Reading Research: The Case of Mrs. Oublier

I.

A Revolution in One Classroom: The Case of Mrs. Oublier (link) is an oft-cited piece of education research by David K. Cohen. It’s a case study of just a single teacher (Mrs. O) and her math teaching, at a time (the ’80s) when California lawmakers sought to radically transform math teaching in the state.

Mrs. Oublier is a pseudonym, oublier meaning “forgotten” in French. She’s earned this pseudonym for thinking her teaching had undergone a revolution, though in the eyes of Cohen she hardly changed any of the important stuff. I guess the point is that she oublier-ed to make these changes? Or that reformers didn’t help her make them?

Anyway, a lot of the fun of the piece is seeing the funhouse-mirror ways in which Mrs. O interprets those cutting-edge ideas about manipulatives, small group work, and estimation. And Cohen has serious things to say about why policy-makers never quite reached Mrs. O in the way they intended to, though I might question some of his conclusions.

Another thing that’s interesting about this piece is what it’s not: a representative sample from the teaching population. It’s the story of one teacher. Cohen tells us that Mrs. O’s story matters, but why should we believe him?

There’s no denying that Cohen tells a good story. But isn’t research supposed to be more than a good story?

II. 

Mrs. O has been teaching second grade math for four years. The kids like her; colleagues like her; administrators think she’s doing a great job.

As a student, Mrs. O hadn’t liked math much, and she didn’t do too well in school. When she got to college, though, she started doing better. What changed? “I found that if I just didn’t ask so many why’s about things that it all started fitting into place,” she tells Cohen. So, that’s not a great start.

And yet, Mrs. O tells Cohen that she’s interested in helping her students really understand math. She also tells him that she’s experienced a real revolution in her teaching, a departure from the traditional, worksheet+drill methods she used when she began. On the basis of his observations, Cohen is strongly inclined to agree with her on this.

In the centerpiece episode, Cohen catches Oublier in the midst of a fairly ridiculous lesson. Oublier wants to teach her students about place value (so far so good). To do this, she wants to introduce another base system (debatable, but not necessarily a disaster). So Oublier gives each kid a cup of beans and a half-white/half-blue board.

Mrs. O had “place value boards” given to each student. She held her board up [eight by eleven, roughly, one half blue and the other white], and said: “We call this a place value board. What do you notice about it?”

Cathy Jones, who turned out to be a steady infielder on Mrs. O’s team, said: “There’s a smiling face at the top.”

On a personal note, I have been teaching 3rd and 4th Graders for four years and the idea of giving kids those little cups of beans gives me minor terrors. What if the cups spills? How early do you have to get to school to set up the beans? What if a kid eats a bean?

Anyway, after Mrs. O has ensured that all the kids noticed that their boards are half-white and half-blue, she starts the game. The game is supposed to be about grouping and regrouping in place value systems, but it’s really entirely about beans. She calls out a command, and the kids add a bean. At no time does she connect the beans to numbers.

According to Cohen, this was no accident, as Mrs. O wasn’t really a fan of making numbers explicit in her activities:

This was a crucial point in the lesson. The class was moving from what might be regarded as a concrete representation of addition with regrouping, to a similar representation of subtraction with regrouping. Yet she did not comment on or explain this reversal of direction. It would have been an obvious moment for some such comment or discussion, at least if one saw the articulation of ideas as part of understanding mathematics. Mrs. O did not teach as though she took that view. Hers seemed to be an activity-based approach: It was as though she thought that all the important ideas were implicit, and better that way.

Oublier is a huge believer in manipulatives — in fact, the transition from worksheets to manipulatives seems to be a big part of what her “revolution” entailed. For Mrs. O, kids learn through the physical manipulation of the objects. As in, learning is the direct result of touching beans:

Why did Mrs. O teach in this fashion? In an interview following the lesson I asked her what she thought the children learned from the exercise. She said that it helped them to understand what goes on in addition and subtraction with regrouping. Manipulating the materials really helps kids to understand math, she said. Mrs. O seemed quite convinced that these physical experiences caused learning, that mathematical knowledge arose from the activities.

