Was The Las Montanas Math Lesson “Good” Teaching? (Part 2)

For well over a century, a perennial dilemma has haunted (and taunted) teachers of high school English, social studies, math, and science. Should they teach students existing subject-matter in approved courses of study and textbooks (e.g., know key dates and people, geometry proofs, and Periodic Table of Elements) or should they focus on students understanding concepts and learning how to inquire, think, and problem-solve (e.g.,teach critical thinking skills in history and English, use Geometric Supposer software that allows students to move figures, estimate changes in quadrangles, circles, etc. and construct their own understanding of concepts).

With the onset of electronic technologies, using high tech devices has become entangled in that perennial curricular dilemma of content vs. skills: should new technologies help teachers transmit the existing curriculum or should new technologies shift traditional ways of teaching subject matter toward ambitious classroom practices of building students’ creativity, inquiry skills and problem-solving.

Of course, I pose these as mutually exclusive issues but when policymakers consider stakeholder interests, political context, (e.g., the current press for test-based accountability and national curriculum standards) and available resources–compromises get made and hybrid policies emerge in practice melding the two positions. Everyone takes college prep courses is the current policymaker mantra, for example, yet career/technical academies and other options for youth pop up daily.

Even with these hybrid policies, strongly-held beliefs about knowledge, teaching, and learning have divided policymakers, practitioners, parents, and researchers into different camps for decades and go well beyond the usual labels of “progressives” vs. “traditionalists.” Imagine E.D. Hirsch inviting Alfie Kohn to go for a long hike on the Appalachian Trail.

Now consider that math lesson I described. For those who champion national curriculum standards, Core Knowledge schools, Everyone Goes to College, using test scores to evaluate teachers, and similar policies, the math lesson would be “good.” The teacher executed efficiently and with brio a familiar “warm-up,” introduced new material, directed students to practice what they learned, and assigned homework. Moreover, the lesson would be considered “good” because her students were attentive–no one went to sleep or had to be admonished–and she used a new technology to both engage students and help them learn the concept of Scale.

Others, however, would grade the lesson mediocre. Why? Because information transfer–as some would put it–was the goal of the lesson, not getting students to ask questions, pose different ways of solving the stated problem, or provide alternative answers. Even if such student actions did occur–the description of the lesson suggests they some did happen–they were accidental, not intentional. Moreover,the use of the IWB only strengthened a traditional geometry lesson. Sure, it was a nice touch to have students use the stylus, have a calculator magically appear on the IWB, and similar novelties but, in the end, the new technology altered neither how the teacher taught or how students learned. Same old, same old

So here are two competing judgments of the same lesson filtered through ideologically tinted lens that disagree over whether it was “good.” To complicate matters further, recall an earlier distinction I made (see post of February 28, 2010 “Great Teachers?”) between “good” and “successful” teaching. “Successful” teaching defines whether students actually learned the concept by supplying evidence from tests, verbal responses to teacher, or actual application of concept, say on the IWB.

Evidence of “success” in this math lesson can be found in teacher questioning of different students, as she walked around the room inspecting students’ working as they worked in pairs. Questioning a student who was stuck is another instance of determining “success.” But these are “soft” measures. Students’ test scores on CST items dealing with geometry would be “hard” measures. Those I do not have.

So where are we now? Two disparate judgments of a “good” lesson and only “soft” evidence of “success” presented. For many policymakers advocating the use of students’ test scores to evaluate teachers, there is a solution that ends the distinction of content vs. skills and “good” vs. “successful.”

In Washington, D.C., Los Angeles, and other places, value-added analysis of test scores are being used to determine the “success” of teachers. For those elementary school teachers (not easily done for high school teachers) whose student test scores show gains over time, they are rated both “successful” and “good.”

