Narrative of A Teaching Theory

A discussion of a teaching scenario—what happens after you hand the test back.
Dan Riordan
October 20, 2008

I am not sure that I can precisely define either a model or a theory with enough precision to differentiate the two. However I recently had an experience that has caused me to analyze actions in terms of theory (or model, I am not sure just yet). My analysis led me to phrase the kind of deeper learning question that SOTL can investigate.

Three math teachers sat in my office. We got to talking about tests and student complaints. All three had almost exactly the same story. It went like this: After the test is returned, a student emails the teacher, or asks (confronts?) the teacher about an answer that has been marked wrong. The student says that the grade is unfair because the teacher had never taught the problem that the student had been asked to solve. The teacher responds by pointing out at least three instances in which a problem of the type in question has been either assigned as homework or has been solved in class. The teacher feels that his/her actions are entirely fair, and what the student should know to expect.

I would like to examine this story. It seems to me to be very typical of student/teacher dynamic after a test. I would venture two interpretations—one that deals with morality and the other with theory.

In terms of morality the teacher assumes that he/she has acted in a just (or fair or moral or good) manner in presenting iterations of a problem that she/he expects the student to master because such mastery is essential to understanding essential concepts of the course. The student assumes that he/she has been treated unfairly (or in a bad, unjust, or evil manner) because the teacher has played a trick by not using the problems that had been previously treated in class. Or else the student feels unfairly treated by being marked down as a result of not remembering that the item was treated in class. Either way, the parties find the situation frustrating, so say the least.

In terms of theory, though, the teacher and the student have widely divergent, practically dysfunctional, theories of learning. The teacher assumes that learning occurs as a result of iterative treatment of specific problems that are of the same type. As a result of the iterative treatment the learner grasps the essential concepts and rules of action (in this case the parts of the formula and the appropriate places to apply the formula), and as a result can identify in a new problem, with new specifics, the elements that require using the formula to solve. The student, however, assumes that learning occurs as a result of being given in class a preview of the contents of a test. Having been given that preview, the proof of learning is the ability to identify the previewed problem and repeat the action that was initially performed to solve it. In this case a new problem, one never previewed, is irrelevant to proof of learning because it could not be learned because it had not been previewed.

It seems to me that all of us teachers can resonate to this scenario; we all have some version of this story. If we resonate and if we look at the story in moral terms (or as we often point out, in maturity terms), it is easy to get a good laugh. However, suppose we look at the scenario in learning terms. If my analysis is correct, what is operating here is an amazing disconnect in learning theories. If both groups continue to hold the theories they have, neither will convince the other that learning has occurred. At this point what occurs is one of those incredible “learning moment” opportunities. A teacher will no doubt be asked/confronted in frustrated moral terms, but the discussion could be turned to learning terms. If the discussion were successful the teacher would convince the student that he/she must abandon a currently held learning theory and replace it with a new, much more productive one.

Now, two more questions arise. How can the teacher do that? And Is the analysis I have presented of the student-held theory accurate? At this juncture, SOTL comes in. As a SOTL research director I can see two lines of inquiry here. First is there a way to determine what the student’s theory actually is? Second, what approach would facilitate the “conversion” to a new theory? At this point, I am not prepared to suggest a methodology for investigating these two questions, but it does seem to me that the results of such an investigation could be enormously helpful to all teachers, not just those in a particular discipline. It is possible that not only the student but also the teacher will have to alter her/his theory. It could be, for instance, that the iterative treatment is not as effective as the theory claims it will be, and, thus, something will have to be added to the pedagogical actions.

And a third question—am I correct in naming each of the actions a theory? By so doing I am assuming that a theory is an approach to a set of data that predicts a certain outcome by the use of the approach. Is that a good way to define theory? If we teachers are going to enter into this discussion, and this research, we need to have clear definitions of these concepts so we can guide our students to the growth and deeper understanding that our concepts, we hope, will produce.

And so, the end for now. Thanks to Jill, Nelu, Eileen, and Laura for a wonderful discussion.