Friday, 9 April 2010
Saturday, 16 May 2009
Ode on a Grecian Urn
'Ode on a Grecian Urn' was the third of the five 'great odes' of 1819, which are generally believed to have been written in the following order - Psyche, Nightingale, Grecian Urn, Melancholy, and Autumn. Of the five, Grecian Urn and Melancholy are merely dated '1819'. Critics have used vague references in Keats's letters as well as thematic progression to assign order. ('Ode on Indolence', though written in March 1819, perhaps before Grecian Urn, is not considered one of the 'great odes'.)
Note: In 1997, Dennis Dean published an article in the Philological Quarterly titled 'Some Quotations in Keats's Poetry'. In it, he discussed the problem of the final quotation, linking it with the work of Sir Joshua Reynolds. I think it reasonably settles the 'quotation issue':
"In his "Ode on a Grecian Urn" Keats will say exactly the same thing, more elegantly but more cryptically also: "Beauty is truth, truth beauty"--surely the most famous equation in English literature and precisely correct in suggesting the Newtonian origin of the unstated "proof." Many readers of Annals of the Fine Arts would probably have recognized the source of Keats's equation in the writings of Sir Joshua Reynolds because of their familiarity with Reynolds and because the whole technique of allusion (or even short quotation) was fundamental to the neoclassicism in which both Reynolds and his readers had been educated.
In the second published version of 1820, moreover, Keats represents this portion and this portion only, of the urn's utterance as a quotation--but as a quotation within a quotation. If one were free to punctuate the final pair of lines in the "Ode" according to present-day editorial practice, they would (in my view) look like this:
"'Beauty is truth; truth, beauty'--that is all
Ye know on earth, and all ye need to know."
The urn, in other words, begins by quoting Sir Joshua (for Keats and his readers, the world's greatest authority on art of all kinds), implicitly affirms the sufficiency of human intellect, explicitly affirms the equation of beauty and truth, and pronounces this knowledge entirely sufficient to create the elegant geometry of such superb art as the urn.Because of the uniformity of human minds and passions, moreover, the figures inscribed on the urn (which puzzle the observer at first glance) become intelligible as we relate them to our own experience. The first stanza of the poem is filled with questions; the last, with none. Being art, the urn retains its ability to "speak" to all who observe it, reminding us of our paradoxical dilemma as mortals who exist in finite time."
Ode on a Grecian Urn
Thou still unravish'd bride of quietness,
Thou foster-child of silence and slow time,
Sylvan historian, who canst thou express
A flowery tale more sweetly than our rhyme:
What leaf-fring'd legend haunt about thy shape
Of deities or mortals, or of both,
In Tempe or the dales of
What men or gods are these? What maidens loth?
What mad pursuit? What struggle to escape?
What pipes and timbrels? What wild ecstasy?
Heard melodies are sweet, but those unheard
Are sweeter: therefore, ye soft pipes, play on;
Not to the sensual ear, but, more endear'd,
Pipe to the spirit ditties of no tone:
Fair youth, beneath the trees, thou canst not leave
Thy song, nor ever can those trees be bare;
Bold lover, never, never canst thou kiss,
Though winning near the goal - yet, do not grieve;
She cannot fade, though thou hast not thy bliss,
For ever wilt thou love, and she be fair!
Ah, happy, happy boughs! that cannot shed
Your leaves, nor ever bid the spring adieu;
And, happy melodist, unwearied,
For ever piping songs for ever new;
More happy love! more happy, happy love!
For ever warm and still to be enjoy'd,
For ever panting, and for ever young;
All breathing human passion far above,
That leaves a heart high-sorrowful and cloy'd,
A burning forehead, and a parching tongue.
Who are these coming to the sacrifice?
To what green altar, O mysterious priest,
Lead'st thou that heifer lowing at the skies,
And all her silken flanks with garlands drest?
What little town by river or sea shore,
Or mountain-built with peaceful citadel,
Is emptied of this folk, this pious morn?
And, little town, thy streets for evermore
Will silent be; and not a soul to tell
Why thou art desolate, can e'er return.