Oublier tells Cohen that she relies heavily on a textbook, Mathematics Their Way, and that this text was the major source of some of her new ideas about physical activities and teaching math. From poking around, it looks like the whole text has been posted online, including the lesson that Mrs. O was caught teaching. Here’s what the bean-counting activity looks like in the text:

Screenshot 2017-06-11 at 8.55.38 PM.png

OK, now the next page of that activity:

Screenshot 2017-06-11 at 9.11.52 PM.png

But you won’t believe what’s on the page after that:

Screenshot 2017-06-11 at 9.12.43 PM.png

This is sort of getting repetitive so I’ll just skip ahead five pages:

Screenshot 2017-06-11 at 9.13.37 PM.png

Cohen comes down pretty hard on this curriculum, and on Mrs. O for using it:

Math Their Way fairly oozes the belief that physical representations are much more real than symbols. This fascinating idea is a recent mathematical mutation of the belief, at least as old as Rousseau, Pestalozzi, and James Fenimore Cooper, that experience is a better teacher than mere books. For experience is vivid, vital, and immediate, whereas books are all abstract ideas and dead formulations.

I’ve focused on the manipulative episode, but that’s just part of her teaching that’s detailed in the piece. According to Cohen, Oublier generally seems to adopt the exterior of cutting-edge math teaching while sort of missing their points. She asks kids to estimate, but doesn’t give them chances to think or share ideas. She uses manipulatives, but doesn’t really ask kids to think much with them. She puts kids into small groups, but basically uses this as a classroom management structure. She avoids numbers and abstraction wherever possible.

This was certainly not what California’s math reformers had in mind.

III. 

The point, for Cohen, is that California’s math reformers let Mrs. O down. But how, exactly?

I found myself needing more context for the California reforms than Cohen provides. Fortunately, the journal issue in which Mrs. O originally appeared was entirely dedicated to the California math reforms. (In fact, every piece in that issue was a different in-depth case study like Mrs. O.)

Cohen actually leads off the issue with a helpful summary of the aims and methods of the 1985 math reforms (link). At their center was a document, the California Math Framework. The Framework called for a transformation of math teaching away from rote memorization and drill, and towards a focus on conceptual understanding, teaching kids to communicate about math, problem solve, work in groups, make sense of math, etc.

So far, nothing new. Reform groups like NCTM have been pumping out these documents for a century.

What was new was the muscle California chose to employ. The state education office said that they would only reimburse districts for textbooks that met the standards of the Framework. And then they actually followed through by rejecting all the texts that publishers initially submitted. Eventually, the state got what they wanted and created an approved list of textbooks for districts to choose from.

(As Alan Schoenfeld notes in his Math Wars piece, California — along with Texas and New York — determine what gets published nationally because of the size of their markets. The publishers basically design their books for the big states, and the rest of the country gets dragged along. So California’s reform muscle had national implications.)

This was half the plan. The other half was to change the state tests for kids so that they also reflected the vision of the Framework. The idea was that if textbooks and tests were in place, teachers would come around all on their own.

I missed this the first few times, but this is why Cohen dwells so much on Oublier’s textbook choice. Oublier’s favored Math Their Way text was not an accepted California text, and Oublier’s district had adopted something else. Oublier likes Math Their Way, though, so she just uses that in her classroom instead. None of her superiors seems to mind either.

In other words, that entire “change teaching by making a list of textbooks” plan was sort of stupid. It failed to account for the ability of teachers to get other textbooks if they wanted to.

The fundamental assumption of the policy seemed to be that teachers need permission, or perhaps incentives, to teach in new ways. As Cohen points out — over and over — this is not the case. Teaching in fundamentally different ways implies believing that you should teach differently as well as knowing how to do so.

It’s pretty simple, actually: if you want to change teaching, you can’t ignore the teachers.

IV. 

Even as Cohen critiques the California reforms, he still seemed to me pretty cheery about the potential for policy to impact reform.

First, he really does seem to give a lot of agency to math textbooks. He keeps on talking about the influence of the Math Their Way book on Mrs. O. On the one hand, the book’s influence on her comes at the expense of the Framework’s reach. At the same time, if a textbook can really have such a strong impact on a teacher, then the premise of the California reforms has been upheld. If you’re a reformer reading Cohen, I imagine that your mind starts wandering: imagine what would’ve happened if we could’ve gotten the right book in her hands!

Beyond Cohen’s implicit optimism about textbook reform, he also wonders aloud about the possibility that a bit of incentive-engineering could have steered someone like Mrs. O towards better teaching:

“The only apparent rewards were those that she might create for herself, or that her students might offer. Nor could I detect any penalties for non-improvement, offered either by the state or her school district.”

These two sources of optimism, when put in context, seemed a bit dated to me. Cohen published this article in 1990, just after NCTM published its Principles and Standards for School Mathematics in 1989. This was, in many ways, a higher-profile go at California’s Framework, and (surprisingly to all involved) it took off, becoming a blockbuster for NCTM.

