Wednesday, June 21, 2006

How do students play at their schoolwork?

I was reading Barbara Ganley’s latest post this morning, and since I’m mentioned I feel compelled to respond in some way. Before I do, however, let me make some more mundane observations. Barbara says Middlebury has 12-week semesters. Jeez! Here it’s 15 weeks and another week afterwards for finals. They’ve got higher prices and smaller portions. How can we publics compete?

On a different and perhaps more interesting point demonstrating yet again how small the world is and how even if we start from very different places there is a good chance our paths will cross, Barbara cited Will Richardson who cited Donald Murray, and as I’m reading that on Barbara’s blog, before reading the post on Will’s blog, I’m saying to myself, “Donald Murray, that name sounds familiar. Where do I know that from?” And while I had not read Expecting the Unexpected I had read part of a different book by Donald Murray that I came to because I was attracted by the title. And perhaps still more to the point, I came to that before I was even vaguely aware of other Edu bloggers who were writing on similar issues.

That earlier post of mine also shows my Econ training coming through and why I’m probably unlike other Edu bloggers in some respects – at the core I believe in tradeoffs, not perfection – and by poking holes in arguments as best as I can I hope to elucidate some of the tradeoffs being made that otherwise seem to go unnoticed.

Barbara wrote a lot, as is her want, and below I’m going to focus only on one paragraph, but there is much meat in it, perhaps the heart of the matter, at least it is in my view.

Sometimes a great talk can stir debate and inquiry, and foster learning. Yes, I agree. But the problem is that too many teachers rely on this method as the primary method. We also focus on the impossible timeframes for our courses and measured amounts of material to be covered rather than thinking about ways we can assist our students to learn about how to learn within our field. We err on the side of the accumulation of what we call the basic materials of our disciplines--often through reading and lecture instead of providing ample time for messy learning curves or the relationship between hands-on authentic learning activities and deep learning. We do not have enough time for our students to go find examples of processes we study in the classroom out there in the world and to play around, to be imaginative, to see what would happen if they mixed A with B. We ask them to gather information and soak in knowledge rather than play around with it. And our students are stressed out. We are stressed out. As we know, with the Web, information and knowledge are easily accessible. But how do students learn how to play around with that information if we don't give them opportunities to do so-- collaboratively--discussing, conversing, arguing, doing, inventing, failing. This is the beauty of a school, it seems to me--that we have the potential to grow rich, diverse learning communities that reach out beyond their own scope to the complex world beyond.

Until I became a full time administrator and hence when teaching did so as an overload and as a gift to the Econ department so I could choose the course I would teach, I did a lot of teaching in a large section of intermediate microeconomics, with up to 180 students, and a substantial amount of lecturing of the type that Barbara questions in the above paragraph. So I have a good deal of hands on experience at that sort of thing and agree that as a rule it is not particularly satisfying, for students or instructor. But there are several qualifiers to that and it is the qualifiers which I want to emphasize.

When I was in high school, either 11th or 12th grade and now I can’t recall which, I along with two other guys in my graduating class would travel to NYU on Saturday mornings (one of the parents would take us to the subway stop in Jamaica and then we rode that into the City) to attend a lecture. In the fall it was on Relativity and Geometry. There was no taking attendance and no grades. This was just getting bright high school kids exposed to an interesting approach to college level thinking.

One of the things I recall from this experience was a critique of the standardized tests in Math asking questions of the form, which is the next in the sequence. Here is a specific example.

Q: 4, 14, 23, 34, 42, 50. What comes next?

A: Lexington Avenue. Those are stops on the F-Train.

The point, meant to be a serious one, is that one can rationalize a finite sequence of numbers with an infinite family of different polynomials. Then what comes next in the sequence depends on which particular polynomial was used to generate the first few terms. The professor did teach us the “method of successive differences,” which if applied correctly guarantees (according to him) the “right answer” on any of the standardized tests. This I recall some 35 years later. Unfortunately, I don’t recall any of the relativity. C’est la vie.

