MEMO1
 Some things that OLPC could do.

Topics:  
	Grade-Segregation  - Age-Based Classes 
	The 50-minute hour
	Subjects and Projects
	Imprimers  (older-students, web-friends, etc)
	Texts vs. Classes Education: Classics vs. Textbooks!
	Learning to Learn?
	Teaching Critical Thinking: 
	What is Mathematics? Why is Math so hard to learn? Mathematics is Vertical.
	Belonging to an Intellectual Community
Learning to Learn

A conventional school teaches various "subjects"-but the students are rarely exposed to discussions 0r theories about how human learning works.

[We do occasionally give advice about (for example) how much time to spend, etc.  But children very in many ways, etc.)

Why not ? I suspect that this may be mainly because, today, we have many theories of how people learn-and these theories disagree in so many ways that teachers cannot decide which ones to teach. So we tend to avoid these controversial issues and talk, instead, about various simplistic, behavioristic models.  {Success is rewarded, reinforcement, etc.}{mostly based on animals!  But consider "Jack teaching his dog: quote from TEM here.}

[The popular view:  find section about putting knowledge into a box, and then taking it out.  The trouble is that this is too simplistic; we tend to use the single word "learn" for many kinds of processes; does not face the fact that we use various structure we use for representing our knowledge and skills-and we do not yet have a well-established view of how all these are organinzed.  See xxx, yyy,  

TEM ¤2.5  'remembering' is not simple at all.  On the surface, it might seem easy enough-like dropping a note into a box, and then taking it out when you need it.  But when we look more closely, we see that this must involve many processes: You first must decide what items your note should contain, and find suitable ways to represent them-and then you must make some connections to them, so that after you store those parts away, you'll be able to reassemble them.

You might think of your memory as like a writing-pad, on which you can jot down mental notes.   Or perhaps for each significant event, you store "it" away in some kind of memory-box and later, when you want it back, you somehow bring "it" out of that box-if you are lucky enough to find it.   But, what kinds of structures do we use to represent those "its" and how do we bring them back when we need them?   Our recollections would be useless unless (1) they are relevant to our goals and (2) we also have ways to retrieve the ones that we need at the times when we need them.

Student: Can't we explain all this with the old idea that, for each of our accomplishments, we just 'reinforce' our successful reactions? In other words, we simply "associate" the problem we faced with the action or actions that solved it, by making one more If-Then rule.

That might help to describe what learning does-when seen from outside-but it doesn't explain how learning works.  For, neither 'the problem we faced ' nor  'the actions we took' are simple objects that we can connect-so, first your brain will need to construct descriptions for both that If and that Then.  Of course, the quality of what you learn will depend on the content of those two descriptions:

The If must describe some relevant features and relationships of the situation you faced.
The Then must describe some relevant aspects of the successful actions you took.

For Carol to learn effectively, her brain will need to identify which of her tactics turned out to help, and which of them only wasted her time.  For example, after her struggled to fill the cup, should Carol attribute her final success to the shoes or the dress she was wearing then, or whether the weather was cloudy or clear, or to the location in which those events occurred?

To retrieve information rapidly, a computer expert might suggest that we store everything in some single "database" and use some general-purpose "matching" technique.   However, most such systems still classify things in terms of how those things have been described instead of in terms of the goals that they can help us to achieve. This is extremely important because we usually know less about the type of thing we are looking for, than about the goal that we want to accomplish with it-because we're always facing some obstacles, and want to know how to deal with them.  

So, instead of using some "general" method, I suspect that every child develops ways to link each new fragment of knowledge to some particular goals it might help to achieve, and thus help to answer questions like these:

What kinds of goals might this item serve?  Which kinds of problems could it help to solve? What obstacles could it help to overcome? 
In which situations might it be relevant? In which contexts is this likely to help?  What subgoals must first be achieved? 
How has it been applied in the past?  What were some similar previous cases? What other records might be relevant? See Credit Assignment in section 8-5.

Each fragment of knowledge may also need links to some knowledge about its deficiencies-and the dangers and costs of using it:

What are its most likely side effects? Is it likely to do us more harm or more good?
How much will it cost to use it? Will it repay the effort of using it?
What are its common exceptions and bugs? In which contexts is it likely to fail us-and what might be good alternatives? 
We also link each item to information about its sources and to what certain other persons might know.