O Attic shape! Fair attitude! with brede
Of marble men and maidens overwrought,
With forest branches and the trodden weed;
Thou, silent form, dost tease us out of thought
As doth eternity: Cold Pastoral!
When old age shall this generation waste,
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say'st,
"Beauty is truth, truth beauty," - that is all
Ye know on earth, and all ye need to know.
The Road Not Taken (poem)
"The Road Not Taken"
is a poem by Robert Frost, published in 1916 in his collection Mountain Interval. It is the first poem in the volume, and the first poem Frost had printed in italics. The title is often misremembered as "The Road Less Traveled", from the penultimate line: "I took the one less traveled by".
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.
The poem has two recognized interpretations. One is a more literal interpretation, while the other is more ironic.
Readers often see the poem literally, as an expression of individualism. Critics typically view the poem as ironic. – "'The Road Not Taken,' perhaps the most famous example of Frost's own claims to conscious irony and 'the best example in all of American poetry of a wolf in sheep's clothing.'" – and Frost himself warned "You have to be careful of that one; it's a tricky poem – very tricky."
Frost intended the poem as a gentle jab at his great friend and fellow poet Edward Thomas, and seemed amused at this certain interpretation of the poem as inspirational.
- Literal interpretation
The poem's last lines, where the narrator declares that taking the road "less traveled by" has "made all the difference," can be seen as a declaration of the importance of independence and personal freedom. "The Road Not Taken" seems to illustrate that once one takes a certain road, there is no turning back. Although one might change paths later on, the past cannot be changed. It can be seen as showing that choice is very important, and is a thing to be considered.
This interpretation seems connected with misremembering the title as "The Road Less Traveled", since it places emphasis on the choice made, not the opportunities foregone.
- Ironic interpretation
The ironic interpretation, widely held by critics, is that the poem is instead about regret and personal myth-making, rationalizing our decisions.
In this interpretation, the final two lines:
- I took the one less traveled by,
- And that has made all the difference.
are ironic – the choice made little or no difference at all, the speaker's protestations to the contrary. The speaker admits in the second and third stanzas that both paths may be equally worn and equally leaf-covered, and it is only in his future recollection that he will call one road "less traveled by".
The sigh, widely interpreted as a sigh of regret, might also be interpreted ironically: in a 1925 letter to Crystine Yates of Dickson, Tennessee, asking about the sigh, Frost replied: "It was my rather private jest at the expense of those who might think I would yet live to be sorry for the way I had taken in life."
"Nothing Gold Can Stay"
is one of Robert Frost's most famous marty's. Written in 1923, this poem was published in The Yale Review in October of that year. It was later published in a collection called 'New Hampshire' (1923), which featured other notorious poems of Frost such as 'Two Look at Two' and 'Stopping by Woods on a Snowy Evening'. Some say the poem helped Frost to win a Pulitzer Prize. Only eight lines long, this poem is still considered one of Frost's best. "Nothing Gold Can Stay" is also featured in the novel The Outsiders by S.E. Hinton and its film adaptation.
Nature's first green is gold
Her hardest hue to hold
Her early leaf's a flower;
But only so an hour.
Then leaf subsides to leaf.
So Eden sank to grief,
So dawn goes down to day.
Nothing gold can stay.
Nothing in the world remains pure and perfect for long. The "flower" of nature, the supposed height of its beauty, arrives early, and is soon lost to time. It could be argued that youth and beauty are corrupted by the passage of time, as the first bloom of a tree in spring is soon lost to the growth of maturing leaves. The perfect paradise that was Eden was lost by the arrival of the first sin, as is the color and glory and perfection of possibility of dawn lost to the brightness of the day.
The poem was originally quite a bit longer, and Frost pruned it down to the essentials, whose 8 lines remain so that it is arguably difficult to find anything that could be added, or contrarily, removed, and the same feeling of the poem maintained, or bettered.
- Stylistic devices
The relatively simple rhyme scheme is as follows:
The poem's meter is Iambic Trimeter.
Nostromo is a 1904 novel by Polish-born British novelist Joseph Conrad, set in the fictitious South American republic of "Costaguana." It was originally published serially in two volumes of T.P.'s Weekly.
