I took only sporadic notes during the presentations at the CIME workshop I attended last week, assuming that the speakers would post their slides at some point.  (This may have been rash; videos from the previous workshops in the series can be found here, but there don’t seem to be any lecture notes.)  Here are some quotes I wrote down; apologies to the speakers for any transcription errors.

  • Alan Schoenfeld:  “Formative assessment is not summative assessment given frequently.”
  • Deborah Ball:  “We don’t have names for how we ask questions.  What does ‘good question’ mean?”
  • Kristin Umland:  “We make inferences about what students know.” (If I recall correctly, this was a response to an audience member who suggested that tests show us exactly what students know.)
  • Ann Shannon quoted one student talking to another about a shared task:  “We don’t have to do any math!  We can just think about it!”  Ann went on, “they think math is just about remembering how to do things.”
  • Phil Darrow (one of the three lead CCSSM writers):  “Sleeping problems have been awakened by Common Core.  Why are people saying CC is so much harder?  We’ve been hiding the math that teachers didn’t know.”
  • Sara Rezvi (a high school teacher and Math for America fellow):  “I have, on average, 33 kids in class for 55 minutes.  We teachers on the front lines need support.  [The improvement we want is] not going to happen unless there’s a fundamental shift in support for teachers.”

I see that I’m about to lose all battery power; no outlet nearby at this lovely Berkeley coffee shop.  Incisive commentary on the above to follow…or not.


About Priscilla Bremser

Professor of Mathematics Middlebury College
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3 Responses to Snippets

  1. Rob Root says:

    Love these quotes. I have to say, I have a pretty good answer to Deborah Ball’s question: a good question is one that shows that the questioner has been thinking. Questions that indicate a lack of attention to what has just been said are usually not good. Questions the show that the questioner sees that what was just said has implications are generally very good. My favorite way to teach is in a classroom where the presentation is largely driven by questions. The development of the material doesn’t always go the way I planned for, but this is a small price to pay for students who are anticipating the implications of what they are seeing.

    Anyone reading my comments here will know that I heartily agree with Phil Darrow’s remark. In my mind, the VMI is just the kind of culture-shifting institution that is desperately needed to alter teacher’s perspective on what it is to teach mathematics, and why it is so important. Ann Shannon’s comment simply reinforces this view. The students view math mechanically because they are taught it that way.

    The simple arithmetic of Sara Revzi’s comment is chilling. Teaching math is labor intensive, especially at the elementary level. I suspect that we would need far fewer college-level faculty and they could teach their subjects far more effectively if students arrived at college with a clearer idea of what mathematics is and where its value derives from. Getting to this state would require an enormous investment in the teaching of elementary mathematics. Not just clarifying for teachers what it means to teach mathematics, but–yes–probably more teachers. Many countries accomplish this by having mathematics taught by specialists even in the early elementary grades. It is critically important that teachers like Revzi not just have assistants who can begin to offer students something like personal attention, but that those assistants have a crystal clear idea of what needs to be taught, and that they be exemplary role models. Much has been made of higher education’s affliction with Baumol’s cost disease. I suspect that elementary education has an even worse case.

  2. Priscilla Bremser says:

    Right, Rob — students view math mechanically because they have been taught that way. I would add that those who are taught that way (not all, thank goodness) have teachers who were taught that way, and so on.
    To be honest, I’ve never heard of Baumol’s cost disease, so I went to Wikipedia (ahem). I don’t buy the musician analogy, because I think the job of being an elementary school teacher has changed tremendously since I had Miss Millspaugh in first grade. Could you clarify what you mean?

  3. Rob Root says:

    Although Baumol’s cost disease is most commonly exemplified by the example of an ensemble of musicians playing a piece of classical music, it is really an economic idea. There are certain economic activities that are not prone to large gains in productivity over time, and those stand out in comparison with other activities that technological or economic innovation tend to make more efficient. One farmer in the 20-teens can be many times more productive than a similar farmer one hundred years earlier, but an elementary school teacher today teaches roughly the same number of pupils in roughly the same interval of time as her antecedent a century ago. (I hope that referring to a generic elementary school teacher in the feminine will be taken as being realistic but not imposing a stereotype.) I don’t meant to say that the job is the same. For one thing, the rise of families with two working parents or of single-parent families has shifted more of the societal burden for child-rearing onto the teacher, rendering the productivity expectations on her much higher. This is to say nothing of the raised expectations in terms of academic achievement that today’s teacher is held to.

    So, here is further evidence that the industrial model for education is a serious obstacle for clear understanding and effective reform: One hundred years ago, one teacher took one year to take one class of students through one grade of schooling, and today the relationship between a teacher’s time and the outcome are about the same. I’m not going to argue that what gets taught in a grade is the same; I believe that it is much more, and it needs to be. The social and scholastic skills needed for a young person to develop into a contributing member of society are far greater than they were 100 years ago. So, a teacher needs to be paid a competitive wage for today, not for 100 years ago, even though in simplistic terms her productivity hasn’t increased. (Ironically, much of the increase in productivity in economic spheres beyond education can be pretty directly attributed to innovations in education.)

    This makes teaching really very different from the vast majority of careers, though not the vast majority of professions. Baumol’s cost disease has much to do with the increasing cost of health care and the increasing inaccessibility of legal representation, too, for instance. So, my point is that a society ought to expect to spend an increasing fraction of its economic output on education. We can see this happening in higher education and health care, but we seem oblivious to the need to spend ever more of our treasure on preK-12 education. This is Baumol’s cost disease in a nutshell: as the pie gets larger, the fraction going to elementary school teachers ought to get larger, too, even though the “one teacher for one class through one grade in one year” representation of education suggests that there is no increase in productivity to justify it.

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