Was it learned from a reliable source?  Some informants may simply be wrong, while others may mean to mislead us.
Is it likely to be outdated soon?   That's why this book does not discuss most current theories about how human brains work. 
Which other people are likely to know it?   Our social activities strongly depend on knowing what others may understand.

All this raises questions about how we make so many connections to and from each new fragment of knowledge. I suspect that we can't do this all at once-and indeed there is some evidence that it normally takes some hours or days (including some sessions of dream-laden sleep) to establish new long-term memories.  Also, we probably add more links each time we retrieve a fragment of knowledge, because then we're likely to ask ourselves,  "How did this item help (or hinder) me at overcoming this obstacle?" Indeed, some research in recent years suggests that our so-called long-term memories are not so permanent as we used to think; it seems that they can be altered by suggestions and other experiences.

We all know that our memory systems can fail.  There are things that we can't remember at all.   And sometimes we tend to recollect, not what actually happened to us, but versions that seem more plausible.   At other times we fail to remember something relevant until-after several minutes or days-suddenly the answer appears-and you say to yourself, "How stupid of me; I knew that all along!"  (That could happen either because an existing record took long to retrieve, or because it was never actually there, and you had to construct a new idea by using some process of reasoning.) 

In any case, we should expect such "lapses" because our recollections must be selective; section 4-4 discussed how bad it would be to remember everything all the time: it would overwhelm us to recall all the millions of things that we know.   However, none of this answers the question of how we usually retrieve the knowledge that we currently need.  I suspect that we do this mainly by already having prepared in advance the sort of links discussed above.    [More in TEM Chapter 8-5.

[INDEED< WE DON'T TEACH THEORIES OF THINKING!  Again, because this is too controversial.  But then, we should teach the controversies!!!] 
[From new Yorker profile]  The 'secret' of intelligence is to have some parts of the mind that know certain things, and other parts of the mind that know things about the first part. If you want to learn something, the most important thing is for there to exist a "learning expert" part of your mind that know which other parts of your min dmight be good at learning that kind of thing. 

How do people build well-developed skills?  

Theory 1.  One learns many different fragments of knowledge, and then finds ways to piece them together.
Theory 2.  One already knows a somewhat similar specialty, and builds the new one [by analogy-that is, using the old one as a model to copy.]

And this suggests that we ought to put a priority on helping each child to a few extensive areas of expertise.   Note that this is quite a radical idea, because it is opposed to the conventional view that we should make every child focus on acquiring a "general education".

What is involved in developing an extensive specialty? Thesis: horizontal knowledge helps, but one also needs some organization so that one can retrieve and apply that knowledge.

Micro-aspects: finding good representations, procedures, organizations, and bodies of knowledge.
Learning: one needs multiple representations, so that when one gets stuck, one already knows some alternatives.
Attention Span

A friend of mine has a reputation for rudeness, because in the midst of a conversation, he sometimes abruptly walks out of the room!  What his companions don't realize is that this is actually a compliment --because he was so engaged by someone's idea that he needed a quiet place in which to think about it!

Similarly, when a child in a classroom appears to turn off, while trying to think about some new idea, a teacher may ask him to "be more attentive"  But what do we mean when we talk about such concepts like concentration, attention, and focusing on?

The teacher goes on, but the.  There are many kinds of "attention spans"
* The ability to keep absorbing stuff, without taking 'time out' to think about it.
* That's related to tolerating interruptions, and returning to previous states.
* --Limits to STM and LTM, etc.
* Different points of interest, and making appropriate sideways connections, etc.

What happens when a child watches TV for hours?
What happens when a child plays a computer game for hours?  Plays with sand?  Etc.

Here is a typical statement I found in an essay about early education: "A normal attention span is 3 to 5 minutes per year of a child's age. Therefore, a 2-year-old should be able to concentrate on a particular task for at least 6 minutes, and a child entering kindergarten should be able to concentrate for at least 15 minutes." - http://www.vibrantelectroniccourse.com/Education/p7.htm

 [So there can be basic conflicts between thinking and lectures.  There is no possible way to "pace" a lecture so that each member of the audience will have just the right amount of time to absorb and consider each point that is made.  Myself, I usually sit close to an exit so that I can discreetly leave, if I need some time to quietly think.]

Playing computer games.
The Big THING: learning a lot about some specific thing: The idea: general education cannot work and very well unless and until one has  been through the experience of understanding of  some complex,  deep structure.    (is what can happen when a child develops a specific engagement or obsession with particular hobby or activity. 