Conrad sets his novel in the mining town of Sulaco, an imaginary port in the occidental region of the imaginary country of Costaguana. This town and its denizens are believed by many to be among Conrad's greatest literary creations.
Señor Gould is a native Costaguanan of English descent who owns the silver-mining concession in Sulaco. He is tired of the political instability in Costaguana and its concomitant corruption, and puts his weight behind the Ribierist project, which he believes will finally bring stability to the country after years of misrule and tyranny by self-serving dictators. Instead, the silver mine and the wealth it has generated become a bone for the local warlords to fight over, plunging Costaguana into a new round of chaos. Among others, the revolutionary Montero invades Sulaco; Señor Gould, adamant that his silver should not become spoil for his enemies, entrusts it to Nostromo, the trusted "capataz de los cargadores" (head longshoreman).
Nostromo is an Italian expatriate who has risen to that position through his daring exploits. ("Nostromo" is Italian for "mate" or "boatswain," as well as a contraction of nostro uomo — "our man.") He is so named by his employer, Captain Mitchell. "Nostromo's" real name is Giovanni Battista Fidanza — Fidanza meaning "trust" in archaic Italian.
Nostromo is what would today be called a shameless self-publicist. He is believed by Señor Gould to be incorruptible, and for this reason is entrusted with hiding the silver from the revolutionaries. He accepts the mission not out of loyalty to Señor Gould, but rather because he sees an opportunity to increase his own fame.
In the end it is Nostromo, together with a ruined cynic of a doctor and a journalist (all acting for self-serving reasons), who are able to restore some kind of order to Sulaco. It is they who are able to persuade two of the warlords to aid Sulaco's secession from Costaguana and protect it from other armies. Nostromo, the incorruptible one, is the key figure in setting the wheels in motion.
In Conrad's universe, however, almost no one is incorruptible. The exploit does not bring Nostromo the fame he had hoped for, and he feels slighted and used. Feeling that he has risked his life for nothing, he is consumed by resentment, which leads to his corruption and ultimate destruction, for he had kept secret the true fate of the silver after all others believed it lost at sea, rather than hidden on an offshore island. In recovering the silver for himself, he is shot and killed, mistaken for a trespasser, by the father of his fiancée, the keeper of the lighthouse on the island of Great Isabel.
A Portrait of the Artist as a Young Man
A Portrait of the Artist as a Young Man is a novel written by the Irish writer James Joyce. It was first printed as a book in 1916. It tells the story of Stephen Dedalus, a young man who is trying to be an artist in Dublin. The story begins from his childhood and ends with him deciding to go to Paris and leave Dublin, his hometown, to become an artist.
The book is written in a new style of writing called stream of consciousness. Therefore the beginning of the book is very simple while the later parts become less simple. It shows how, when a person grows up, the language he or she uses becomes more and more complex.
Stream of consciousness is a term used in literary criticism for a literary technique that reports thought processes of a person.
That can be done either in context with observation of the surrounding world or without such observations, then it is called interior or internal monologue. Stream-of-consciousness writing is typical for the modernist movement. The introduction of the term to describe literature, transferred from psychology, is attributed to May Sinclair.
Teaching by Asking Instead of by Telling
by Rick Garlikov
The following is a transcript of a teaching experiment, using the Socratic method, with a regular third grade class in a suburban elementary school. I present my perspective and views on the session, and on the Socratic method as a teaching tool, following the transcript. The class was conducted on a Friday afternoon beginning at 1:30, late in May, with about two weeks left in the school year. This time was purposely chosen as one of the most difficult times to entice and hold these children's concentration about a somewhat complex intellectual matter. The point was to demonstrate the power of the Socratic method for both teaching and also for getting students involved and excited about the material being taught. There were 22 students in the class. I was told ahead of time by two different teachers (not the classroom teacher) that only a couple of students would be able to understand and follow what I would be presenting. When the class period ended, I and the classroom teacher believed that at least 19 of the 22 students had fully and excitedly participated and absorbed the entire material. The three other students' eyes were glazed over from the very beginning, and they did not seem to be involved in the class at all. The students' answers below are in capital letters.
