Monday, June 14, 2010

The dangers of generality...

... and the greener pastures of practicality first

Over recent years, I've found myself often pondering over the ways in which subjects (or las materias) are taught or presented. Why is it that some lecturers can make a subject interesting and above all guide true understanding and insight, while others can make even potentially interesting subjects dull tedium? Though this may not hold for everyone, I'm starting to believe that presentation style has a lot to do with the effectiveness of teaching and learning.

Firstly, some examples:
Example 1
A lecturer has prepared a set of PowerPoint presentations, with each slide containing all the lecture notes. The slides follow a pretty predictable format: an overview of the sections of material in the series of lectures, followed by several slides packed with formal definitions, and then a set of questions/examples that are worked out by hand during the lecture. Lecturing basically involves reading out the content of the slides, and then solving the examples with some class input. There is a "course reader" that is a bound copy of all these slides, and also copies of these slides available as downloadable PDFs.

Example 2
Another lecturer also has a set of slides, and also follows these relatively closely. However, visual/physical explanations ad-libed while going over this material, and examples are worked out by hand too during the lecture (though once again with explanations of the process as necessary). There are also handouts of these slides made available, but there isn't any overview of the content other than that.

Example 3
Yet another lecturer lectures without using slides (except for occasional pictorial demonstrations) or providing any handouts at all. Lecturing consists of explaining concepts verbally, sketching/scribbling notes, and working through examples. No overviews of lectures are given apart from a rough guide to the course material.

So, what do these examples show us?
The first example makes sure that all the necessary material is covered, with the necessary theory having been presented before examples so that sense can be made of the examples. Also, this structured style makes finding notes easier and gives a solid basis of knowledge suitable for passing examinations, at the expense of making the lectures and general learning experience "boring" and "dull". The net result, is that this style of lecturing is less effective for fostering understanding, since maintaining concentration when faced with a constant stream of definitions is difficult when there isn't any direct context to see how the definition can be applied.

In contrast, the second example makes the lectures more interesting, with the practical demonstrations and 'alternative' explanations improving understanding by enriching the provided notes. This is especially true when there is a bit less formalism used during the initial stages of the lecture, with formalism being progressively introduced at later stages (and also provided by the notes and/or textbooks). Overall, this approach does foster the development of understanding rather than just knowledge-vacuum-cleaner.

The third example represents a bit of an extreme, in that there is little rigid structure in the lectures, and is perhaps a more traditional way of lecturing. I personally expected to see this a lot more than I have so far at University, though it's understandable that many lecturers feel that students would appreciate the orderliness of PowerPoint slides to scrawly scribbles and roadkill sketches. At this point I should also add here that I have a bit of a soft-spot for blackboards over whiteboards, which are quite a rare species these days in all but older-style lecture theatres, since besides their aesthetic appeal they generally have much better contrast/visibility factors when properly used (i.e. clean! This point is all the more memorable due to a lecturer who insisted on personally cleaning the blackboard before each lecture, as he said that knowledge was sacred and should be respected, which includes not presenting it on a dirty board).

Anywhoo, with this more freeform style of teaching, there is perhaps a greater burden of risk - both for the lecturer, who must manage to navigate through 50 minutes of material with no complicated visual artifacts to hide behind, and the students, who must attend all lectures to have a chance of understanding the material covered. Due to this reduced safety net, perhaps this style is in decline (as well as successful marketing and cultural change campaigns by Microsoft). However, in this age of course materials being readily available, and heavy reliance on PowerPoint slides to 'carry' lectures, student attendance in class is reduced due to the safety net being a bit too generous. Also, this style offers a bit more leeway for lecturers to develop a rapport with the students, allowing lecturers to adapt their presentation more towards the class than a predefined set of slides can offer, which ultimately makes a difference between encouraging understanding and just familiarity with facts.

Where does this lead us then?
As with everything where a degree of subjectivity is involved, there is no definite "correct" answer, but because of this, we must also accept that there may have to be some compromises.

Firstly, I believe that there is an over-reliance on PowerPoint presentations (and derivative materials) as the primary medium for teaching and learning to occur. Preparation of PowerPoint presentations usually leads to more "textbook-style" structuring of material, which encourages material to be presented in a way in which it all gets laid out in logical sections (i.e. a bunch of descriptions, a bunch of examples), but does not encourage the formation of understanding (i.e. how these sections are linked together). Consequently, students become a bit lazier, since attending lectures is effectively the same as just referencing the given material.