As for me, while I do not have “hard” evidence that the lesson was “successful,” I consider it a “good” traditional lesson taught by a skilled, knowledgeable teacher working within a system of district and state test-driven curriculum-standards, testing, and accountability (one that distributes few rewards and many penalties for low test scores). It is a system that assumes an “information transfer” framework and expects teachers to do what is expected. Some teachers do it well, as in this lesson, and some teachers do it poorly.



Filed under how teachers teach, technology use

7 responses to “Was The Las Montanas Math Lesson “Good” Teaching? (Part 2)

  1. Larry, you and I are light years apart in our perspectives of a lot of things educational. But, if I may, I will put forth a few thoughts.

    I have no idea if this is good teaching or bad. I’m not sure it makes any sense to try to make a judgment from this simple description. I’ll give you a lot of credit for describing at all. I have long felt that simple accurate description is woefully missing in educational studies. A short description is much better than no description at all.

    But consider the following situation. Same classroom, same lesson, but instead of you taking notes and describing, there are four cameras in the classroom. Each camera is remotely controlled. Everyone knows the cameras are there, but they are very little noticed. They’ve been there since the beginning of the school year, but they are never commented on by the teacher, and students never see any of the results of these cameras. Both students and parents knew before the school year started that they would be there, and consented to it. Researchers may play and replay some segments extensively in order to investigate some pedagogical question. Most segments are stored away and never viewed. Let us suppose for a moment that your brief description is accompanied by a few CD, DVDs, whatever it takes, to make available a detailed video record of what you describe. Would this then allow us to decide whether this is good teaching or not so good?

    Maybe. Or maybe not. I can imagine spending hours and hours on the videos and coming away with what to me is a very important question. Is real geometry being taught? Call me a grinch, but to me real geometry means Euclidean geometry. Anything else is a pale imitation of the real thing, a cheap substitute, a sinful cheat. Of course I am thinking of a pretty normal class of tenth graders here. I have a bit of experience teaching geometry and I know it is not for everyone. Maybe this class is served better by something less than the real thing. To make that judgment might not be easy, even with a full video record.

    If I may digress for just a moment I’ll explain my perspective in a bit more detail. My wife and I adopted all our children, (they’re all grown up now) and each came with different special needs. One is smart. Her special needs were entirely physical. The others are special education. So I know something about different levels of ability. Euclidean geometry would not be suitable for any of our kids but one. For that one, anything less than the real thing, Euclidean geometry, would indeed be a sinful cheat. (Did she get it? I don’t know she took geometry in the ninth grade, but it has never been clear whether it was a good course or not.) So if this is a class of normal tenth graders they should be getting real Euclidean geometry. If they are not then it’s hard to say that they are getting good teaching.

    This goes directly to your “perennial dilemma”. You ask whether teachers should “teach students existing subject-matter . . .” or “focus on students understanding concepts and learning how to inquire, think, and problem-solve . . .” Call me a sour grinch again, but where you see a dilemma I see a false dichotomy. Of course we should focus on students understanding concepts and learning how to inquire, think, and problem-solve. Every good teacher struggles with that everyday. They always have. They always will. And how do we do it? Simple. We teach students existing subject-matter. There’s no dilemma. That’s as good as it gets. That’s how you teach students to understand concepts, to think, to inquire, to problem solve. There’s no other way. There never has been. There’s no magic. There never will be.

    I know your dilemma has a long history, going back a hundred years anyway. Educators have been talking about child-centered versus teacher-centered for about that long. And many practicing teachers have been irritated by those terms for that long. I see no convincing evidence for your dilemma. I see no convincing rationale for your dilemma I find no intuitive feeling for your dilemma. I find nothing in my experience that leads to your dilemma. All my experience and intuition leads me to my perspective, that there is no dilemma, that you teach critical thinking by teaching subjects well, than child-centered versus teacher-centered has always been nothing more that faddish terminology. I do understand that my experience and intuition will convince you no more than your experience and intuition can convince me. But, for what it’s worth, there is the vast difference in our perspectives. I’ll keep trying to understand your perspective, and I hope you will do the same.