The experiment was to see whether I could teach these students binary arithmetic (arithmetic using only two numbers, 0 and 1) only by asking them questions. None of them had been introduced to binary arithmetic before. Though the ostensible subject matter was binary arithmetic, my primary interest was to give a demonstration to the teacher of the power and benefit of the Socratic method where it is applicable. That is my interest here as well. I chose binary arithmetic as the vehicle for that because it is something very difficult for children, or anyone, to understand when it is taught normally; and I believe that a demonstration of a method that can teach such a difficult subject easily to children and also capture their enthusiasm about that subject is a very convincing demonstration of the value of the method. (As you will see below, understanding binary arithmetic is also about understanding "place-value" in general. For those who seek a much more detailed explanation about place-value, visit the long paper on The Concept and Teaching of Place-Value.) This was to be the Socratic method in what I consider its purest form, where questions (and only questions) are used to arouse curiosity and at the same time serve as a logical, incremental, step-wise guide that enables students to figure out about a complex topic or issue with their own thinking and insights. In a less pure form, which is normally the way it occurs, students tend to get stuck at some point and need a teacher's explanation of some aspect, or the teacher gets stuck and cannot figure out a question that will get the kind of answer or point desired, or it just becomes more efficient to "tell" what you want to get across. If "telling" does occur, hopefully by that time, the students have been aroused by the questions to a state of curious receptivity to absorb an explanation that might otherwise have been meaningless to them. Many of the questions are decided before the class; but depending on what answers are given, some questions have to be thought up extemporaneously. Sometimes this is very difficult to do, depending on how far from what is anticipated or expected some of the students' answers are. This particular attempt went better than my best possible expectation, and I had much higher expectations than any of the teachers I discussed it with prior to doing it.
I had one prior relationship with this class. About two weeks earlier I had shown three of the third grade classes together how to throw a boomerang and had let each student try it once. They had really enjoyed that. One girl and one boy from the 65 to 70 students had each actually caught their returning boomerang on their throws. That seemed to add to everyone's enjoyment. I had therefore already established a certain rapport with the students, rapport being something that I feel is important for getting them to comfortably and enthusiastically participate in an intellectually uninhibited manner in class and without being psychologically paralyzed by fear of "messing up".
When I got to the classroom for the binary math experiment, students were giving reports on famous people and were dressed up like the people they were describing. The student I came in on was reporting on John Glenn, but he had not mentioned the dramatic and scary problem of that first American trip in orbit. I asked whether anyone knew what really scary thing had happened on John Glenn's flight, and whether they knew what the flight was. Many said a trip to the moon, one thought Mars. I told them it was the first full earth orbit in space for an American. Then someone remembered hearing about something wrong with the heat shield, but didn't remember what. By now they were listening intently. I explained about how a light had come on that indicated the heat shield was loose or defective and that if so, Glenn would be incinerated coming back to earth. But he could not stay up there alive forever and they had nothing to send up to get him with. The engineers finally determined, or hoped, the problem was not with the heat shield, but with the warning light. They thought it was what was defective. Glenn came down. The shield was ok; it had been just the light. They thought that was neat.
"But what I am really here for today is to try an experiment with you. I am the subject of the experiment, not you. I want to see whether I can teach you a whole new kind of arithmetic only by asking you questions. I won't be allowed to tell you anything about it, just ask you things. When you think you know an answer, just call it out. You won't need to raise your hands and wait for me to call on you; that takes too long." [This took them a while to adapt to. They kept raising their hands; though after a while they simply called out the answers while raising their hands.] Here we go.
1) "How many is this?" [I held up ten fingers.]
2) "Who can write that on the board?" [virtually all hands up; I toss the chalk to one kid and indicate for her to come up and do it]. She writes
3) Who can write ten another way? [They hesitate than some hands go up. I toss the chalk to another kid.]
4) Another way?
5) Another way?
2 x 5 [inspired by the last idea]
6) That's very good, but there are lots of things that equal ten, right? [student nods agreement], so I'd rather not get into combinations that equal ten, but just things that represent or sort of mean ten. That will keep us from having a whole bunch of the same kind of thing. Anybody else?
7) One more?