In the 90s, NSF would fund the development of new math texts that were aligned with the NCTM standards. My sense is that they didn’t live up to the expectations of the textbook-optimists. The texts were just texts, tools that teachers could use well or poorly depending on their understanding of math and of teaching.

It turns out: textbooks can’t transform teachers.

(Textbooks, it also turns out, can become highly visible targets of controversy, and nearly all use of the reform textbooks became contentious in the 90s. So that seems like it needs to be part of the textbook-reform calculus.)

Cohen seems to think that Math Their Way transformed Mrs. O, but he also thinks that she didn’t really revolutionize her teaching. The changes were cosmetic. And there’s a huge difficulty determining how the text impacted because of the plain fact that she chose this curriculum. Presumably, she chose it because she was disposed to. It fit with her understanding of math and of teaching. It didn’t fundamentally challenge her, and I see no reason to think that a text has any such power of a teacher, even when imposed.

Cohen’s other musing — about incentives — has echoes in No Child Left Behind and performance pay reforms. These reforms have also failed to live up to the dreams of the reformers, as all reforms do, and teaching chugs along, mostly as it has.

At times, it seemed to me that Cohen believes that the fundamental problem, for Mrs. O, is that her views on the nature of math remain unchanged:

…however much mathematics she knew, Mrs. O knew it as a fixed body of truths, rather than as a particular way of framing and solving problems. Questioning, arguing, and explaining seemed quite foreign to her knowledge of this subject. Her assignment, she seemed to think, was to somehow make the fixed truths accessible to her students.

I’m not particularly sympathetic to this critique. Math, among other things, is a fixed body of truths (theorems, facts, relationships) that we ought to help students know.

But forget that for a moment. Cohen sometimes seems to think that this isn’t just a problem for Mrs. O, but the root problem. If we could just help Oublier see that math isn’t quite as she thinks it is — that it’s dynamic, a source of puzzles, it’s about thinking and not just about knowing — then her teaching really would undergo a real revolution.

This seems to be where we are, right now, in math education reform. We’re not trying to save the world with NSF-funded textbooks, and we’re not hoping to incentivise great teaching. We believe, like Cohen, that the fundamental problem is one of learning, and that the fundamental problem is a fundamental problem, some ambitiously big thing that, if we can help teachers attain, the rest of their teaching will fall into place.

Right now, one version of the “fundamental problem” is productive struggle. NCTM has included this in their latest set of reform standards, the Principles to Actions standards. And if you’re in Baltimore this July, you can attend a three-day summer institute focused on productive struggle. The workshop promises to show how productive struggle is tied to every dimension of effective math instruction, from planning to feedback to wider advocacy.

I don’t think I believe in this sort of reform either. Cohen keeps drawing comparisons in this piece between teacher and student learning — both are challenging, he says, both take time. And that’s true. But imagine if we treated students like teachers. In other words, imagine if instead of teaching math to kids we had a workshop a few times a year where we tried to fundamentally alter their conceptions of math, and then sort of hoped that the rest of their math learning would just fall into place.

I know the comparison isn’t exactly direct, or fair, but I don’t believe that any knowledge can be altered by changing one fundamental element. Knowledge isn’t really structured that way, it seems to me. It’s not built on a foundation. To alter teaching you’d have to alter it broadly, not centrally. And broad change just can’t happen in a three-day workshop.

The final source of optimism that Cohen raises is that maybe Mrs. O represents progress for math reform. Though she hasn’t seemed to internalize the message of the reform, this sort of messy progress is what progress actually looks like.

I have no way of knowing if that’s true, but it certainly strikes me as possible. I haven’t read more recent work of Cohen’s. I wonder if, looking back on the last 30 years of reform, he’s still as optimistic.

V.

Hey, wait a second! This is just a single case study. We were swept along in this gripping tale (aptly summarized) and assumed she represented some larger trend, but that’s just the illusion of focus. Cohen’s fooled us, then, hasn’t he? Maybe Mrs. O means nothing at all. (Or, at least, nothing beyond her own case.)

There are two things that temper this sort of skepticism. First, the journal that published Mrs. O also published four other case studies in the same issue (open version). So in addition to the case of Mrs. O, you also get the case of Carol Turner, Cathy Swift, Joe Scott, and Mark Black.

(Unclear if the other pseudonyms are also supposed to be deeply meaningful. Mark Black, because policymakers treat him like a black box. Cathy Swift, because the reforms were too fast! The other two stump me. Maybe they’re anagrams? Joe Scott = COOT JEST.)