    You ask why reforms come around again and again. Easy. Because there’s no magic. There never will be. But students can learn. And teachers can teach. There’s just no magic. And who needs it. Real teaching and learning is satisfying and exciting, for students and teachers.

    I know you consider yourself skeptical of the magic in technology, but I don’t think you’re skeptical enough. In your description again and again your mention the technology and I wonder why. I can’t think of anything in your description where the technology was relevant at all. You say the teachers “used computers daily at home and school, . . “ Sure. And mechanics use wrenches. And salesmen use telephones. What about it? With an “electronic pen” a student put his answer on the board. What is the relevance that the pen and board were electronic? “The teacher checked out his answer on a calculator that appeared on the IWB after a tap from her pen.” There is something very relevant here. The problem was computational. It was a calculator problem. That is part of what prompted me to ask if it is real geometry. There’s nothing here to prove that technology is perverting subject matter, but it does present the possibility. There’s very little computation in real geometry.

    “They were looking up math URLs that the teacher had given the class earlier . . .” Now this bothers me. Looking up anything detracts from listening to the teacher. The romantic notion of the Internet is that it makes a vast array of resources available to students at the touch of a few buttons. I compare that to a shelf of algebra books. Theoretically a lot of algebra books can be a greater resource than a single algebra book. As a practical matter a lot of time can be wasted thumbing through books.

    Good teaching can be defined in many ways, and by different perspectives. But a very important consideration is making good use of the student’s time and efforts. Practice in one form or another is important in learning any subject. Practice usually takes the form of doing homework. A well chosen or well designed homework assignment can be very good use of the students’ time and effort. A poorly chosen or poorly designed homework assignment can waste time and cause frustration. Nothing about this is evident in your description. The video record might help, but actually looking at what is assigned would be best.

    The coherence of a course over the long term can also be important. This is impossible to judge from a brief description. It might be equally impossible to judge from a video record, but valuable clues might be gleaned.

    Good teaching involves good classroom control. No discipline problems are evident in the description, and one might guess that no discipline problems would be evident from a detailed video record. That is important, but it is also very important how that happy state of affairs is established and maintained.

    I don’t know how to judge good or poor teaching. But it has always seemed very strange to me that anyone would think that an administrator can watch a class for fifteen or twenty minutes and make a good judgment about teaching. I can understand why they must try. But researchers ought to look a lot closer.

    So is this good teaching? I haven’t a clue.

    • larrycuban

      Thank you for taking the time to comment at length on this post.

      You are correct that descriptions, be they brief or extended, are constructions of the writer based upon what he or she sees–and filtered through the writer’s ideas, experiences, and values. What you call a perspective. The video recordings of the class that you suggested certainly might capture what occurred with students and teacher in a particular lesson. Any viewer of that accurate record who wants to determine the “goodness” of the lesson (let’s say you) would still have to construct an account of that class from that video record. In that account, you would cite evidence from the video to justify any judgments you would render. Since you believe unreservedly that there is only one true version of geometry (“Call me a grinch, but to me real geometry means Euclidean geometry. Anything else is a pale imitation of the real thing, a cheap substitute, a sinful cheat”) inevitably your beliefs, your perspective, would color the account that you would construct from the video record of the lesson.

      Which brings me to your point of there being no perennial dilemma only a false dichotomy. Perhaps. By a dilemma, I mean a conflict in values, in this instance, within a teacher who, over 180 days in a school year, constructs a course that meets his or her personal values, the district’s required curriculum, and the mandated tests that students take. There is no dilemma for a teacher who believes that the only version of true geometry is Euclidean. So you are right. For you, there is no dilemma. Lessons in non-Euclidean geometry, lessons–even video recorded ones–that don’t focus on proofs cannot, in your perspective, be “good.” For other teachers, researchers, parents, and policymakers who do not share your convictions, there may be uncertainties over which kinds of content and skills are worth teaching. For those folks, there are dilemmas.