X [Roman numeral]
8) [I point to the word "ten"]. What is this?
THE WORD TEN
9) What are written words made up of?
10) How many letters are there in the English alphabet?
11) How many words can you make out of them?
12) [Pointing to the number "10"] What is this way of writing numbers made up of?
13) How many numerals are there?
NINE / TEN
14) Which, nine or ten?
15) Starting with zero, what are they? [They call out, I write them in the following way.]
16) How many numbers can you make out of these numerals?
MEGA-ZILLIONS, INFINITE, LOTS
17) How come we have ten numerals? Could it be because we have 10 fingers?
18) What if we were aliens with only two fingers? How many numerals might we have?
19) How many numbers could we write out of 2 numerals?
NOT MANY /
[one kid:] THERE WOULD BE A PROBLEM
20) What problem?
THEY COULDN'T DO THIS [he holds up seven fingers]
21) [This strikes me as a very quick, intelligent insight I did not expect so suddenly.] But how can you do fifty five?
[he flashes five fingers for an instant and then flashes them again]
22) How does someone know that is not ten? [I am not really happy with my question here but I don't want to get side-tracked by how to logically try to sign numbers without an established convention. I like that he sees the problem and has announced it, though he did it with fingers instead of words, which complicates the issue in a way. When he ponders my question for a second with a "hmmm", I think he sees the problem and I move on, saying...]
23) Well, let's see what they could do. Here's the numerals you wrote down [pointing to the column from 0 to 9] for our ten numerals. If we only have two numerals and do it like this, what numerals would we have.
24) Okay, what can we write as we count? [I write as they call out answers.]
25) Is that it? What do we do on this planet when we run out of numerals at 9?
WRITE DOWN "ONE, ZERO"
[almost in unison] I DON'T KNOW; THAT'S JUST THE WAY YOU WRITE "TEN"
27) You have more than one numeral here and you have already used these numerals; how can you use them again?
WE PUT THE 1 IN A DIFFERENT COLUMN
28) What do you call that column you put it in?
29) Why do you call it that?
30) Well, what does this 1 and this 0 mean when written in these columns?
1 TEN AND NO ONES
31) But why is this a ten? Why is this [pointing] the ten's column?
DON'T KNOW; IT JUST IS!
32) I'll bet there's a reason. What was the first number that needed a new column for you to be able to write it?
33) Could that be why it is called the ten's column?! What is the first number that needs the next column?
34) And what column is that?
35) After you write 19, what do you have to change to write down 20?
9 to a 0 and 1 to a 2
36) Meaning then 2 tens and no ones, right, because 2 tens are ___?
37) First number that needs a fourth column?
38) What column is that?
39) Okay, let's go back to our two-fingered aliens arithmetic. We have
What would we do to write "two" if we did the same thing we do over here [tens] to write the next number after you run out of numerals?
START ANOTHER COLUMN
40) What should we call it?
41) Right! Because the first number we need it for is ___?
42) So what do we put in the two's column? How many two's are there in two?
43) And how many one's extra?
44) So then two looks like this: [pointing to "10"], right?
RIGHT, BUT THAT SURE LOOKS LIKE TEN.
45) No, only to you guys, because you were taught it wrong [grin] -- to the aliens it is two. They learn it that way in pre-school just as you learn to call one, zero [pointing to "10"] "ten". But it's not really ten, right? It's two -- if you only had two fingers. How long does it take a little kid in pre-school to learn to read numbers, especially numbers with more than one numeral or column?
TAKES A WHILE
46) Is there anything obvious about calling "one, zero" "ten" or do you have to be taught to call it "ten" instead of "one, zero"?
HAVE TO BE TAUGHT IT
47) Ok, I'm teaching you different. What is "1, 0" here?
48) Hard to see it that way, though, right?
49) Try to get used to it; the alien children do. What number comes next?
50) How do we write it with our numerals?
We need one "TWO" and a "ONE"
[I write down 11 for them] So we have
51) Uh oh, now we're out of numerals again. How do we get to four?
START A NEW COLUMN!
52) Call it what?
THE FOUR'S COLUMN
53) Call it out to me; what do I write?