Then, one may be able to do apply this 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 a specific educational structure coax summation
Grade-Segregation

Most large schools group pupils into "age-based grades."  But when you put several students in the same room and teach the same things to all of them, some will get bored, and some will get stressed-because children develop at different rates.  Whatever we teach, it is hard to design a curriculum that will suit the needs of pupils with different abilities.

This segregation-by-age can also lead to a cultural kind of stagnation.  For when you assign a collection of six-year-olds to a single classroom in school, this leads them to share the values, outlooks, and ways to think that are common among those six-year-olds.  Then next year, when those same children are 7 years-old, they will tend to maintain those same cultural views-so as they proceed through their K-12 grades, large portions of their social minds will remain much like those of six-year-olds!  (This is less likely to happen in smaller schools, where classes are more heterogeneous.)

Of course, the classroom is not the whole of life: children also learn much from their parents and teachers.  But still, age-based classrooms will tend to constrain the range of those children's development-by limiting their interactions with older, more experienced people.

Mentors and Communities: 

Of course we all want to improve schools, and get better teachers and so forth.   But another way OLPC can advance education is by opening networks that make it more feasible for younger people to become connected, or even apprenticed, to new friends who can lead them to develop deeper skills-by working on more substantial projects. Our interactive networks can thus offer children new ways to escape into more advanced intellectual communities. 

If a child is in a small community, but develops a specialized interest, it is unlikely that any local person can be of much help.  However, as we develop more global connections, it becomes more possible to find others with similar interests, and the child can join (or help form) such a community.  Otherwise, the child is confined to develop in a circumscribed world of ideas, and to never have any contact whatever with those who grow up in more technical cultures. 

Important for a child to get attached to someone who shows that it is exciting to learn new things-and to learn to do things that others don't do!    Most cultures reward you most for being the same as others!   

I've people suggest that children should play a large role in deciding what they should learn.  

Pro: It is hard to persuade a child to learn a subject until (or unless) that subject engages the child's interest.  So we're likely to be more successful at this, if the child already has such a goal.

Con: Otherwise, it is unlikely that the child has enough knowledge to make good such selections!

So we also need mentors who know more, so that they can guess what each child needs-and might be good at, and interested.

Sources of Mentors.  The world-population is aging, and soon we may have as many retired persons as young ones.  This means that we can begin to envision a competent adult with enough "spare time" to serve as a mentor for every young child.  But can we find effective ways to match them together?  Can OLPC develop a suitable "intellectual dating service?"

Communities

Defense: Of course we can try to explain the appearance of communities in evolutionary terms: a group of individuals who support one another will be able to overcome attacks from outside. Otherwise, individuals could be picked off one at a time. 

Commonsense knowledge: Intellectual  development of isolated individuals appears to be almost impossible. To learn the kinds of things one needs to know in that complex civilization requires language and other ways to communicate. Unless one is in a community there is no way for memes to spread, so civilizations cannot develop. No single person by itself can ever survive through enough experience to develop the sorts of collections of thoughts that we see in every human community.

Coherence:  Here, insert a discussion of the chaotic result that would come from having too many different Imprimers. 

Cognitive Efficiency: The beliefs and dogmas of each community provide standardized ways to deal with common questions that we have no other good ways to answer"What caused the world?", or by their nature cannot be answered, "Which goals should I hold? 'or where the answer does not matter; but still one needs to make a decision such as which foot should I start with?  Fixed answers to questions like these save people from wasting excessive amounts of time (that is, on problems that cannot yet be solved in our present state development. 

Comfort and Community: This becomes a goal of some (or most)  individuals, and then is served by various organizations and/or communities.  However, those organizational entities then evolve other goals that help them survive.  (Every 'level of organization' could develop additional, different kinds of Goals and Critics!)

The 50-minute hour

Another problem with classroom-based schooling is that it requires a synchronized schedule: each activity must be constrained to an hour-and then each child is forced to switch to one or another subject or topic.  This may be necessary for a school's organization, but may not be an effective way to develop each child's abilities.  For any particular activity, that unit of time is unlikely to be right for any particular child or teacher.

Those conventional "hours" are often justified by assuming that most children have short "attention spans" -but I don't see any sound basis for this.  Indeed, we often see a child return to the same activity for hours or even for days-that is, when enough time is available.  And when children pursue what we call "hobbies," we often see degrees of focused intensity that would put many busy adults to shame-but classroom-based "periods" interfere with this. 