Five case studies are only a bit better than one, but these other four cases present a lot of the same mixed-success-at-best themes as Mrs. O’s case. That helps.

The other thing that tempers skepticism about Mrs. O’s relevance is that Cohen actually also identified the “forgotten teacher” problem in a very different piece of research.

That other piece is called Instructional Policy and Classroom Performance: The Mathematics Reform in CaliforniaThis time around, Cohen and his team do pretty much the opposite of “sit in the back of a classroom and watch.” They survey 1,000 California elementary teachers. They ask teachers to rate how frequently they employ various instructional activities in class. Hey, they ask, wouldn’t it be nice if all these teacher responses really pointed to two types of teachers? We could call them “traditional” and “reform-friendly”…

Err, did I say “traditional”? I meant “conventional”:

Screenshot 2017-06-12 at 10.51.01 PM.png

 

Anyway, Cohen’s group also asked teachers what professional learning opportunities they had, in relation to the math reforms. (I love that ‘Marilyn Burns’ is an option.)

Screenshot 2017-06-12 at 10.52.30 PM.png

 

What they find basically supports Cohen’s take in his Mrs. O piece — reform is possible, but only when it focuses on professional development that targets teacher learning:

Our results suggest that one may expect such links when teachers’ opportunities to learn are:

  • grounded in the curriculum that students study;
  • connected to several elements of instruction (for example, not only
    curriculum but also assessment);
  • and extended in time.

Such opportunities are quite unusual in American education, for professional
development rarely has been grounded either in the academic content of schooling or in knowledge of students’ performance. That is probably why so few studies of
professional development report connections with teachers’ practice, and why so many studies of instructional policy report weak implementation: teachers’ work as learners was not tied to the academic content of their work with students.

Some people love the Mrs. O piece, but hated the sort of study that we previously read here, the one about teacher-centered instruction for first graders. First, because they rely on teacher responses to survey questions, and how much can you really learn from that? Second, because the statistical work can hide researcher assumptions that then become tricky to dig out. Third, because with scale comes quality control issues. You really no longer know what you’re dealing with.

To which, we might ask, why did Cohen produce exactly this kind of study when it came to evaluate the success of California’s reforms?

I talk to just as many people, though, who hold the complete opposite view. To them, something like the Mrs. O study is useless, as it doesn’t help us identify the causal forces at work. Maybe the reform failed Mrs. O, but compared to what? There are no controls, and without some sort of random assignment to a treatment can we really be sure that a focus on teacher-learning would make the difference Cohen said it would?

Is it too soft of me to say that both critiques are right?

It’s not my job to study teaching, but it sure seems hard. Every research approach has trade-offs. The way I see things, it’s best to use multiple, incompatible approaches to study the same things in teaching from wildly different perspectives. Why? Because of how it’s possible to take wildly different incompatible perspectives on teaching.

At one point, Cohen points out that Mrs. Oublier seemed comfortable living in contradiction:

Elements in her teaching that seemed contradictory to an observer therefore
seemed entirely consistent to her, and could be handled with little trouble.

But there really isn’t anything strange here at all. Everyone is willing to live with some contradictions in their lives. Contradictions can be unlivable, but they can also be productive — in teaching, in life, but also in research. Intellectually incompatible perspectives can be desirable.

Anyway, enough about all this. What should we read next?

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9 thoughts on “Reading Research: The Case of Mrs. Oublier

  1. “In other words, imagine if instead of teaching math to kids we had a workshop a few times a year where we tried to fundamentally alter their conceptions of math, and then sort of hoped that the rest of their math learning would just fall into place.”

    In this single blistering analogy you laid bare the folly of the dominant model of professional development.

    Liked by 2 people

  2. “But isn’t research supposed to be more than a good story?”

    Just as there are many ways to prove things in mathematics (induction, deduction, brute force, counterexample), there are many ways to advance knowledge in educational research. At the time of this article, there was tremendous optimism on how changing the infrastructure for teaching (e.g., curriculum, standards) could transform classroom practice. This case study (along with the others in the same special issue of EEPA) demonstrated the flaw in that theory of action, akin to a counterexample.

    You might find it fun to use the web of science to see how this paper has been cited over the years — it’s been cited over 1000 times. You can use tools like google scholar too. This will help you better understand the arguments have built on this finding. That is a total rabbit hole, of course, but what else are summers for?