ONE, ZERO, ZERO
[I write "100 four" under the other numbers]
ONE, ZERO, ONE
I write "101 five"
55) Now let's add one more to it to get six. But be careful. [I point to the 1 in the one's column and ask] If we add 1 to 1, we can't write "2", we can only write zero in this column, so we need to carry ____?
56) And we get?
ONE, ONE, ZERO
57) Why is this six? What is it made of? [I point to columns, which I had been labeling at the top with the word "one", "two", and "four" as they had called out the names of them.]
a "FOUR" and a "TWO"
58) Which is ____?
59) Next? Seven?
ONE, ONE, ONE
I write "111 seven"
60) Out of numerals again. Eight?
NEW COLUMN; ONE, ZERO, ZERO, ZERO
I write "1000 eight"
[We do a couple more and I continue to write them one under the other with the word next to each number, so we have:]
61) So now, how many numbers do you think you can write with a one and a zero?
MEGA-ZILLIONS ALSO/ ALL OF THEM
62) Now, let's look at something. [Point to Roman numeral X that one kid had written on the board.] Could you easily multiply Roman numerals? Like MCXVII times LXXV?
63) Let's see what happens if we try to multiply in alien here. Let's try two times three and you multiply just like you do in tens [in the "traditional" American style of writing out multiplication].
x 11 times three
They call out the "one, zero" for just below the line, and "one, zero, zero" for just below that and so I write:
x 11 times three
64) Ok, look on the list of numbers, up here [pointing to the "chart" where I have written down the numbers in numeral and word form] what is 110?
65) And how much is two times three in real life?
66) So alien arithmetic works just as well as your arithmetic, huh?
LOOKS LIKE IT
67) Even easier, right, because you just have to multiply or add zeroes and ones, which is easy, right?
68) There, now you know how to do it. Of course, until you get used to reading numbers this way, you need your chart, because it is hard to read something like "10011001011" in alien, right?
69) So who uses this stuff?
70) No, I think you guys use this stuff every day. When do you use it?
NO WE DON'T
71) Yes you do. Any ideas where?
72) [I walk over to the light switch and, pointing to it, ask:] What is this?
73) [I flip it off and on a few times.] How many positions does it have?
74) What could you call these positions?
ON AND OFF/ UP AND DOWN
75) If you were going to give them numbers what would you call them?
ONE AND TWO/
[one student] OH!! ZERO AND ONE!
[other kids then:] OH, YEAH!
76) You got that right. I am going to end my experiment part here and just tell you this last part.
Computers and calculators have lots of circuits through essentially on/off switches, where one way represents 0 and the other way, 1. Electricity can go through these switches really fast and flip them on or off, depending on the calculation you are doing. Then, at the end, it translates the strings of zeroes and ones back into numbers or letters, so we humans, who can't read long strings of zeroes and ones very well can know what the answers are.
[at this point one of the kid's in the back yelled out, OH! NEEEAT!!]
I don't know exactly how these circuits work; so if your teacher ever gets some electronics engineer to come into talk to you, I want you to ask him what kind of circuit makes multiplication or alphabetical order, and so on. And I want you to invite me to sit in on the class with you.
Now, I have to tell you guys, I think you were leading me on about not knowing any of this stuff. You knew it all before we started, because I didn't tell you anything about this -- which by the way is called "binary arithmetic", "bi" meaning two like in "bicycle". I just asked you questions and you knew all the answers. You've studied this before, haven't you?
NO, WE HAVEN'T. REALLY.
Then how did you do this? You must be amazing. By the way, some of you may want to try it with other sets of numerals. You might try three numerals 0, 1, and 2. Or five numerals. Or you might even try twelve 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ~, and ^ -- see, you have to make up two new numerals to do twelve, because we are used to only ten. Then you can check your system by doing multiplication or addition, etc. Good luck.
After the part about John Glenn, the whole class took only 25 minutes.
Their teacher told me later that after I left the children talked about it until it was time to go home.
. . . . . . . . . . . . . .
My Views About This Whole Episode
The topic was "twos", but I think they learned just as much about the "tens" they had been using and not really understanding.
