Wednesday, July 9, 2014

Pólya was a humanist. That puts him at odds with the education reform movement.

What do I mean when I say that George Pólya was a humanist and imply that movement reformers (at least the ones that matter) are not? All too often, people use 'humanist' or 'humanistic' simply as an impressive way of saying nice or decent. While I certainly believe that Pólya was both a nice and decent man, I have something much more specific in mind here.

Pólya's approach to mathematics pedagogy was humanistic in the sense that it was based on certain assumptions about human nature, viewing students as playful and inquisitive animals who were naturally inclined to learn and to solve problems. That natural inclination meant that the best way to help students was through "common sense" suggestions (a phrase that featured prominently in How To Solve It).

He also focused a great deal of attention on the emotional and psychological state of the student. It was explicitly part of the teacher's job to instill self esteem, self-confidence, and self-reliance in the student, even if it occasionally meant giving the student an exaggerated sense of accomplishment.

"If the student is not able to do much, the teacher should leave him at least some illusion of independent work. In order to do so, the teacher should help the student discreetly, unobtrusively." [emphasis in the original text.]

This humanistic view of learning math lead unsurprisingly to a similar view of teaching with a strong emphasis on empathy and individuality:

"The teacher should put himself in the student's place, he should see the student's case, he should try to understand what is going on in the student's mind and ask a question or indicate a step that could have occurred to the student himself." [emphasis in the original text.]

In order to see how this figures in the larger education debate, we need to introduce the field of scientific management. This field is largely based on the idea that people can be treated like any other component in a complex system. The secret to optimal performance is simply to gather the right data, derive the proper metrics, then use these metrics to put the right components in the right roles and create optimal set of incentives.

The education reform movement with its emphasis on metrics, standardization, and scripted lessons is entirely derived from scientific management. Those scripted lessons in particular represent a complete rejection of Pólya's approach of "getting inside the students head." and personalizing the instruction. Not coincidentally, David Coleman, arguably the intellectual leader of the movement, started out as a management consultant.

Another area of sharp contrast between David Coleman and Pólya is Coleman's strong support of deliberate practice in mathematics education. Scientific management is heavily reliant on reductionist approaches and their are few pedagogical techniques more reductionist than deliberate practice. Pólya was wary of reductionist approaches to teaching. He saw drills as a sometimes necessary evil, but as a rule, breaking down problems for the student was a dangerous habit. For Pólya, the process of problem solving was about taking problems and examining them, restating them, generalizing them, simplifying them, comparing them to other problems, and, yes, breaking them down into sub-problems, but the important part of that process is deciding what to do. To break the problem down for the student is to defeat the purpose.

Many, if not most, of those horrible, multi-step math problems which have become associated with Common Core are not what Pólya would consider problems at all. The problem solving has all been done in the preparation of the lesson; all that's left for the student is the mechanics.

As a side note, Pólya believed that any method you use to solve a problem was acceptable as long as you understood the problem and could prove that your answer was right. This included guessing. Pólya even joked that his initials stood for "Guess and Prove." This approach allowed him to make a string of major discoveries in Twentieth Century mathematics but it would not have gotten him a passing grade in a Coomon Core influenced elementary school.

Pólya's humanistic approach no doubt reflected and underlying philosophy but there was another more practical reason for adopting this approach. Put bluntly, after a long and successful career doing and teaching mathematics, Pólya had a strong sense of what worked. I will get into the practical underpinnings of Pólya's humanism in the next post.

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