This type of going to lecture was not an isolated event for me. I graduated from Cornell in January 1976 and then hung around Ithaca for another semester. I did some Library research for a prof in political science on Congressional voting on Educational measures (my recollection is that even then the argument was that so called Great Society spending programs actually redistributed wealth toward the richer school districts rather than to the poorer ones as is generally perceived) and I washed pots in a Sorority in exchange for my meals. But that left a lot of free time on my hands and part of what I did with that was to attend an introductory Political Science lecture with a girl I was pretty crazy about at the time. She was a grad student. So both of us went for the benefit of the lecture itself and that only. I’d call it the entertainment value or the intellectual stimulation value. There is something to that and I believe lecture should be considered in that light quite independent of the “power relations” that Barbara stresses in her post and that is also a big deal in the paper by Ron Burnett that she cites.

A different sort of qualifier stems from this observation. The bulk of the students whom I taught in intermediate microeconomics were Business majors or Business major wannabes, and for the most part they really detested the course. They didn’t understand why they were required to take it and they were frustrated that my course entailed more work than courses in their major. There would always be a smattering of engineering students and occasionally a few Econ majors with enough of a Math background to have a realistic shot of getting into a decent Econ grad school program. Those kids really liked the course and appreciated the way I taught.

To get a better feel why, consider the following problem.

A father and his young son are at a beach that abuts the ocean. They are staring out at the water and see several large vessels, some near to shore, others further out. After a fashion the son asks the dad, “Looking straight out there on the horizon in any direction, how far is it to the point where the ocean touches the sky?” The father responds, “You know, I’m taller than you, just about twice your height. So I see a different point on the horizon than you do where the ocean and sky touch, even if we follow the exact same line. In fact I probably see out twice as far as you.”

Is the father right? And in either case just how far is it to that particular point on the horizon?

I’m not going to answer that one. Instead, let me say there are those type of people (I’m one of them) who find the challenge of this sort of problem fun, as is using the appropriate math to solve the problem. And there are other people who would find spending time on something like this more painful than going to the dentist. Among the engineering students, there are many of the first type of person. Among the business students, there are mostly the second type. The problem itself has absolutely nothing to do with economics, but identifying types this way would go very far in predicting whether the individual valued and felt they learned anything from my intermediate microeconomics course.

My conjecture is that if one sorted types this way then lecture on a “math oriented” course such as intermediate microeconomics would be a fine way to teach, presuming there are only the engineering types in the class. This is pretty much for the reasons Barbara identified. They are self-directed in the learning. They do play with the material and make it for their own in that fashion. And the lecture for them serves as new stimuli, a source of yet other problems that they haven’t yet considered but are eager to solve.

I will conjecture further, that if one could identify a different type of play that the students should be doing in other disciplinary settings, for example in taking a history course where the above type of problem solving affinity is likely useless, then one could be effective with lecture that promoted that appropriate type of play, again viewing the lecture as a source of stimulus and the students largely self-directed.

And still one more conjecture. In the setting where the lecture and the play are interconnected in this way, the power relationships that Barbara laments become less important. The tests will be perceived as “fair” and the students will regard them as giving appropriate feedback on their own sense of understanding. Instructors will generally enjoy teaching in this setting and will feel less of a need to exert ego to establish authority. And students will enjoy the class too, in spite of the fact that lecture is the predominant mode of instruction.

These conjectures notwithstanding, the scenarios being depicted above don’t coincide with my realm of experience in teaching intermediate micro. Many of the students who exert effort in the intermediate micro course don’t engage in play at all. Instead, they memorize and seemingly act on the belief that the one is a substitute for the other. They memorize in spite of my exhortations to the contrary, a conditioned response qua school survival skills that has literally been drilled into them since the early grades in primary school. Many of the students I’ve seen have extraordinary capacity for memorization and in some respect that is awe inspiring. But, of course, unless the memorization is accompanied by some other activity that incorporates interesting use of what has been memorized, there is no deep learning.

Indeed, I’d be inclined to say there is no learning whatsoever. And that’s what seemingly happens in much of college “education” today. For example, see my little thread with Gary Brown. I don’t believe there is much if any disagreement between us (or between Barbara and me) on what is happening in many, many classrooms and it is something to be alarmed about.

The disagreement is with how the problem is best addressed. Right now I believe, though I may be stereotyping a bit in which case give me a virtual slap in the head, every teacher who has moved away from the lecture approach that I know teaches critical thinking anew, as if that course is the first time students have a chance to reflect in this mature manner, their entire prior formal education being done in the pour into the student’s head manner.

Suppose instead, that students do have some successful teaching earlier on what critical thinking is like – they learn to play with ideas, issues, and materials on their own, to turn things inside out and try them on just for the heck of it, and make their own sense of meaning from that process. And they learn to discuss and share their experiences with like minded peers and benefit from that. What would you do in the subsequent course?

