delphi

Check out this fascinating interactive map that plots the “Peopling of the World”.

I believe in teaching through inquiry: asking questions that guide a student to think critically about a subject, rather than pedantically feeding facts and explanations to the student.

Perhaps the oldest surviving thorough treatment of this educational notion is the following passage from Plato’s Meno:

MENO: Yes, Socrates; but what do you mean by saying that we do not learn,
and that what we call learning is only a process of recollection? Can you
teach me how this is?

SOCRATES: I told you, Meno, just now that you were a rogue, and now you
ask whether I can teach you, when I am saying that there is no teaching,
but only recollection; and thus you imagine that you will involve me in a
contradiction.

MENO: Indeed, Socrates, I protest that I had no such intention. I only
asked the question from habit; but if you can prove to me that what you say
is true, I wish that you would.

SOCRATES: It will be no easy matter, but I will try to please you to the
utmost of my power. Suppose that you call one of your numerous attendants,
that I may demonstrate on him.

MENO: Certainly. Come hither, boy.

SOCRATES: He is Greek, and speaks Greek, does he not?

MENO: Yes, indeed; he was born in the house.

SOCRATES: Attend now to the questions which I ask him, and observe whether
he learns of me or only remembers.

MENO: I will.

SOCRATES: Tell me, boy, do you know that a figure like this is a square?

BOY: I do.

SOCRATES: And you know that a square figure has these four lines equal?

BOY: Certainly.

SOCRATES: And these lines which I have drawn through the middle of the
square are also equal?

BOY: Yes.

SOCRATES: A square may be of any size?

BOY: Certainly.

SOCRATES: And if one side of the figure be of two feet, and the other side
be of two feet, how much will the whole be? Let me explain: if in one
direction the space was of two feet, and in the other direction of one
foot, the whole would be of two feet taken once?

BOY: Yes.

SOCRATES: But since this side is also of two feet, there are twice two
feet?

BOY: There are.

SOCRATES: Then the square is of twice two feet?

BOY: Yes.

SOCRATES: And how many are twice two feet? count and tell me.

BOY: Four, Socrates.

SOCRATES: And might there not be another square twice as large as this,
and having like this the lines equal?

BOY: Yes.

SOCRATES: And of how many feet will that be?

BOY: Of eight feet.

SOCRATES: And now try and tell me the length of the line which forms the
side of that double square: this is two feet–what will that be?

BOY: Clearly, Socrates, it will be double.

SOCRATES: Do you observe, Meno, that I am not teaching the boy anything,
but only asking him questions; and now he fancies that he knows how long a
line is necessary in order to produce a figure of eight square feet; does
he not?

MENO: Yes.

SOCRATES: And does he really know?

MENO: Certainly not.

SOCRATES: He only guesses that because the square is double, the line is
double.

MENO: True.

SOCRATES: Observe him while he recalls the steps in regular order. (To
the Boy:) Tell me, boy, do you assert that a double space comes from a
double line? Remember that I am not speaking of an oblong, but of a figure
equal every way, and twice the size of this–that is to say of eight feet;
and I want to know whether you still say that a double square comes from
double line?

BOY: Yes.

SOCRATES: But does not this line become doubled if we add another such
line here?

BOY: Certainly.

SOCRATES: And four such lines will make a space containing eight feet?

BOY: Yes.

SOCRATES: Let us describe such a figure: Would you not say that this is
the figure of eight feet?

BOY: Yes.

SOCRATES: And are there not these four divisions in the figure, each of
which is equal to the figure of four feet?

BOY: True.

SOCRATES: And is not that four times four?

BOY: Certainly.

SOCRATES: And four times is not double?

BOY: No, indeed.

SOCRATES: But how much?

BOY: Four times as much.

SOCRATES: Therefore the double line, boy, has given a space, not twice,
but four times as much.

BOY: True.

SOCRATES: Four times four are sixteen–are they not?

BOY: Yes.

SOCRATES: What line would give you a space of eight feet, as this gives
one of sixteen feet;–do you see?