      While we disagree, Brian, I do appreciate very much your taking the time to comment on this post.

  2. Jane

    Larry, I don’t think Brian is saying that “there’s no dilemma because only one kind of Geometry is acceptable,” (he is saying that Euclidian Geometry is best for those who can master it but that other types are better for students for whom proofs are too challenging). He seems, rather, to be saying that there’s no dilemma because both teacher-centered and student-centered instructional techniques can be appropriate and that those who claim that exclusive reliance on one or the other is best, are mistaken.

  3. Jane

    PS — Brian is also saying that there’s no conflict between teaching students “existing subject matter,” and teaching them to ask questions, think creatively, etc. I would agree. All of my best teachers prepared us to think creatively and ask new questions, and a big part of how they did that was by helping us master the “existing subject matter,” so that we had a platform of basic knowledge on which to build our questions.

  4. Well, sort of, Jane. But more essentially I am challenging the helpfulness of the teacher-centered-student-centered idea (or the related student-centered-subject-centered idea). I won’t say it’s totally without meaning. People can use the idea to classify different practices if they wish. But I have always thought a good parallel is this. Do you use verb-centered sentences, or do you use subject-centered sentences? The distinction can be made, if you want to, but that by itself does not necessarily convince anyone that the distinction is helpful in any way. Hopefully every sentence of mine will have both a subject and a verb.

    The verb, to teach, requires both a direct and an indirect object (though that distinction can be a little muddled, at least in my mind), as well as a subject. More essentially the concept of teaching requires all three things, a subject, a direct object, and an indirect object. So what kind of a teacher am I? Well, obviously I am a student centered teacher. Students are involved. And obviously I am a subject centered teacher. A subject is involved. And obviously I am a teacher centered teacher. I am involved. If someone else insists that I am a subject-centered teacher, I probably won’t bother to argue very much, but that doesn’t mean I’m convinced.

    We might think of some other distinctions or dichotomies, roughly parallel to these, that are useful in some situations. Does it make sense to say that the service department of one car dealer is fuel system centered, while the service department of another car dealer is electrical system centered? Possibly it is, if they get reputations at being better at one or the other. But normally both service departments have to be competent in both areas. Does it make sense to say I want a location centered weather report, while someone else wants a phenomenon centered weather report? Well, it could. If I have absolutely no interest in the weather anywhere else but here, no matter how newsworthy, and another person wants only to hear of thunderstorms, no matter where they are, and nothing else, then the distinction could be both meaningful and useful.

    But in all cases a distinction is valuable only if it is indeed valuable, if it has some practical use, or if it has some explanatory value, or something. Here again, of course, we have different perspectives. If you say a distinction has meaning and value, and I say I don’t get it, that doesn’t prove anything one way or the other. I have made distinctions myself that others seem to find no value in. (Here’s a good example: http://www.brianrude.com/Tchap13.htm)

    My hope is that by articulating our different perspectives we might make some progress in finding common ground, and much more importantly, in developing a pedagogy worthy of the name.

  5. Jane

    Make that, BRIAN, agreed!

  6. I didn’t chime in on the previous post because I felt I couldn’t answer the question. I thought about it a bit and this new post seems to look at a part of my discomfort.

    The *other* part has to do with my problem with measurement of a highly variable system.

    While the lesson, the teacher, and the students are presented as a static model for measurement as they must, the reality is different. Bruce Baker at Rutgers has an interesting take on the issue.

    I suppose it depends on the degree of variance you *think* is present. I see it like the global warming debate (if you’ll bear with my digression.) The folks in favor of the various flavors of accountability check the thermometer and say it’s cold or hot outside, using a baseline of ten, twenty or fifty years, they don’t see anything important happening other than it being wither too hot or too cold on an given day. On the other hand, climate modelers use five or six complimentary metrics and try their best to reconcile the resulting trends over a period thousands of times greater.

    Current systems of measurement just seem cheap. We may as well roll a die.

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