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    1. I feel like I got myself in trouble with the “good story” line at the start of the piece, especially since my answer (at the very end) was “no, research shouldn’t be more than a good story.” We gain from different research perspectives on the same messy issues. I’m totally with you, I think. There are many ways to advance knowledge in education, and I think a world without case studies (like these, or like Benny) would be an impoverished one. More on this from me in the closing paragraphs of the post.

      And, yeah! Me and Google Scholar are friends.

      On twitter we have one nomination for a good follow-up read, which is Natasha Speer’s Connecting Beliefs and Practices. I just took a quick look, but Speer’s piece looks interesting. If we want to talk about teachers beliefs/practice, I also know that there are some papers from the IMAP project that I never got around to looking closely at. These all seem bloggable.

      Definitely still seeking recommendations for future reading, though!

      One direction for future reading/writing is further exploring this whole literature of reform-meets-classroom, a lot of whom cite Cohen: Labaree’s Someone Has To Fail, Cuban and Tyack’s Tinkering Toward Utopia, Mary Kennedy’s Inside Teaching, Jack Schneider’s From the Ivory Tower to the Classroom. Larry Cuban’s How Teachers Taught is cited by Cohen, but I’ve been wanting to read that for a while.

      Another direction could be reading more about what the heck was going on in California in the 80s. One book that I came across while writing this piece (and Marilyn Burns recommends) is California Dreaming, a history of this entire reform mess.

      Another direction would be to pick up on the methodological pluralism and keep on exploring that. I’m not sure where that would take us, though I’m reading a pretty doctrinaire book by a psychologist right now, and that might be fun to blog about.

      ANYWAY: recommendations appreciated!

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  3. If you haven’t read Liping Ma’s “Knowing and Teaching Elementary Mathematics,” I recommend that.

    Your summary of “The Case of Mrs. Oublier” reminded me a little of Schoenfeld’s ‘The Disaster of “Well-Taught” Mathematics Classes.’ I’m not sure if the Schoenfeld piece adds something to the discussion beyond “Mrs. Oublier,” but I’d be curious to hear your thoughts on it.

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    1. Thanks for pointing me/us to this Schoenfeld piece! I’m not sure I want to give it the full post treatment right now, but I just read it and have a few quick thoughts to share.

      Schoenfeld, at the beginning of the piece, talks a bit about misconceptions research and the implications that work has on our understanding of teaching. As I understand the standard story, research on teaching had operated within a paradigm that focused on the observables of teaching and learning. Research focused on correlating teacher actions with student performance.

      Then, along comes misconceptions research and shows that you miss a TON if you only focus on the observables of teaching. There is clearly lots of interesting stuff about learning happening inside kids’ heads, as there are persistent misconceptions that students seem to have. Teaching can produce these misconceptions; teaching can help kids move past them. Misconceptions research helps usher in a new research paradigm that is more cognitively focused.

      So misconceptions research chugs along, finding things here and there that kids seem to persistently mess up.

      And then along comes the critique. Misconceptions Reconceived is one of my favorite pieces of writing about teaching. It’s so, so good. And it challenges the misconceptions research initiative.

      (I promise I’ll get back to Schoenfeld in a second.)

      In particular, it challenges the idea that misconceptions are best addressed by directly confronting them, and it also sort of rejects the entire framework that misconceptions research assumes. It’s subtle, and worth reading, but my main takeaway is that learning is about building knowledge atop of knowledge. You can’t learn by rejecting knowledge. You can only reject knowledge when you have knowledge.

      In other words, we need to spend less time detailing the problems that kids have with learning, since in teaching knowing a misconception doesn’t tell you much about how to develop a good, useful, true conception.

      Back to Schoenfeld, and Mrs. O too. Both of these case studies (along with Benny and the other cases in this issue) remind me of misconceptions research on student learning. In a way, these cases are about teacher misconceptions about teaching.

      And, while all sorts of misconceptions research might have been useful at the time, the critique of Misconceptions Reconceived could be applied to Schoenfeld/Cohen too, I think. Sure, OK, lots of teachers think they’re hot-stuff but actually aren’t. There is learning that these teachers could be doing. Just as misconception research helped orient researchers to student learning, perhaps these cases helped reorient everyone to teacher learning.

      Having made that shift, though, these papers offer us comparatively little. Knowing the failures of the profession doesn’t tell us how to improve it, no more than knowing that students think that negative powers yield negative numbers helps us teach exponents effectively.

      So here we are in 2017, and I don’t know how much good these cases do for us. It’s good to know what common student misconceptions are, and it’s also good to know the common ways in which teaching can fail, too. But need to know how to help teachers improve, not just how teachers are failing.

