21 Jan 2006 - 20:50

teaching binary like Socrates

Rick Garlikov is a kind of modern-day Socrates, living in Birmingham, Alabama. He has a business mentoring students and their parents, and his philosophical writings are available online. Charlie Martin sent me a link to an article by Rick, entitled The Socratic Method: Teaching by Asking instead of Telling. The specific thing he is teaching is the notion of binary numbers, to a group of typical third graders.

Have a look: the whole transcript of the class session is there, and it's interesting. The guy can think on his feet. But it's more his interpretation of the situation that I wanted to dwell on here.

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.

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 like that he is not arguing that the Socratic method can replace other methods as the bread-and-butter teaching method in the classroom.

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.

But I don't agree with everything he says:

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.

Note the implicit assumption that lecturing to children 'stifles' their thinking. I doubt this very much; I expect that what really stifles their thinking is a constant diet of television.

Catch the reference to teaching being more interesting with the Socratic method. Teacher boredom is a real problem in the classroom; while a constantly changing group of kids is struggling to come up to speed on the material the teacher is teaching, so that they can move on, the teacher may never move on. It's up to the teacher to figure out ways to grow him or herself professionally, in such a way that it helps and doesn't harm the children's learning.

I disagree with the claim that the children learn the idea deeply the first time it is taught by the Socratic method. That's nonsense. We've all had the experience of listening to a really great teacher explain something, feeling we know it cold and are greatly enriched by the lecture, only to find we really remember none of it when it's time to sit down and do the homework -- i.e., to actively produce the knowledge ourselves. It's producing the knowledge yourself that leads to deep understanding. Leading questions are still just leading; what could be more 'sage on the stage'?

The other thing I disagree with is the notion that Socratic teaching serves as a type of in situ formative assessment:

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.

These claims may be true of the one or two children who are tracking the teacher all the way through the process. As usual, there will be some number of children who aren't following the discussion, or who develop some real misunderstanding of what's going on. Those kids are probably not going to speak up during a Socratic method class, any more than they would a normal class; and trying to correct those misapprehensions would derail the discussion, probably in a direction that Socrates wouldn't want to go. Good formative assessment has to assess everyone.

-- CarolynJohnston - 21 Jan 2006

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Testing comments

-- CarolynJohnston - 22 Jan 2006

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As a law student some 20 years ago, I experienced many variations of the Socratic method. Like most other law students, I used commercial outlines and hornbooks to learn the "black letter law" to mastery. I also took extensive notes during class (basically, I wrote down everything that was said). My lecture notes then served as an invaluable study aid.

As I recall, my Estate and Gift Tax professor primarily used a Direct Instruction approach. He would occasionally ask probative questions so that we would learn to think more deeply about the material, but his primary focus was to make sure we understood the complex principles involved. We also worked story problems in order to put the law into a context. However, without an understanding of the rules, we would have had a hard time applying them.

I mention this because I think there are parallels between learning and applying tax law and learning and applying math. Learning tax law was painful enough using the Direct Instruction method. Had our professor used the Socratic method,I'm pretty sure I would have been completely lost.

-- KarenA - 22 Jan 2006

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I just re-read my post and what I am trying to say is that I agree with Carolyn--there is no way that math can be deeply learned the first time through with the Socratic method!!

-- KarenA - 22 Jan 2006

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Thaks for a good and open minded discussion of the Socratic method. Here's one part I didn't quite agree with:

Carolyn said: "I disagree with the claim that the children learn the idea deeply the first time it is taught by the Socratic method. That's nonsense. We've all had the experience of listening to a really great teacher explain something, feeling we know it cold and are greatly enriched by the lecture, only to find we really remember none of it when it's time to sit down and do the homework -- i.e., to actively produce the knowledge ourselves. It's producing the knowledge yourself that leads to deep understanding. Leading questions are still just leading; what could be more 'sage on the stage'?"

The Socratic method is supposed to be producing the knowledge yourself - as a class at least. I don't know whether it would work to teach math at a deep level or not, as I only really experienced it in law school. But it is more like learning through solving homework problems than it is like listening to a traditional lecture. I also don't know how well it works with children, for the same reason. I use it all the time with my children, but I know pretty where they are in terms of knowledge and interest, and there are only two of them.

Regarding kids paying attention all the way through: my experience is that one pays better attention in a Socratic discussion because you might get the next question. Also, watching other students who are at the same level you are try to work through the issues has some inherent interest because you relate to where they are.

What I liked a lot about this article was it explained how much hard work a good Socratic discussion is. When this came up before, someone compared it to telling a student to look something up themselves. I think this article makes it clear that this is something completely different.

It is like the Montessori system: it is kind of true to say the children are teaching themselves, but first both the environment and the children must be carefully prepared, and then just the right amount of nudging and guidance must be done. It only looks easy.

-- EmmaAnne - 23 Jan 2006

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The Socratic method is supposed to be producing the knowledge yourself - as a class at least. I don't know whether it would work to teach math at a deep level or not, as I only really experienced it in law school. But it is more like learning through solving homework problems than it is like listening to a traditional lecture.

It's just that I can all too easily imagine following the discussion point by point, being led from one point to the next, only to find at the end that I'd lost the main thread of the discussion.

Not that lectures are all that great; they're not. I've always preferred learning by reading, and being able to ask a teacher when I came up against something I couldn't follow. But I don't learn by hearing, very well -- probably from years of inattention and wandering-mindness. But I still think that nothing beats really having to produce the knowledge on your own.

-- CarolynJohnston - 24 Jan 2006

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And by 'producing the knowledge on your own' I don't mean constructivism -- I mean being able to apply it. I think that being able to apply it on your own is more important by far than inventing it.

-- CarolynJohnston - 24 Jan 2006

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Hi C. I knew you meant being able to apply it, and that is what I was saying also. I think a good Socratic discussion does involve the students applying the knowledge - to solve problems (again, as a class at least).

-- EmmaAnne - 24 Jan 2006

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Emma

Yes, I knew you would know -- but didn't want a casual reader to misunderstand me.

-- CarolynJohnston - 24 Jan 2006

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Have you seen this article on "What is Important in School Mathematics" by the Mathematics Standards Study Group? I apologize if this has already been posted. My head is swimming with too much information.

http://www.maa.org/pmet/resources/MSSG_important.html

"Almost all mathematics instruction should be devoted to developing deeper mastery of core topics through computation, problem-solving and logical reasoning."

"In keeping with our concern for in-depth learning, we would prefer to see a solid development of data analysis for, say, six weeks during one year in high school, rather than a two-week chapter of data analysis every year starting somewhere in the elementary grades."

-- SusanJ - 24 Jan 2006