Why Problem Solving Doesn't Work (According to One Author)

The following article makes a pretty strong case that direct instruction is the best way to teach:

http://www.aft.org/pdfs/americaneducator/spring2012/Clark.pdf

The basic idea is that when asked to solve problems that they don't know how to do, a student's working memory gets overloaded and they can't function well.  People solve problems best when the means for solving them is somewhere in their long term memory.  Experts can solve problems because they have a lot of schema in their long term memory, and each of these processes only counts as one item in their short term working memory when they pull them out to help solve a problem.

In other words, people solve problems most effectively when they already know how to solve them.  So the best way to get students to solve problems is by simply showing them how to do it.

This conclusion directly contradicts what I have been trying to do in my class, and I think it is important to occasionally question my premises.  But the author seems a bit too confident for my taste.  For example,  I think the relationship between long term memory and working memory is more complex than the author lets on.  In particular, the presence of a schema in long term memory is not either yes or no.  Students can "know" something in a very superficial way.  All of my students "know" the Pythagorean Theorem in the form a^2 + b^2 = c^2.  But many of them have a very hard time with the distance formula (which is equivalent to the Pythagorean Theorem), even if I suggest that they plot the points and make a right triangle.  This is probably because their working memory is overloaded by the process of plotting points, when what they really want to do is remember a formula.

What I see is a deficiency in being able to put together small steps to reach a goal.  I don't think that most students will ever even use the distance formula.  But it takes practice to have confidence making a small step, flushing your working memory, and seeing the problem anew.  That is, I am still a believer that the students need to learn problem solving itself, more so than they need to learn any one given formula.  In some professions it may be the case that all an expert must do is learn a limited set of algorithms and repeatedly apply them.  But what if we ever come across a situation that we have never seen before?

Having stated my objections to the theory of the paper, I should mention that there is actual research that shows that students learn better by direct instruction.  The theory is partially just an attempt to explain the data.  But I am equally skeptical about the data.  For one thing, education research is inherently hard to do.  The teaching methods used in the studies to represent discovery or problem based learning don't bear a very close resemblance to what I do in my class.  And the methods of measuring learning are not always flawless.  The design of the study also makes a huge difference.  In one case, researchers repeated one study that "proved" direct instruction was better with one key difference:  they continued to measure mastery over a longer period of time.  The results were diametrically opposed to the conclusions of the first study.  Over a longer period, the students taught by direct instruction forgot everything, and those who discovered the material slowly began to really understand.

I don't think this one study proves the case for discovery learning, but it should make us pause.  Research in education is hard to do, and it is always flawed.  This is unfortunate because it would be great to have some reliable data.   Theorizing by itself often leads to wrong conclusions.  At this point I am mostly convinced by what I have seen with my own eyes:  students who have been taught primarily by direct instruction are not very good at solving problems, and many of them are not very good at remembering what they have learned.  However, as mentioned in the article favoring direct instruction, problem solving in class can be very easily dominated by a few eager students and while the rest of the class remains passive and unengaged.