BOY: Yes.

SOCRATES: And the space of four feet is made from this half line?

BOY: Yes.

SOCRATES: Good; and is not a space of eight feet twice the size of this,
and half the size of the other?

BOY: Certainly.

SOCRATES: Such a space, then, will be made out of a line greater than this
one, and less than that one?

BOY: Yes; I think so.

SOCRATES: Very good; I like to hear you say what you think. And now tell
me, is not this a line of two feet and that of four?

BOY: Yes.

SOCRATES: Then the line which forms the side of eight feet ought to be
more than this line of two feet, and less than the other of four feet?

BOY: It ought.

SOCRATES: Try and see if you can tell me how much it will be.

BOY: Three feet.

SOCRATES: Then if we add a half to this line of two, that will be the line
of three. Here are two and there is one; and on the other side, here are
two also and there is one: and that makes the figure of which you speak?

BOY: Yes.

SOCRATES: But if there are three feet this way and three feet that way,
the whole space will be three times three feet?

BOY: That is evident.

SOCRATES: And how much are three times three feet?

BOY: Nine.

SOCRATES: And how much is the double of four?

BOY: Eight.

SOCRATES: Then the figure of eight is not made out of a line of three?

BOY: No.

SOCRATES: But from what line?–tell me exactly; and if you would rather
not reckon, try and show me the line.

BOY: Indeed, Socrates, I do not know.

SOCRATES: Do you see, Meno, what advances he has made in his power of
recollection? He did not know at first, and he does not know now, what is
the side of a figure of eight feet: but then he thought that he knew, and
answered confidently as if he knew, and had no difficulty; now he has a
difficulty, and neither knows nor fancies that he knows.

MENO: True.

SOCRATES: Is he not better off in knowing his ignorance?

MENO: I think that he is.

SOCRATES: If we have made him doubt, and given him the ‘torpedo’s shock,’
have we done him any harm?

MENO: I think not.

SOCRATES: We have certainly, as would seem, assisted him in some degree to
the discovery of the truth; and now he will wish to remedy his ignorance,
but then he would have been ready to tell all the world again and again
that the double space should have a double side.

MENO: True.

SOCRATES: But do you suppose that he would ever have enquired into or
learned what he fancied that he knew, though he was really ignorant of it,
until he had fallen into perplexity under the idea that he did not know,
and had desired to know?

MENO: I think not, Socrates.

SOCRATES: Then he was the better for the torpedo’s touch?

MENO: I think so.

SOCRATES: Mark now the farther development. I shall only ask him, and not
teach him, and he shall share the enquiry with me: and do you watch and
see if you find me telling or explaining anything to him, instead of
eliciting his opinion. Tell me, boy, is not this a square of four feet
which I have drawn?

BOY: Yes.

SOCRATES: And now I add another square equal to the former one?

BOY: Yes.

SOCRATES: And a third, which is equal to either of them?

BOY: Yes.

SOCRATES: Suppose that we fill up the vacant corner?

BOY: Very good.

SOCRATES: Here, then, there are four equal spaces?

BOY: Yes.

SOCRATES: And how many times larger is this space than this other?

BOY: Four times.

SOCRATES: But it ought to have been twice only, as you will remember.

BOY: True.

SOCRATES: And does not this line, reaching from corner to corner, bisect
each of these spaces?

BOY: Yes.

SOCRATES: And are there not here four equal lines which contain this
space?

BOY: There are.

SOCRATES: Look and see how much this space is.

BOY: I do not understand.

SOCRATES: Has not each interior line cut off half of the four spaces?

BOY: Yes.

SOCRATES: And how many spaces are there in this section?

BOY: Four.

SOCRATES: And how many in this?

BOY: Two.

SOCRATES: And four is how many times two?

BOY: Twice.

SOCRATES: And this space is of how many feet?

BOY: Of eight feet.

SOCRATES: And from what line do you get this figure?

BOY: From this.

SOCRATES: That is, from the line which extends from corner to corner of
the figure of four feet?

BOY: Yes.

