Teaching the Teachers

I have been thinking about cats today. I almost killed one through the application of a stumbling-pre-dawn misstep this morning. The cat is OK, but it made a sound I would have thought could only have been produced by the vigorous application of severe torture. Every morning one of the cats in my house closely orbits my feet while I stumble to the kitchen; every few months I step on it. You’d think it would learn.

There are things that cannot be grasped with the feline brain, but it is difficult to tell what they are. If we reduce the complexity of the brain to less than that of a cat (no this is not a sendup for a Glenn Beck joke…) to something like a bird it is possible to dispassionately weigh behavior against applied stimulus.

Burrhus Frederic Skinner worked extensively with stimulus-response training of simple-brained animals. He famously taught pigeons to play ping-pong; though they did not play well. Skinner showed that rewards (positive reinforcement) were much more effective than punishments (negative reinforcement) in altering behavior. Skinner’s work has been used as a critical part of the foundation that modern teaching methods are built upon.

Many experienced teachers will tell you that Skinner’s work is wrong.

“What works for birds” they will tell you “Doesn’t work for people”.

They have data to back up their claims. The data is so universal that it can be generalized as follows:

1. Students who perform exceptionally well at a task, and are rewarded, perform much worse at the task the next time they attempt it. The strength of the reward has no effect on this relationship.
2. Students who perform exceptionally poorly at a task, and are punished, perform much better at the task the next time they attempt it. The strength of the punishment has little effect on this relationship.

The above generalization can be supported with objective data from a variety of sources; I will provide a relatively dependable way of generating your own later on in this entry. It would appear that the human mind works opposite to the way a bird’s brain works, at least as the workings relate to behaviorism. But if we scratch the surface of the experienced teacher’s (ET) knowledge we see a slightly different story.

ETs believe they are speaking about how their students learn from them, but what they are really relating is what they think they themselves have learned about their students. If the Skinnerism holds their learning would be reinforced better through rewards. To stick with teaching long enough to become an ET requires that the teacher partially responds to the positive stimuli of successfully teaching. What they are correct about in their teaching methods would provide for a more lasting impression in their minds.

The more ET notices the outcome the greater is the impression on their mind. This means that if the deviant ability (either very poor or very good) is exceptional the effect that ET’s teaching method produces is more important to that ET. Similarly, the more ET cares about the student’s progress the more lasting the memory of the effect of ET’s response to the ability.

The problem is that the more ET cares about the student or the exceptional ability the more the ET reinforces in their mind a pattern of responses that does not exist. Once ET recognizes the positive effect of their punishment on their students they have created a delusion that will only be reinforced by continued attention to the data source upon which it is based.

Let me propose a data source that will illustrate this. You will need to supply ET. I suggest that the test is conducted by e-mail. You could get a bunch of teachers to reply to you a couple of times a day in a scenario-based test like this:

Tell the teachers that you are going to test the effectiveness of years of teacher experience on their ability to moderate rewards and punishments to a group of students. It can help if you make clear that neither the rewards nor punishments are severe. The teachers can provide a number from 1 to 10 on how great the reward or punishment should be. Then you provide the teachers with regular performance updates in the form of numbers. The teachers are regularly given a number from -10 to +10 which they are told represents their anonymous students’ performance. After the test the teachers provide answers to a question like: “Did the reward or punishment prove the most effective way to alter the students’ performance?”.


Then to generate the performance numbers you flip coins. Since the mean behavior of a coin toss is HTHTHTHT… we assign a 0 to any sequence of HT or TH. If two heads are flipped in a row we interpret that as a +1. Two tails in a row generates a -1. Three heads generates a +2, four heads a +3, five +4, six +5, seven +6, eight +7, nine +8, ten +9, and eleven heads in a row generates a +10. The same scoring is used for sequences of tails in a row, but the numbers are negative.

Because of the statistical property of “regression to the mean” what ET will see in the above thought experiment is this: whenever ET provides reward for exceptionally good performance they will usually see the performance decline, and when they provide punishment for exceptionally poor performance they will usually see the performance get markedly better. If ET examines their notes and modulates their rewards and punishments they will see that, on average, the punishment does a consistently much better job. The more the teachers are made to care about the outcome the less they will be able to identify the true randomness behind the performance numbers. If one imposes a slight linear increase in the performance values it is almost impossible for even the slightly concerned ET to see the randomness in the values.

I have written on how imposing patterns on the mind leads to conceptual bias, and how these patterns can be reinforced by a lack of data. Here is a situation where the inerrant patterns in data with true randomness reinforces the concept of a very non-random pattern of cultural responses in the mind.

I have framed this entry in the form of a discussion about teachers, but the effects of reward and punishment are used in many aspects of our civilization. Conflicts and wars are often understood as forms of international punishment.

Our spending priorities also mirror what experience-based learning teaches those most interested about rewards and punishments. Estimates had suggested that right about now observed trends would have more of the California budget going towards prisons than education. The estimates had $15.3 billion California state dollars going to education, and $15.4 billion to prisons. The problem economy made that happen sooner. Higher education is the worst hit; 7.5% percent of the CA budget goes to higher education, and 11% goes towards prisons. The per individual discrepancy is even larger; CA pays over $45,000.00 per year for an average prison inmate, and a little over $5,000.00 a year for the average California State University student’s education.

Perhaps California should start hiring their laid off teachers as prison guards. I’m sure ET would see the logic in that.