ However, this doesn’t answer those questions at all, but only diverts our attention from them, because ‘intelligence’ is one of those suitcase-like words that we use at different times, for different kinds of purposes—while switching those meanings so fluently that we’re rarely aware of doing this. So, using the word ‘intelligence’ can lead to a sense of helplessness, because of offering nothing that you could change or do. However, as Papert pointed out, once you come to envision yourself as a host of different programs or processes, then, when you disappoint yourself, you can look for ways to ‘debug’ some of those processes!
Select appropriate representations: To think about any subject or question, you first need some ways to represent situations, goals, plans, ideas, and relationships—for example, as a verbal description, a pictorial diagram, or a list of constraints to be satisfied. How can we help our children to learn to develop new, better ways to represent knowledge—along with the kinds of processes one needs to manipulate those representations.?
Find appropriate analogies: Of course, one of best ways to solve a problem is to already know how to solve it. However, no two situations are ever exactly the same, So you can’t expect to remember as answer—unless you have also developed processes that can recognize useful analogies.
Negative Expertise: To deal with any hard kind of problem, a person must know some possibly useful strategies—but also one will need to know the most common mistakes that one’s likely to make. A superficial survey won’t help because one cannot achieve much competence unless, along with each separate fragment of knowledge, one also knows enough about the reputation of that fragment’s source, its common exceptions, the contexts it works in, and (when it fails) some alternative paths.
Construct more realistic self-models: Perhaps the most powerful way to solve a problem is to ask, “What makes this problem seem so hard me?” But you won’t be able to answer that unless you already have good answers to questions like: How do I make my decisions, and why? How did I get into this situation? What are my goals, and how did I get them? How do I generate new ideas?
In other words, before you can think about trying to change yourself, you’ll need to construct some models of how your mental processes work. However as Freud recognized a century ago, most of those processes work in ways that can’t be directly observed by resources in other parts of your mind; indeed, the higher levels of our minds may even develop ways to suppress or censor such attempts! Nevertheless, by collecting and analyzing evidence, we still can manage to achieve useful levels of self-reflection.
Chapter 7 of The Emotion Machine suggests a variety of mental skills that might contribute to our resourcefulness—such as learning that most ‘facts’ have exceptions, learning the most common kinds of mistakes, avoiding the most common ways to get stuck, and learning what to do when goals conflict. It’s also important to know multiple ways to represent things, so that if one method gets stuck, you can switch to another. And perhaps most important of all is the art of making “cognitive maps” of what one learns, so that one can make good decisions about which levels to work on, and when.
Some hobbies are conceptually “flat” in the sense that they keep applying similar processes to collections of “same-level” knowledge. We see this when children accumulate objects like comic books or statistical facts about movies or sports. In contrast, other more ‘vertical’ hobbies lead to higher towers of concepts about (for example) the causes, sources, and implications of their lower-level fragments of knowledge—and surely that greater range of mental processes will help one to deal with more challenging situations and problems. Consider some examples of these.
Thinking about Mathematic Concepts. Instead of the conventional trek through the desert of grade-school arithmetic, we can encourage children to start climbing the hills of ideas about symmetries, maps, and analogies—beginning with easy concepts about geometry, logic, group-theory, and topology. Such explorations can lead to more knowledge and power with less effort and time—and eventually make many other subjects easier.
Composing Music or Stories or Plays. Writing a stories, sonatas, or songs can involve many levels of plans and designs: one needs to construct a plausible plot and populate it with themes or characters with interesting and conflicts and tensions, all of which must be resolved in a structure that one must compress into a single temporal line! 
Athletics: Competitive, team-based sports are often claimed to help children develop useful ideas about cooperation, tactics, and management skills—and for many children today, this may be their only such activity. However, the enforcement of certain sports in schools causes great fear and shame to quite a few children. To be sure, sports can contribute to physical fitness—but surely we can find alternatives that do not cause so many injuries and disabilities! Also, we ignore the extent to which athletic prowess is largely genetic—hence it’s foolish to choose those champions as role models. Besides, competitive sports don’t always promote good social values; instead, they may even encourage wars, by teaching ways to deal with problems by using superior physical force.