SOCRATES: And that is the line which the learned call the diagonal. And
if this is the proper name, then you, Meno’s slave, are prepared to affirm
that the double space is the square of the diagonal?

BOY: Certainly, Socrates.

SOCRATES: What do you say of him, Meno? Were not all these answers given
out of his own head?

MENO: Yes, they were all his own.

SOCRATES: And yet, as we were just now saying, he did not know?

MENO: True.

SOCRATES: But still he had in him those notions of his–had he not?

MENO: Yes.

SOCRATES: Then he who does not know may still have true notions of that
which he does not know?

MENO: He has.

SOCRATES: And at present these notions have just been stirred up in him,
as in a dream; but if he were frequently asked the same questions, in
different forms, he would know as well as any one at last?

MENO: I dare say.

SOCRATES: Without any one teaching him he will recover his knowledge for
himself, if he is only asked questions?

MENO: Yes.

SOCRATES: And this spontaneous recovery of knowledge in him is
recollection?

MENO: True.

SOCRATES: And this knowledge which he now has must he not either have
acquired or always possessed?

MENO: Yes.

SOCRATES: But if he always possessed this knowledge he would always have
known; or if he has acquired the knowledge he could not have acquired it in
this life, unless he has been taught geometry; for he may be made to do the
same with all geometry and every other branch of knowledge. Now, has any
one ever taught him all this? You must know about him, if, as you say, he
was born and bred in your house.

MENO: And I am certain that no one ever did teach him.

SOCRATES: And yet he has the knowledge?

MENO: The fact, Socrates, is undeniable.

SOCRATES: But if he did not acquire the knowledge in this life, then he
must have had and learned it at some other time?

MENO: Clearly he must.

10 Ways to Improve Your Mind by Reading the Classics.

I think the most interesting questions in history are the unsettled ones. Glossing over academic controversies, and pretending that history is settled (something to be swallowed, and not wrestled with) does the student no service.

With that in mind here are some open history questions that I would love to explore with students in the future:

• Was the Trojan War real?
• Were the Hyksos (a people who, for a time, conquered Egypt) Amorites (a semitic group of nomads) or Aryan (horse-riding warriors)? (See Penguin Atlas of Ancient History, p 38)
• Were the Sea Peoples (another enemy of Pharoanic Egypt) Greeks? What about the biblical Philistines?
• Did Altaians (a group of central Asians which includes Huns and Mongols) learn about horse-riding from Aryans? (See Penguin Atlas of Ancient History, p 38)

Human children have evolved to mimic adults, and to enjoy doing it. That’s why babies love to pretend to use phones, and kids love to pretend to work with money. Kids would enjoy helping adults with research as too. Instead of being commanded to do completely independent research projects by incurious, lazy teachers, they should be help an enthusiastic teacher research a subject that the teacher is genuinely interested in. The researching teacher would then be teaching the student research methods by example.

The effects of too-easy curriculum on bright kids, from Scientific Americans:

The result plays out in children like Jonathan, who coast through the early grades under the dangerous notion that no-effort academic achievement defines them as smart or gifted. Such children hold an implicit belief that intelligence is innate and fixed, making striving to learn seem far less important than being (or looking) smart. This belief also makes them see challenges, mistakes and even the need to exert effort as threats to their ego rather than as opportunities to improve. And it causes them to lose confidence and motivation when the work is no longer easy for them.