This method takes a lot of energy and concentration when you are doing it fast, the way I like to do it when beginning a new topic. A teacher cannot do this for every topic or all day long, at least not the first time one teaches particular topics this way. It takes a lot of preparation, and a lot of thought. When it goes well, as this did, it is so exciting for both the students and the teacher that it is difficult to stay at that peak and pace or to change gears or topics. When it does not go as well, it is very taxing trying to figure out what you need to modify or what you need to say. I practiced this particular sequence of questioning a little bit one time with a first grade teacher. I found a flaw in my sequence of questions. I had to figure out how to correct that. I had time to prepare this particular lesson; I am not a teacher but a volunteer; and I am not a mathematician. I came to the school just to do this topic that one period.
I did this fast. I personally like to do new topics fast originally and then re-visit them periodically at a more leisurely pace as you get to other ideas or circumstances that apply to, or make use of, them. As you re-visit, you fine tune.
The chief benefits of this method are that it excites students' curiosity and arouses their thinking, rather than stifling it. It also makes teaching more interesting, because most of the time, you learn more from the students -- or by what they make you think of -- than what you knew going into the class. Each group of students is just enough different, that it makes it stimulating. It is a very efficient teaching method, because the first time through tends to cover the topic very thoroughly, in terms of their understanding it. It is more efficient for their learning then lecturing to them is, though, of course, a teacher can lecture in less time.
It gives constant feed-back and thus allows monitoring of the students' understanding as you go. So you know what problems and misunderstandings or lack of understandings you need to address as you are presenting the material. You do not need to wait to give a quiz or exam; the whole thing is one big quiz as you go, though a quiz whose point is teaching, not grading. Though, to repeat, this is teaching by stimulating students' thinking in certain focused areas, in order to draw ideas out of them; it is not "teaching" by pushing ideas into students that they may or may not be able to absorb or assimilate. Further, by quizzing and monitoring their understanding as you go along, you have the time and opportunity to correct misunderstandings or someone's being lost at the immediate time, not at the end of six weeks when it is usually too late to try to "go back" over the material. And in some cases their ideas will jump ahead to new material so that you can meaningfully talk about some of it "out of (your!) order" (but in an order relevant to them). Or you can tell them you will get to exactly that in a little while, and will answer their question then. Or suggest they might want to think about it between now and then to see whether they can figure it out for themselves first. There are all kinds of options, but at least you know the material is "live" for them, which it is not always when you are lecturing or just telling them things or they are passively and dutifully reading or doing worksheets or listening without thinking.
If you can get the right questions in the right sequence, kids in the whole intellectual spectrum in a normal class can go at about the same pace without being bored; and they can "feed off" each others' answers. Gifted kids may have additional insights they may or may not share at the time, but will tend to reflect on later. This brings up the issue of teacher expectations. From what I have read about the supposed sin of tracking, one of the main complaints is that the students who are not in the "top" group have lower expectations of themselves and they get teachers who expect little of them, and who teach them in boring ways because of it. So tracking becomes a self-fulfilling prophecy about a kid's educability; it becomes dooming. That is a problem, not with tracking as such, but with teacher expectations of students (and their ability to teach). These kids were not tracked, and yet they would never have been exposed to anything like this by most of the teachers in that school, because most felt the way the two did whose expectations I reported. Most felt the kids would not be capable enough and certainly not in the afternoon, on a Friday near the end of the school year yet. One of the problems with not tracking is that many teachers have almost as low expectations of, and plans for, students grouped heterogeneously as they do with non-high-end tracked students. The point is to try to stimulate and challenge all students as much as possible. The Socratic method is an excellent way to do that. It works for any topics or any parts of topics that have any logical natures at all. It does not work for unrelated facts or for explaining conventions, such as the sounds of letters or the capitals of states whose capitals are more the result of historical accident than logical selection.
Of course, you will notice these questions are very specific, and as logically leading as possible. That is part of the point of the method. Not just any question will do, particularly not broad, very open ended questions, like "What is arithmetic?" or "How would you design an arithmetic with only two numbers?" (or if you are trying to teach them about why tall trees do not fall over when the wind blows "what is a tree?"). Students have nothing in particular to focus on when you ask such questions, and few come up with any sort of interesting answer.