Physical Fabrication Crafts: To build a working model airplane, one needs to learn substantial bodies of knowledge, such as the properties of different materials, ways to form and modify them, and ways to combine them into more complex forms. Then eventually, one may come to see why the forces involved require the wing to be stronger near the body than the tips, etc. Consider how many aspects such a project can have: How to shape materials by using knife, saw, file, and chisel—and when and how to maintain those tools? When and how to melt, mold, press, or bend? How to fasten things together by using nails, screws, solders or glues? How to increase a structure’s strength, by making it more rigid or more flexible, or adding additional braces and struts, and stronger adhesives? 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?
Simulated Fabrications: In recent times, Carpentry has nearly disappeared, and Electronics has turned into opaque ‘chips’—while Erector and Meccano sets have been replaced by boxes of modular LEGO blocks. However, today, children can simulate physical system on their computers; for example, with programs like Armadillo Run—or work with tens or hundreds of thousands of rectangular blocks at virtually no fiscal cost (See http://ldd.lego.com) Furthermore, today one can email one’s mechanical designs to companies that use “3-D Printers” to convert them into working physical models. Such facilities are quite expensive today, but will soon be cheaper: see en.wikipedia.org/wiki/Fab_lab.
Computational Fabrications: Although we may regret the decline of handicrafts, computer programming offers unlimited opportunities to build, test, and apply towers of increasing levels of representations. Hear Seymour Papert describing some early examples of this: “An example of such an experience is writing simple heuristic programs that play games of strategy or try to outguess a child playing tag with a computer controlled ‘turtle’. … A related example is writing teaching programs—like traditional CAl programs, but conceived, written, developed and even tested (on other children) by the children themselves. It is said that the best way to learn something is to teach it—and perhaps writing a teaching program is better still in its insistence on forcing one to consider all possible misunderstandings and mistakes. [Similarly, some such] children become passionately involved in writing programs to teach arithmetic and in the pros and cons of criticisms of one another's programs.” 
We need to recognize and remedy the common forms of hostility that ‘intellectual’ children are likely to face from popular ‘jocks’ in their communities; they often get called by derisive names like “nerd,” “brain,” or “geek—and are often excluded from other cliques. They may even get physical bullying—whereas there is far less such prejudice against children who excel in less technical fields. I suspect that this type of intolerance is a major problem in many schools, and it could have dangerous results: million, billion, and trillion sound much alike, and unless you comprehend such magnitudes, trillion-dollar deficit does not sound any scarier.
Gerald Sussman: My idea is to present an image to children that it is good to be intellectual, and not to care about the peer pressures to be anti-intellectual. I want every child to turn into a nerd—where that means someone who prefers studying and learning to competing for social dominance, which can unfortunately cause the downward spiral into social rejection.
This memo suggests that schools should provide the children with ample time for each to develop some specialties. I’m not proposing to eliminate all conventional classroom work, but only to allocate more time to higher-level projects and hobbies, and spend less time on drills, tests, and homework.
Of course, few teachers will have enough time or expertise to supervise so many specialized projects—so those children will need additional mentors—most of whom will have to come from outside. This was impractical in the past—but now we’re approaching an era in which a billion retired persons could fill those roles—if we can find ways to connect with them; for every hobby or specialty, we should be able to recruit specialists to give advice and to suggest other ways to proceed.
To what extent can a child’s mind spontaneously ‘self-organize’ its higher levels, without any external guidance? To what extent can we help children to learn how and when to make higher-level abstractions or to resort to self-reflection? I’ve never seen much discussion of this; instead, we assume that such developments happen spontaneously if we just expose a child to the proper kind of curriculum, that child’s mind will somehow construct appropriate systems of processes to represent those experiences. Then, when we come to recognize that some children excel at doing such things, we simply assume that those children are ‘brighter’ than the rest—instead of trying to find out what’s happening.
Would it help for us to discuss such things more explicitly? Memo 5 will suggest some ways to include more ideas about minds into our systems for early education.
 See http://web.media.mit.edu/~minsky/
 See www.sciencemag.org/cgi/reprint/320/5875/454.pdf or http://cogdev.cog.ohio-state.edu/fpo644-Kaminski.pdf. Also see 13.3 of The Society of Mind, and 1.2 of web.media.mit.edu/~minsky/papers/PR1971.html.
 See §8-7 of web.media.mit.edu/~minsky/eb8.html.
 See http://jeb.biologists.org/cgi/content/abstract/211/20/3266
In Teaching Children Thinking, 1980, http://www.citejournal.org/articles/v5i3seminal3.pdf
 This paragraph is adapted from a message by Christopher Becker .