What makes the present-day negligence of Greco-Roman classics in education particularly sad is how fun it can be to young people. The natural starting point to understanding the classical world is by reading Homer. And Homer, if explained properly, can be like comedy-filled super-hero stories. Right now, I’m working through the Iliad with 4 different students: not a “kid-friendly” paraphrase of the epic, but the epic itself in all it’s glory. When others hear of my program, they either think it must either be ridiculously ambitious or terribly boring. But if they were to walk in on one of the sessions, they would find 11 and 12 year olds laughing riotously at a 2,600 year-old narrative. I read the text aloud, while the students follow along with their own copies of the same edition. I’m good with voices, so I read it with various English accents, which the kids always find compelling. And I take frequent pauses to explain what particurly difficult passages mean. Most importantly, I take a pause to explain funny and ridiculous situations in the story. The kids always pick up this ball and run with it, with their own spins on the absurdities at hand. As we progress, the florid language of the text becomes ever less difficult, and the students are able to understand ever more passages without any help. As they become immersed in the universe of the story (of ancient Greek mythology), innumerable questions come to mind, which I can readily answer, because of my being so well-read in the classics myself. The net result of all this is that exploring what is idiotically considered a dry text to be unwillingly endured in a university class is, for 5th, 6th and 7th graders, a read as enjoyable as a Harry Potter book: but which also provides a basis for a budding classical education.

There is something fundamentally wrong about the approach generally taken to mathematics education. I haven’t quite figured out exactly what it is yet, but I’m working on it.

The biggest gripe students have with math is that they don’t see why it matters. And I think that’s because they are presented with mathematical operations and concepts completely in the abstract and out of context. When the math is presented in context, in the form of word problems, there is little reason to care about the “world” set up in the word problem, because it is completely discarded as soon as the problem is completed.

I think there should almost always be interesting context to flesh out the math. This interesting context could be real-life projects (science and engineering), simulations and games, or by exploring the “world” of an interesting narrative quantitatively. This last type is my next project.

Any situation can be explored quantitatively. What matters is if the student is interested in the situation to care about any quantitative exploration of it. The world of a one-paragraph word problem, again, is too quickly discarded to care about. But the worlds of a narrative (especially of fantasy narratives like those of Homer, Tolkien and Rowling) are hugely compelling, because a reader becomes so immersed in it. So my theory is that students who are reading the story will find math problems about the situations presented in it very interesting.

So this week, with several students, I’ll be exploring the world of The Iliad, Homer’s immortal tale of the siege of Troy, quantitatively, with word problems that star the characters of the story. The situations presented in the word problems will follow the situations of the narrative. They will generally involve decisions characters have to make: this aspect, I think, will give the student a fun feeling of role play in tackling the problem. After they get the hang of it, I’ll have the students make up their own word problems, with quotes from the text provided as prompts. I’ll report back how it goes.

Albert Jay Nock on why abandoning classical education was a bad idea:

The literatures of Greece and Rome comprise the longest and fullest continuous record available to us, of what the human mind has been busy about in practically every department of spiritual and social activity — every department, I think, except one: music. This record covers twenty-five hundred consecutive years of the human mind’s operations in poetry, drama, law, agriculture, philosophy, architecture, natural history, philology, rhetoric, astronomy, politics, medicine, theology, geography, everything. Hence the mind that has attentively canvassed this record is not only a disciplined mind but an experienced mind — a mind that instinctively views any contemporary phenomenon from the vantage point of an immensely long perspective attained through this profound and weighty experience of the human spirit’s operations.

These words are just as true in 2007 as they were in 1931 when Nock spoke them. The perspective given by a classical education is just as important now as it was then. No young person should profess a religion without being first challenged by Lucretius; espouse a political ideology without considering Plato; or accept a scientific claim without reflecting on the epistemology of Aristotle.

I would like to introduce a new program: the one I am most excited about.

I call it “Encyclia”, named after the “Enkyklios Paideia”, the secular education program of ancient Alexandria, which covered letters, mathematics and science. Basically it’s a combination of many of my previous offerings. It will be 1.5 - 3 hour sessions with groups of 2-6, weaving together math, history, literature, and computer technology.

The session starts with readings from a classic, presenting it with humor and full historical context. Then, the students will play mathematical games exploring quantitatively some element of the story or the society in which it takes place. Finally the students will create a computer-based project, creatively illuminating some aspect of the subject: either with HTML web sites, video game editors, audio/video technology, 3-D graphics software, or mapping software.

I believe this integrated approach could have a dramatic effect on how kids regard scholarship and the thoughtful life.

Please let me know if you would like to start an Encyclia club this fall.

Best wishes,
Daniel