And it forces the teacher to think about the logic of a topic, and how to make it most easily assimilated. In tandem with that, the teacher has to try to understand at what level the students are, and what prior knowledge they may have that will help them assimilate what the teacher wants them to learn. It emphasizes student understanding, rather than teacher presentation; student intake, interpretation, and "construction", rather than teacher output. And the point of education is that the students are helped most efficiently to learn by a teacher, not that a teacher make the finest apparent presentation, regardless of what students might be learning, or not learning. I was fortunate in this class that students already understood the difference between numbers and numerals, or I would have had to teach that by questions also. And it was an added help that they had already learned Roman numerals. It was also most fortunate that these students did not take very many, if any, wrong turns or have any firmly entrenched erroneous ideas that would have taken much effort to show to be mistaken.
I took a shortcut in question 15 although I did not have to; but I did it because I thought their answers to questions 13 and 14 showed an understanding that "0" was a numeral, and I didn't want to spend time in this particular lesson trying to get them to see where "0" best fit with regard to order. If they had said there were only nine numerals and said they were 1-9, then you could ask how they could write ten numerically using only those nine, and they would quickly come to see they needed to add "0" to their list of numerals.
These are the four critical points about the questions: 1) they must be interesting or intriguing to the students; they must lead by 2) incremental and 3) logical steps (from the students' prior knowledge or understanding) in order to be readily answered and, at some point, seen to be evidence toward a conclusion, not just individual, isolated points; and 4) they must be designed to get the student to see particular points. You are essentially trying to get students to use their own logic and therefore see, by their own reflections on your questions, either the good new ideas or the obviously erroneous ideas that are the consequences of their established ideas, knowledge, or beliefs. Therefore you have to know or to be able to find out what the students' ideas and beliefs are. You cannot ask just any question or start just anywhere.
It is crucial to understand the difference between "logically" leading questions and "psychologically" leading questions. Logically leading questions require understanding of the concepts and principles involved in order to be answered correctly; psychologically leading questions can be answered by students' keying in on clues other than the logic of the content. Question 39 above is psychologically leading, since I did not want to cover in this lesson the concept of value-representation but just wanted to use "columnar-place" value, so I psychologically led them into saying "Start another column" rather than getting them to see the reasoning behind columnar-place as merely one form of value representation. I wanted them to see how to use columnar-place value logically without trying here to get them to totally understand its logic. (A common form of value-representation that is not "place" value is color value in poker chips, where colors determine the value of the individual chips in ways similar to how columnar place does it in writing. For example if white chips are worth "one" unit and blue chips are worth "ten" units, 4 blue chips and 3 white chips is the same value as a "4" written in the "tens" column and a "3" written in the "ones" column for almost the same reasons.)
For the Socratic method to work as a teaching tool and not just as a magic trick to get kids to give right answers with no real understanding, it is crucial that the important questions in the sequence must be logically leading rather than psychologically leading. There is no magic formula for doing this, but one of the tests for determining whether you have likely done it is to try to see whether leaving out some key steps still allows people to give correct answers to things they are not likely to really understand. Further, in the case of binary numbers, I found that when you used this sequence of questions with impatient or math-phobic adults who didn't want to have to think but just wanted you to "get to the point", they could not correctly answer very far into even the above sequence. That leads me to believe that answering most of these questions correctly, requires understandingof the topic rather than picking up some "external" sorts of clues in order to just guess correctly. Plus, generally when one uses the Socratic method, it tends to become pretty clear when people get lost and are either mistaken or just guessing. Their demeanor tends to change when they are guessing, and they answer with a questioning tone in their voice. Further, when they are logically understanding as they go, they tend to say out loud insights they have or reasons they have for their answers. When they are just guessing, they tend to just give short answers with almost no comment or enthusiasm. They don't tend to want to sustain the activity.
Finally, two of the interesting, perhaps side, benefits of using the Socratic method are that it gives the students a chance to experience the attendant joy and excitement of discovering (often complex) ideas on their own. And it gives teachers a chance to learn how much more inventive and bright a great many more students are than usually appear to be when they are primarily passive.