I would lecture.


Burks said...

Lanny - Regarding the problem of the distance to the horizon:

1.17 times the square root of your height of eye (in feet) = distance to the horizon (in nautical miles)


SquareRoot (height above surface in feet / 0.5736) = distance to horizon in miles

-- Burks

Lanny Arvan said...

Burks - thanks for the references. But does the answer depend on whether you're at the equator or the poles? and if so where is it further (and why)?


Barbara Ganley said...


Interesting response -- I much appreciated the link back to your 2005 post, as well, in which you struggle with the very issues we've been discussing on our blogs.

Your stories of wonderful lecturers remind me of a couple of professors I had at Williams (I was an art history major) who could weave magic about the slides they showed us. I took in a good deal of information, and a particular way of approaching art from them,and I absolutely enjoyed the show. But I didn't come to understand the art history covered in those syllabi as something that mattered under my skin--I never took it inside and made it mine--it was always an intellectual exercise in class, riveting yet remote. It was performance art. The best lecturers demonstrate and model, pose provoking, open-ended questions designed to get you thinking. Sure sure, that's quite splendid. But I still say, every time I sit through a classroom lecture, look at the waste of all those minds sitting in that room only taking in from that single direction rather than also discovering together-- out of the messiness of collaborative discovery learning emerges often remarkable outcomes for them well beyond the strict confines of the one class.

But you yourself have put your finger on it--there's nothing wrong with a lecture (goodness knows I go around yammering away at people all over the world at conferences and such--lecturing) if it is woven skillfully into the rich tapestry of a learner-with- subject-centered pedagogy. But I don't quite understand why at the end of your post you separate the discovery methodology from the lecture--you would really lecture through an entire course? Why not weave them together, challenging yourself before every lecture to justify why you need to be the giver of the knowledge and the asker of the question?

Lanny Arvan said...

Barbara - thanks for the comments. I am glad that you used the word "struggle" in your first sentence, because really that is what I believe. There are conflicting ideas and we are all trying to fit the pieces together. So I argued a bit over aggressively on behalf of the lecture as a counterpoint to your initial post that caused me to comment.

The benefit from that, I hope, is to go a step or two farther by generating the questions in your last paragraph and giving some response to those.

Here is my starting point and potentially it may be on this issue that discipline really matters. I believe that much of the discovery a good student will do has to happen out of class.

For example, for the distance to the horizon problem where Burks found the Web sites that provide the forumlas, suppose the teacher's next assignment is this. "Ok, we know the forumla. Now derive it from primitives."

The teacher then divides the class up into pairs of students who can work on that assignment. A possible first dialog between the two:

Student one - "I have no clue how to do this."

Student two - "Me neither."

So the first step is that they are stuck. And within the confines of the class period they might very well stay stuck. Then it might occur to one of them to draw some diagrams, since those Web sites have diagrams, and then after a fashion and perhaps several diagrams that end up in the waste basket, the crucial insight comes that for this purpose think of the earth as a circle and with the three points determined by the point where the viewer is, the point on the horizon, and the center of the earth, we have a triangle where we know the length of two of the sides so can calculate the third.

I know the Physics folks think in class time for discovery of this sort is a very good thing to be doing, but ratchet up the complexity of the problem a bit and then the time to the Aha! can be quite unpredictable and much longer than the class session.

Once you buy the argument that much of the discovery has to happen out of class (and in spite of my comment about potential disciplinary difference here, I do believe this pertains to writing as well) then it is fairly straightforward that substantial in class time must be viewed as instrumental to promote/encourage/support that out of class discovery.

The only other point here is that we teachers don't have to bear witness to the student discovery. We do have to know that it is happening, but that should be evident from the work they produce. For the students to learn, making overt the process that generated the work is not necessary. There may be less joy for the instructor this way, because the instructor will not see how the in class work ties to the out of class discovery, but that shouldn't matter at all for the student learning itself.

Then the question is what should be done in class? While straight presentation of some content is necessary, just to build the set of tools to work with, I mostly favor Socratic dialog, because to me it most closely models the discovery process itself.

Before I close and to offer a quick self-critique, I believe the above can be criticized as focusing too much on left-brain type of problem solving. Perhaps. I want to take the issue up in one of my next posts.