What produces the ability to pursue an idea for as long as takes to develop it.

Some of the best times in my early years came when, because of being slightly ill, I was able to stay home from school-and to enjoy a whole uninterrupted day to think!  (I also recall complaining of becoming "bored"-but I can't quite remember just what that meant, because it hasn't happened since childhood-except when confined to fixed-time events.) [Edit] 
Conflicts between Subjects and Projects

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 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?

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.

What are examples of productive large projects?
	Organizing large programs
	TMRC: entire railroad
	A tower theory in mathematics.  Group theory: so much from so few axioms.
	Organizing a business.

Thesis: until a child has had some such experiences- of knowing what it is like to build a "cognitive tower"-that child won't have any good models of how to organize larger [subject, activity, project, etc.]  
This is 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!  

Education: Classics vs. Textbooks!
  Textbooks are too fragmented.  
Textbooks are generally dysfuntional-because they are mainly designed to teach TESTABLE units!  For Homework, Tests, Uniformity, and "availability": If a person can only have a few books, 
They avoid higher-level issues because it is hard to make homework and compact tests for them!  And it is hard to evaluate larger projects.

Until now, textbooks have been expensive.  BUT NOW, MOST CLASSICS ARE FREE!!  So each child can access whichever books are best for that particular child's state of development!

In fact, we now can start to design "adaptive" texts that work at each child's current needs and levels.

Galileo: from Two New Sciences.  Essay about Infinity.

SIMP. If I should ask further how many squares there are one might reply truly that there are as many as the corresponding number of roots, since every square has its own root and every root its own square, while no square has more than one root and no root more than one square. 

SIMP. Precisely so. 

SALV. But if I inquire how many roots there are, it cannot be denied that there are as many as there are numbers because every number is a root of some square. This being granted we must say that there are as many squares as there are numbers because they are just as numerous as their roots, and all the numbers are roots. Yet at the outset we said there are many more numbers than squares, since the larger portion of them are not squares. Not only so, but the proportionate number of squares diminishes as we pass to larger numbers. Thus up to 100 we have 10 squares, that is, the squares constitute 1/10 part of all the numbers; up to 10000, we find only 1/100 _[79] _part to be squares; and up to a million only 1/1000 part; on the other hand in an infinite number, if one could conceive of such a thing, he would be forced to admit that there are as many squares as there are numbers all taken together. 

SAGR. What then must one conclude under these circumstances? 

SALV. So far as I see we can only infer that the totality of all numbers is infinite, that the number of squares is infinite, and that the number of their roots is infinite; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally the attributes "equal," greater," and "less," are not applicable to infinite, _(33)_but only to finite, quantities. 

Read: http://galileoandeinstein.physics.virginia.edu/tns_draft/tns_109to152.html
Galileo: from Two New Sciences.  Essay about Strength of a Beam.

To illustrate briefly, I have sketched a bone whose natural length has been increased three times and whose thickness has been multiplied until, for a correspondingly large animal, it would perform the same function which the small bone performs for its small animal. From the figures here shown you can see how out of proportion the enlarged bone appears. Clearly then if one wishes to maintain in a great giant the same proportion of limb as that found in an ordinary man he must either find a harder and stronger material for making the __bones, or he must admit a diminution of strength in comparison with men of medium stature; for if his height be increased inordinately he will fall and be crushed under his own weight. Whereas, if the size of a body be diminished, the strength of that body is not diminished in the same proportion; indeed the smaller the body the greater its relative strength. Thus a small dog could probably carry on his back two or three dogs of his own size; but I believe that a horse could not carry even one of his own size.

Lesson: extending geometry to statics and mechanics!  What better use of "similar triangles!  Then the children can build the things (using construction toys, or real materials!)  
Learning to Learn?

As Seymour Papert often remarked, it is strange how much of our educational system are engaged in learning many particular subjects-while rarely if ever focusing on questions about what is involved in "learning" itself. 

In other words, in a typical school, each [child takes many separate "courses."  However, I am inclined to take the opposite view: that the principal goal of a school should be to help each child to acquire good sets of skills for learning new subjects!   

Conjecture: this may best be accomplished by encouraging each student to undertake number of what we'll call "projects."\  [Edit]   This is a good place to recount two stories about Michael:

  The learning to write via the "Adventure" computer game.  Punchline: I didn't see any use for reading of writing!
  The "Math Table" story.  Punchline: The child has no realistic (or useful) high-level map or representation of the whole subject or how it connects with other knowledge, skills, or situations!

