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Modeling Teaching

Tomorrow's Teaching and Learning

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Effective professional development, improved teaching, has been Schoenfeld\'s goal throughout his career, improved mathematics teaching in the beginning and with How We Think, improved teaching generally. The aim in constructing a model of teaching has not been the creation of a mold to shape teaching, but the discovery of a tool for understanding it more deeply. As with DNA, each effective teacher will have traits in common with other effective teachers while remaining unique at the same time.



The posting below looks at the work of Alan Schoenfeld in developing models for effective teaching. It is by James Rhem, executive director of The National Teaching and Learning Forum (NT&LF) and is #64 in a series of selected excerpts from the publication reproduced here as part of our \\\\\"Shared Mission Partnership.\\\\\" NT&LF has a wealth of information on all aspects of teaching and learning. If you are not already a subscriber, you can check it out at [] The on-line edition of the Forum - like the printed version - offers subscribers insight from colleagues eager to share new ways of helping students reach the highest levels of learning. National Teaching and Learning Forum Newsletter, Volume 22, No 2, February 2013. Copyright ©John Wiley & Sons, Professional and Trade Subscription Content, One Montgomery Street, Suite 1200, San Francisco, CA 94104-4594. Reprinted with permission.



Rick Reis

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Tomorrow's Teaching and Learning

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Modeling Teaching


Recall the power of models as tools of inquiry in the growth of human knowledge - the importance of Watson and Crick's double helix model of DNA for example. Models have always been important as means of drawing together careful observation into an informed hypothesis about how things work. They become a testing ground, a tool, a foundation on which further understanding can be built. But amino acids are one thing and student-teacher interactions are another; or are they? Could careful, analytical observation of teaching lead to a useful general model of teaching? Alan Schoenfeld thinks so and his book How We Think: A Theory of Goal-Oriented Decision Making and its Educational Applications (Routeledge, 2011), the culmination of decades of such observation, lays out a robust case for such a model.

Many engaging discussions of teaching live in a semantic world creating and refining metaphors to describe it. Schoenfeld, a mathematician and a professor at the UC Berkeley Graduate School of Education, approaches the discussion empirically. Internationally recognized for his work in math education, his confidence in models emerges as a natural expression of his mode of thinking and learning. \"A very nice thing about models, and

a compelling reason for building them,\" he says, \"is that they can tell you when you don't have things quite right.\" Even the best metaphors don't do that, at least in the same way.

Building A Model

Thus, following the success of his influential Mathematical Problem Solving (Academic Press, 1985), Schoenfeld and the Teacher Model Group he heads at Berkeley began investigating student-teacher interactions in the classroom seeking to derive a testable model of them as a means of understanding the deep dynamics of teaching. In numerous charts, graphics, and complete transcripts, How We Think lays out the careful analyses of videotapes of three different teachers spanning the range from expert to novice, from college to grade school, plus analysis of an audio tape of a consultation with a physician. The goal-oriented decision-making model Schoenfeld came up with stands on three legs - resources, goals, and orientations or beliefs - each intertwined with the others and each with its layers of complexity.

Resources, Goals, Orientation/Beliefs

All three of the teachers studied were teaching math and even some of Schoenfeld's colleagues saw that as the fatal flaw in his noble effort. \"'Math is so precise but history and literature are so vague.' That's precisely the argument some colleagues put to me when I was in the middle of this research,\" Schoenfeld recalls. \"'You're not going to be able to model these goals in history and so on,' they said.\"

Schoenfeld didn't agree: \"I argued back, 'No, it's because you don't understand mathematics.'\" For Schoenfeld mathematics has more to do with sense making than with \"right\" answers. The theorems, formulas, and logarithms of math should be compared with the rules of grammar in his view, useful tools in expressing an understanding of things almost always more complex than we can fully grasp, at least for very long.

He points to the most common uses of math in daily life, things like predicting the weather. \"What these uses of math produce are actually probability distributions,\" he says. They are models that embrace the idea that \" . . . this thing is so complex I can't understand it, but I can build a model that let's me come close.\" \"And when you do that,\" says Schoenfeld, \"you are approaching the same sort of thinking you do in studying history.\"

An empirically derived model might not explain everything about teaching, but it could establish a framework for greatly enriching our understanding.

Convinced of the value of models, Schoenfeld and his team needed a method, a group of guiding assumptions to use in extracting a model from the teaching they observed. Perhaps the most powerful of these was the often unexpressed positive idea that all the teacher's actions were designed to help students learn, to posit that their moment-to-moment decision making was the result either of prior planning or some \"trigger\" within exchanges with the students. However obvious that may have seemed in retrospect, it cleared a path into the larger mystery of effective teaching. What lay behind the teacher's plans? What resources did the teacher bring to the planning? What where the goals for the class? How were they set? And what attitudes or what came to be called \"orientations or beliefs\" governed the planning and its execution? Moreover, how did these resources, goals, and orientations reassemble and re-prioritize in response to different sorts of expected or unexpected \"triggers\"?

What's Not Said

The first teacher examined in depth was Mark Nelson, then in a teacher preparation program, who'd had something unsettling happen in his conduct of a class on reducing fractions. He wanted some help figuring out what had gone awry and ended up bringing videotape to Schoenfeld and the Teacher Model Group. \"It only took us four months to figure out what happen,\" Schoenfeld remembers. \"It turned out to be pretty important. He was in a situation where his understanding of teaching was 'I want to work with the things my students generate for me. So as long as what they say gives me an entry, I can build on that and clarify.' \" Nelson was committed to question and clarification - the familiar IRE mode of \"Initiation-Response-Evaluation.\" He wanted his class to be about sense making. He didn't want to dictate procedures and have students memorize and repeat them. He wanted the concepts not simply to be accepted, but to make sense at every turn. But in the lesson, reducing fractions led to a turning point where, to the students, reducing x5 over x5 to get x0 looked as though x equaled zero instead of one. Nelson needed a student to suggest \"one\" as the answer, and when it didn't come, he was stuck.