Secondly, the process of creating definitions intends to provide "concise, compact, and consistent" ways of describing the various incarnations of a concept. This is where generality comes in, and is particularly a bit of a disease among mathematicians (and also physicists, who are really mathematicians in disguise). Through an understandable desire to be able to describe everything in general terms/forms (i.e. definitions, or formulas populated with subscripts), with these forms then being able to be specialised/convoluted to resemble actual use cases, all concepts end up being introduced in this way. That is, "here is the general form... now, here we manipulate it with $*&@(^) steps... voila! it deals with the problem we had".

The problems with this approach are three-fold:
  1. General forms tend to use a lot of placeholders (i.e. dx_i/dt = k x_i / h^2 + Ae^2x_i + dy/dt), but these placeholders (i.e. symbols with subscripts) have an inherently complex affordance associated with them. This belies the fact that often, many of these placeholders are single quantities from other sources, or that they are representing some (simple) concept/entity we're familar with already (i.e. " " represents something as simple as "a + 5", or "b - c", or even "2 * 9", yet seeing the placeholders in the general form don't make this kind of situation apparent).
  2. Processes described in a general form use careful "lawyer language". I'm sure you'll come across legal license agreements for software that use placeholders (point 1) and unnatural word ordering to be sure that the description can be used to correctly describe the situation. Once again, these careful wranglings mean that the meaning that is relevant most of the time is obfuscated. That is, careful reading under a particular mindset while thinking over a specific example in order to make sense of it.
  3. In our quest for knowledge, we don't normally start with a 'simple' general form. In fact, the order of knowledge acquisition starts from a series of seemingly random examples that somehow 'seem' to have something in common. Through a process of investigation, we find this common ground, thus making a generalisation about the situation with the various examples. We do this so that we can talk about the set of examples as a whole, and that when we encounter a similar example, we know what model we can apply to explain/understand it. By subverting this order of gaining insight and understanding, we're short-circuiting the natural desire to learn/come to grips with the situation we're presented with. In effect, it's like giving an answer without having a question to answer. 
Ok, with this in mind, why then do many teachers still insist on doing top-down, generalised-form/definitions followed by examples? Well, perhaps it's kindof like they're answering some question they've posed, in which case many people would want a general understanding before getting down to nitty-gritty to get a feel for where the discussion is going. However, for students, these questions may not be obvious yet, otherwise why are they learning?

What might work better?
I currently believe that presenting examples and then looking at how we can generalise what we saw in those examples can be quite effective. By doing things this way, students are presented with a series of unfamiliar situations, and the processes and ideas shown while tackling these may start becoming obvious with each example, though probably there still won't be clarity yet. At this point, the generalisations should be introduced, since from these generalisations the students can now begin to see the patterns in the examples they were just shown. Hopefully during this process, what was unclear before now becomes clear. The generalisations now have a purpose (i.e. as an encapsulation of the way we can consistently interpret and handle similar situations) rather than being a set of rules we're supposed to know and apply that somebody "high up" wanted us to learn. Finally, a new example should be given, to see how the generalisation can be used to conquer similar but unfamiliar situations.

On that note, here are a few final examples:
Example 4
A lecturer is teaching his class programming. What does he do? Well, he describes a simple program that he wants to code, opens up a text editor and starts describing the thought process of code that he writes. During this process, he explains why some assumptions on the code to write won't work, scribbling diagrams as necessary, and demonstrates this by compiling and running the code. When he finally has the code running as originally described, he switches to writing on the overhead projector or prepared slides (which are made available to students), and reviews some of the concepts shown in summary form, possibly with a few quick spot quizzes along the way.

This approach can be effective in giving students an practical overview and feel for the processes and concepts involved. However, this is provided the adequate descriptions and explanations are given for the steps taken, and also the overall pacing is reasonable to be followed. The prepared slides offering a summary do just that - acting as an overview/framework for the lecture content while not being a rigid crutch on which the lecture is dragged.

Example 5
A lecturer is teaching about a series of interactions between components of a system. On a set of PowerPoint slides, the lecturer shows diagrams and/or images of the system in various states, while important aspects of the system to be covered in the lecture are presented on an overhead projector or blackboard, and are indicated during the course of the lecture.

Once again, this approach can be effective, since there isn't any reliance on PowerPoint to deliver all the text/points of the lecture in a monotonic presentation. Also, while there may be definitions introduced here, they aren't all going to be presented in a block, with little indication of how they are linked.

Concluding Notes
Well, if you've read up to here, then you should know what I've been talking about in this post by now. If you do, then my point is vindicated - flip over the post again and pay attention to the ordering of stuff.

If not, then oh well, at least I tried... unfortunately we can't please everybody... there are still some "aliens" out there! :P   /jk

No comments:

Post a Comment