What is Mathematics-and why do many people find  Math so hard to learn?

Why do people regard mathematics as hard?  What is mathematics, anyway?  I once was in a classroom where some children were writing LOGO programs.  One program was making colored flowers grow on the screen, and someone asked if the program was using mathematics.  The child replied, "Oh, mathematics isn't anything special: it's just the smart way to understand things."

¤¤ Why, if you have n variables, do you need n equations to determine them?
¤¤ Why are 2 triangles congruent, if SAS, or SSS or ASA are the same? 
      Because, then, there is nothing to bend!  But why does this need 3 (exactly) constraints? 
¤¤ Why does every closed, non-crossing plane curve have exactly one inside and one outside?
¤¤ Why is prime factorization unique?
¤¤ If most A's are B's, and most B's are C's, then must some of the A's be C's?
¤¤ Although we all live in a 3-D world, few people learn good ways to think about 3-D objects. Can you see how to make a cube using 3 identical 5-sided objects?
¤¤ [How many different ways to paint 6 colors on the faces of a cube?] 
¤¤ How does mathematics relate to computer programs.

(Classically, math has been seen as divided into Algebra, Geometry, Topology, Number Theory, and Logic.

¤¤ When do children learn basic statistics?   One often needs this to evaluate evidence: the difference between correlation and cause?  Common forms of biases.  The need to be skeptical of anecdotes, Post hoc vs. proper hoc, common mistakes, etc.  Common mistakes.  The T-test handles a wide range of situations!   Is it possible that when Mr. Smith moved from Company A to Company B, this raised the average IQ of both institutions?

How does mathematics relate to practical life (or relate to teaching History)?  Consider that, when we teach about democracy, few pupils ever recognize that, in an electoral-college voting system, a 26% minority can win an election?  (What it there are 2 tiers of this?  Then 7% can win!)  So, how many votes would one need to change an election?  (Sometimes, just 1.)
[Few children in any school ever learn the landscape of modern mathematics.  This is building a very large organization, with many different levels of abstraction.  [Example, person, family, village, town, city, and country.  Find better examples?]  Hobbies like learning mathematics. arithmetic. Power series, Symmetries and groups.  Abstract groups, homomorphisms, homeomorphisms, etc.  Factors, etc. 

Where does basic Information Theory fit into K-12?  A serious fault in formal "courses" is that many important subjects are too small to fit in any particular place, so they end up being completely omitted.  Antidotes: the 'merit badges' in scouting.  IAP at MIT.

My theory of mind: the Critic Selector theory.
   CRITICS: what kinds of problems do we face? 	World-Related Problems: understanding situations, goals, and obstacles.
	Mind-Related Problems: understanding confusions and other mental states, goals, and obstacles.  Management of energy, time, and memory.   Books like De Bono, etc., seen as discussing Ways to Think.
The "linguistic poverty" of school-mathematics.

There's something peculiar about how we teach math.  If you look at each subject in elementary school-History, English, Social Studies, etc.- you'll see that each pupil learn hundreds of new words in every term. You learn the names of many countries and organizations, the names of leaders and battles and wars, the names of many authors and books-thousands of new words in every year. 

However, this is not the case in school-mathematics: that vocabulary is remarkably small. "Addition" "multiplication," "fraction," "quotient," "divisor." "Rectangle," "Parallelogram," "Cylinder." "Equation," "Variable," "Function," Graph-perhaps less than a dozen new terms each year. Not more than one hundred new words in twelve years!
 
What's the word for when you should use addition? It's when a phenomenon is "linear." What's the word for when you should use multiplication? That's when something is "bilinear" or "quadratic". What's the use of teaching a subject for 12 years, if you do not provide the pupils with a vocabulary that they can use for thinking about it? How can they think about phenomena without having access to terms like "discontinuity" or "homomorphism" or the other hundreds of terms that technical people use? How can you think about a subject without having a language that's rich enough to express good ideas? 

Of course a subject will seem "hard" if you don't have good ways to express its ideas!  Also, there's a community problem:  if a child says "nonlinear" the other children will throw things at her-for trying to be too "technical.  See [Pinker-Language learning] /marvin/ M (WA)/ Theology f/Pinker-Language learning