Teach Process not Material
I invited Professor McGuire to do this guest column after hearing some inspiring comments from him at our weekly Tuesday Science lunch today:
Teach Process not Material by Professor Morgan McGuire
I’ve been thinking lately that one cannot put enough emphasis on process, as opposed to material. In the sciences this means the methodology that we bring to solving problems. That methodology is usually mathematical or experimental. Moreover, I think process is a universal truth that applies equally well to the humanities, as well as outside academia in industry.
Workflow analysis (e.g., the time-motion study) is an industrial example of studying process. Reducing the number of physical motions that a factory worker makes can increase his or her efficiency. Something as simple as moving a lever from one side of a machine to the other, where it is easier to reach, can increase throughput for the factory. These ideas have historically been applied to kitchen design, craft work, and office layout. They’re even critically important for computer work. A student who keeps open all of the files he or she needs for a project rather than continuously opening and closing them has much less overhead to research and will likely finish a paper faster than a peer. The natural extension of this is learning to use the time-saving features of computer tools, like desktop shortcuts, keyboard commands in Word, and macros in Excel to avoid slow or repetitive tasks.
In the educational context, learning how to approach any problem is more important than learning about specific problem domains. Courses purport to teach, for example, Medieval History or Linear Algebra. But they really teach a set of techniques for approaching problems, and use the subject matter as a concrete context for teaching those techniques.
What is interesting is that studying how to solve problems, rather than just solving them, might be new for bright students. Those students might come to college accustomed to solving problems intuitively on inspection. Solving by inspection divides the world into trivial and impossible problems. There should be a smooth gradient, and thinking about how to solve a problem (instead of the problem itself) is the trick to climbing the gradient. It is the only way to approach problems that are too big to “get your head around.”
Some common approaches for solving any problem are:
1. Abstract common operations.
2. Divide it into subproblems (or distinct cases).
3. Reduce it to an already solved problem.
4. Translate it into a more familiar domain (which is really points 2 + 3).
We all know this, but it is easy to forget when actually faced with a challenge. In research work I have to remind myself to step back from the work and ask whether I’m really approaching the problem the right way. I know it is a challenge for some of my students as well. When I see them spending a long time on a problem where they know the material, I realize that I didn’t spend enough time explicitly teaching the techniques to apply to that material. In CS371: Computer Graphics and CS107: Creating Games, most of the class time is explicitly spent on process. This squeezes out some topics I’d like to address, but allows students to learn and work very quickly by the end. I now feel that I should be teaching process even more in other courses I teach.
A final word about point 1: Abstraction. This is a really big idea. I’m partial to it because my entire discipline (computer science) can be seen as the study of abstraction in computation. Abstraction means making your own tools to avoid repetition, reduce the amount you have to think about at any point, and draw attention to important concepts. There are many ways of doing this. Two big ones are defining a new notation that hides boilerplate and transforming data into a visual form in which it is easier to observe relationships and anomalies. Some examples combine both, e.g., chemical diagrams, Feynman diagrams, charts and graphs. In fact, the other approaches listed above—subproblems, reductions, and translations—are all instances of abstraction. So, perhaps my point is that studying details is a weak approach; we should instead think more about abstraction to avoid being overwhelmed by the details.
Professor Morgan McGuire, Computer Science Department, Williams College
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Alan Fekete:
The most inspiring math course I ever studied was Raoul Bott’s Differential Geometry grad class at Harvard. What made it special was the explicit discussion of why one looks at particular things. He didn’t just state the theorem, he explained some of the researcher’s thought process. For example, he explained why one looks for characteristic classes. He also placed a lot of emphasis on the calculations that allow one to test conjectures in simple cases. Much of his style can be found in his Springer GTM coauthored with Tu on “Differential Forms in Algebraic Topology” (though it worked better with his rich mid-European accent and commanding physical presence!)
28 February 2009, 5:23 pmGil Kalai:
It is a little dangerous to follow the rule “Teach process not material.” In Israel (like in other countries) there was a move to teach reading/writing and basic arithmetic via “understanding” and “discovery” and not via teaching the rules. The result was that children simply did not learn to read and write. Teaching the material is quite important.
4 March 2009, 5:06 pmJoe Shipman:
I agree with Mr. Kalai. But it is possible to argue that basic reading/writing/arithmetic are really “process” rather than “content”. The real danger comes later on, when students are discouraged from learning factual material because “critical thinking” is the buzzword — without a solid factual background in history, literature, and science the student will not have the raw materials upon which to exercise critical faculties non-trivially and they will atrophy. Young children are very good at absorbing DATA but adult teachers imagine that learning things like historical dates, geography, botany, anatomy, or particular works of great literature is somehow stunting their ability to think rather than enhancing it.
14 April 2009, 12:44 pmJawad Chohan:
Before any kind of understanding of a topic can occur a student must still have a foundation of factual information. Critical thinking can only occur once someone is aware of all of the facts.
25 January 2010, 7:50 pmSasha Orjiako:
This blog post presents a very relevant argument about the importance of material over procedural anecdotes to solving math problems. In my Modern Geometry class, my teacher emphasizes the importance of learning the concept with the ability of applying it to any problem versus memorizing formulas. In the case of geometry, being able to understand relationship of figures will get you much further.
31 January 2010, 12:37 am