In the previous three posts I looked at a perceived over-obsession with ‘understanding,’ ‘thinking’ and questioning in modern education; not that any of these three things were not desirable, but that their obsessive and blinkered pursuit was perhaps not yielding the gains we would expect.
In this final post in the series, I would like to speculate as to from where this obsession might originate, by looking at Socrates’ thoughts on education, as outlined by Plato.
Let’s start by looking at an excellent example of ‘the Socratic method’ as given by Plato in The Meno:
Socrates asks that Meno bring a slave to them. His being a slave is important, since being born and raised in Meno’s household, Meno can attest that the slave was never taught any geometry, though the slave does understand what a square is, and can count and multiply. The following is paraphrased, since the original dialogue is somewhat convoluted.
Socrates draws a square of side 2 feet, and area 4 square feet.
Socrates asks the slave: “How long will the side be of the square whose area is double this?” The slave responds that its length would be 4 feet. Now, you and I might know that a square of side 4 feet will have an area of 16 square feet, but crucially, rather than telling the slave this, Socrates instead draws the square described by the slave:
Now, the slave can see for himself that the square whose side is 4 does not have an area of 8, but rather, 16. Alright, so if 4 feet was too big, the slave suggests they try a square of side 3 instead.
The slave can see that the area of the square is 9, not 8, so he concludes that a side length of 3 feet doesn’t work either – the slave sees and concludes this for himself, he is not told it by Socrates.
This next part is important: we’ve seen that 3 and 4 are too big, and obviously 2 is too small, so he asks the slave again, what length will work? Or, if you can’t give us a number, show us the line. The slave replies “I do not know.”
First lesson to take from this: the slave first thought he knew the answer, now he is able to confidently state that he does not know. He many not know the answer, but at least now he realises that he doesn’t know! Socrates argues that this is a better state of being; he suggests that, now he knows he doesn’t know, he will want to inquire, whereas when the slave thought he knew, he never would have bothered. Socrates has motivated the slave.
Now on to the ‘instruction’: Socrates is going to ‘teach’ the slave the solution without telling him; he will ask him questions. They return to the 4 x 4 square, constructed this time from 4 of the original 2 x 2 squares:
“How much bigger is the area of this square, than that of the original?” asks Socrates. The slave replies that it is 4 times as big. Now Socrates draws a diagonal across the original square:
Again he poses a question: “What is the size of the shaded area?” The slave replies that the area is 2 square feet. Finally Socrates draws three more lines of equal length, like so:
He again asks a question: “Do these four lines not contain the shaded area?” The slave agrees that they do. Socrates asks “How many of these shaded triangles are there in the area?” The slave replies that there are 4. Socrates repeats his earlier question “What is the area of one of these shaded triangles?” The slave repeats that it is two. Now we get to the crux of the demonstration: “What is the area of the whole shaded region?” asks Socrates. “Eight square feet!” the slave replies. “We have agreed that the shaded area is a square,” says Socrates “and what line is the side of this square?” The slave replies by pointing to the original diagonal.
On several occasions Socrates makes a point of saying to Meno that he should watch closely to see if Socrates actually ‘teaches’ i.e. tells, the slave anything. Socrates’ point is that all of the learning took place only through the asking of questions; the slave ‘discovered’ the solution for himself. Socrates waxes lyrical about this in these lines, for example:
“You see, Meno, that I am not teaching anything, but put everything as a question. He now believes he knows what sort of line the eight feet area comes from.”
“…I am doing nothing except posing questions and not teaching. Be on the lookout for me teaching and spelling it out for him, and not asking for his opinions.”
There are elements of this dialogue that I find curiously reminiscent of ostensibly ‘cutting-edge’ teaching methods. In here I see the importance of questioning, and of thinking, the seeking of ‘understanding,’ as well as the virtues extolled of ‘not teaching’ and of ‘discovering.’
This post underwent four re-writes in almost as many weeks. What I learnt through that process is that this is a complex area for discussion and analysis. Rather than trying to delve deeply into it again, I’m just going to put it out there for people to read and draw their own conclusions.
I will note only these five points:
- In this particular dialogue, Socrates was not showing Meno the best way to teach someone, he was answering ‘Meno’s paradox’: having said that ‘all learning is remembering,’ Meno asked Socrates what he meant by this. Socrates uses these examples to demonstrate that he directly ‘taught’ the slave nothing, therefore he must have already known it all along; Socrates merely drew the slave’s soul back towards what he had forgotten.
- In the dialogue, Socrates engages with one student only. The student has 100% of Socrates’ attention, and has the opportunity to directly respond to all of Socrates’ questions. We teach classes of up to 30 students.
- The first time I heard this proof was in a video lecture; the same is true for the proof that root 2 is irrational. No-one asked me any questions, and I had no opportunity to ask questions of the teachers. Their didactic explanations were, however, delivered with crystal clarity, and I understood their meaning perfectly. In fact having invested hundreds of hours in video and audio courses, as well as reading books, I think I’ve learnt a great deal through the process of having things explained with no opportunity to interact on my part. I’m sure this is something to which anyone reading this blog could attest. It’s not to say that this is therefore the optimal way of teaching at all times, only that it can clearly be effective.
- The theoretical underpinnings of any practical instructional method must be paid their due respect. In his case, Plato’s philosophy of education was based on a belief in an immortal soul that once knew everything before being reborn, as well as belief in the ‘realm of the forms,’ and the ‘tripartite psyche.’ None of these are credible foundations for a modern theory of instruction or of learning, and so we cannot simply accept what we’re given here as is. If there is value to be had in Socrates’ methods, they must be understood and evaluated on their own terms, in the context of modern cognitive psychology, and in the context of a modern classroom.
- This is all two and a half thousand years old. Is it really credible to say that direct explanation is ‘traditional’ and boring, while discovery methods are cutting-edge and ‘progressive’?
I think my starting point in writing this was realising that here we have some very ancient ideas about education that appear to have been lifted and copied onto a contemporary context as part of a rebranding exercise, and with little or no reference to its roots. Both Socrates and Plato were phenomenal thinkers for whom I have masses of respect and in whose ideas I’m always gleaning new insight; time and again I marvel at how relevant their musings and conclusions can be, two thousand years hence. Neither was perfect, however, and with a further two thousand years of thought and scientific advancement behind us, we should study their ideas and evaluate which have genuinely stood the test of time, rather than slavishly adhere to every word.