\"He was ineffective because of his beliefs about what was appropriate to do in the classroom which made it that much harder for him to understand and change,\" says Schoenfeld, \"because those beliefs were implicit. He'd never made them explicit.\" And, of course, things unspoken often have the greatest power.

The Power Of Beliefs

As the research continued, \"beliefs\" continued to emerge as a key, often unarticulated, factor governing teachers' decision making. Analyses of other, more experienced, highly skilled teachers added to the model even as they tested its validity. Teachers enter the classroom with an array of resources. They have knowledge of their subject of course-the facts-but they also have procedural knowledge about how things work and conceptual knowledge of how things fit together into larger systems, and they accrue sets of problem-solving strategies (knowing how to do things). And just as they have these kinds of knowledge about their subject, the more they teach the more they develop parallel sets of knowledge about pedagogy or \"pedagogical content knowledge,\" strategies for navigating troublesome concepts and dealing with the unexpected. But despite such commonalities, teachers teach in different ways. They share a common aim-student learning-but they have different ideas about how to achieve it. And both in their planning and in their moment-to-moment decisions and actions these personal orientations toward teaching shuffle their goals and access to their resources and explain the effectiveness or ineffectiveness of their teaching.

\"So going up a level,\" Schoenfeld continues, \"teachers develop all sorts of beliefs about the nature of mathematics, about the nature of their students and what's appropriate pedagogy. They may well be unaware of those beliefs, but those beliefs shape what they do with students. And that's why the framework of knowledge, beliefs/ orientations, and goals is so critically important. If you want to do professional development, it's not going to take hold unless you actually manage to meet teachers where their beliefs are because if they are unaware of them and those beliefs are shaping what they do, then your professional development is not going to have any impact.\"

Effective professional development, improved teaching, has been Schoenfeld's goal throughout his career, improved mathematics teaching in the beginning and with How We Think, improved teaching generally. The aim in constructing a model of teaching has not been the creation of a mold to shape teaching, but the discovery of a tool for understanding it more deeply. As with DNA, each effective teacher will have traits in common with other effective teachers while remaining unique at the same time.

Using The Model

While Schoenfeld's work springs from analysis of teaching in mathematics, he believes that the processes of teaching, the deep processes, are fundamentally the same across disciplines. What his research has found falls a long way from proof, he admits, but, he says, that's what the next twenty years are for. What seems quite clear, however, is that any productive use of the model for analysis of any teaching and any formative improvement of teaching will have to take on the intimate and dangerous matter of externalizing and making explicit the teacher's personal orientations and beliefs. Because these involve egos and personal histories for teachers just as they do for students, getting them out clearly and calmly remains a complex human challenge. But Schoenfeld has already seen examples of this being done successfully.

Schoenfeld offers a number of examples including work done by Abraham Arcavi who teaches at the Weizmann Institute of Science in Israel. Arcavi also used videotapes, but he began with tapes that weren't close to home, tapes of teachers in Germany and Japan.

\"He knew that there are two initial humps you have to get over,\" says Schoenfeld. \"One is teachers' resistance to letting each other in on each other's practice either live or videotaped. The second is a tendency to be judgmental. You look at a tape and you go 'I would do it differently.'\" And, indeed, when first viewing teaching from Japan where a teacher may spend an hour on one question, the first reaction was \"Well, they can do that in Japan; Japanese kids are different.\"

Arcavi countered by telling his colleagues they weren't there to judge, but to be more analytical and ask, \"What do you think the Japanese teachers were thinking about their students and about learning when they structured their lessons the way they did? What are the things these teachers must believe for them to be acting this way in the classroom?\" These questions turned the discussion toward a search for the positive springs of action and away from traditional critique.

The group moved on to looking at tapes of teachers in the United States who were basically spoon feeding their students answers and then, in time, to reflections on their own teaching.

Schoenfeld says: \"What happens in this kind of context is that people begin to talk about some of these things pretty openly because it's not about them, it's someone on a videotape. If they build the right kind of community where they see that the other people are pursuing those issues without being judgmental, and then you start looking at videotapes from people in your own group. If a couple of people who are a bit more confident start off the conversations, and the conversations work, then they open up and you'll be surprised what happens.\"

Toward the end of our interview, I ask Schoenfeld if time in the trenches acquiring \"pedagogical content knowledge\" isn't perhaps the key. \"That's a part of the story,\" he replies. \"The thing that characterized the true expertise of expert teachers is that they are superb at listening to their students, at hearing what their students are actually saying, meeting the students where they are, and creating a space where the students can learn productively.\"

\"That's a core part of their belief system. What happens is if you think it's important, you can develop that skill, and that's where that body of pedagogical content knowledge gets developed over the years. . . . You can get very good at engaging the kids in activities, but you are not going to develop the pedagogical content knowledge of listening to your kids and adapting appropriately if that's not a focus of yours and you think that good materials will do it.\"

Schoenfeld's model doesn't explain why seeing clearly and listening carefully seem so difficult, but it points clearly to the triumph of learning to do both.