      Of course, I could be badly wrong about all of this! I’d love to know what you (or anyone else) thinks about this.

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  4. Hi Michael,

    I enjoyed your take on Mrs. O. I particularly appreciated your comment at the end that contradictions “can be unlivable, but they can also be productive — in teaching, in life, but also in research. Intellectually incompatible perspectives can be desirable.” This is an idea I’ve been playing around with a bit, influenced in part by Peter Elbow, a rhetoric and composition scholar (see, for example, Elbow, P. (1993). The uses of binary thinking. Journal of Advanced Composition, 12, 51-78.).

    Here’s a brief gloss on Elbow from a paper I’m working on:

    The both/and strategy involves “affirming both sides of a dichotomy as equally true or important, even if they are contradictory”, “accepting, putting up with, indeed seeking the nonresolution of the two terms” (Elbow, 1993, pp. 54, 52). Elbow advocates this strategy as both a thinking tool – keeping issues open allows us to reflect upon them more carefully – and a practical method. Hence, for example, Elbow contends that good writing involves both generating and criticizing, but that these two processes are mutually contradictory since generating requires that we put our critical faculties on hold. Rather than privileging one of the two practices he affirms them both:

    “But whatever the path one takes to good writing, notice that it is not the path of compromise or the golden mean. If we are only sort of generative and sort of critical, we write mediocre stuff: we don’t have so much to choose from, and we reject only the worst. We need extremity in both directions. Instead of negotiating one point on the continuum between two extremes, we need as it were to occupy two points – near both ends.” (p. 56)

    Occupying two points at opposing poles is impossible, unless one does so at different times, i.e. alternating between positions in accordance with the changing demands of the composition process.

    Both/and thinking involves an “epistemology of contradictions”, according to which opposing claims may both be true and useful for understanding complex phenomena.

    And here’s how I end my paper (applying Elbow to educational discourse):

    There is an epistemology of teaching here, similar to Elbow’s epistemology of contradiction. It states, in short, that teaching involves working to meet conflicting goals, and as such constantly places practitioners in situations of ambiguity and dilemmas. The teacher must secure both classroom order and pupil intrinsic motivation, and big Theories such as progressivism and behaviorism are poor guides for responding to the practical, situated problems she encounters.

    If you’re interested, I’ll send you my paper. Or better, here’s a classic math education article that makes similar arguments: Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55(2), 178-195.

    Finally, if you want to pursue the question of what happens when reforms hit the classroom, you might be interested in an article of mine, which builds directly on Cohen and colleagues’ ideas: Lefstein, A. (2008). Changing Classroom Practice through the English National Literacy Strategy: A Micro-Interactional Perspective. American Educational Research Journal, 45(3), 701-737.

    Warm regards,
    Adam

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  5. Michael, First off, I love these essays of yours. So thoughtful and thought-provoking. I’m not sure I have anything to add to the discussion about research and methodology other than to say I find pieces like Cohen’s more enjoyable and enlightening than the stuff with all the stats, charts, and jargon.

    One comment I’ll make is about the book Mathematics Their Way. I used to have that book! I don’t remember where I got it, maybe it was recommended by a math methods professor I had back in the mid-1980’s. I never used it; once I began teaching we had a curriculum that needed to be followed and that book wasn’t part of it. But looking at it again brought back some memories. I think that Cohen may have been overly harsh in his criticism. Looking at the lessons that come after the bean lesson I see that the place value ideas that are building in the lesson are articulated and symbolic representation is added. I don’t think it’s a bad thing if, in that one particular lesson that Cohen saw, she doesn’t get to all the other ideas. I’d like to really sit down and read through the book in its entirety before I make a judgement about it. I think there are some good things there.

    I like that Mrs. Oublier was willing to change. Many teachers aren’t. I’d rather have my kid in her class than in a class doing worksheets and drills. What I would encourage her to do is to be more self-reflective. She seems to feel that her transformation is complete, that there’s no more work to be done. But she needs to continue to grow and improve her craft.

    I love this series and I’ll read whatever’s next!

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  6. Michael,

    As always, I love reading your thinking and how you, yourself, live with ambiguity.

    One very small point: The idea that California, Texas, and Florida determine what everyone else gets for textbooks is substantially less true than it used to be (though it definitely used to be the case). The advents of both state standards/testing and technologies that make it much easier to make multiple versions of materials have made it worth publishers’ while to do state-specific versions of materials that reflect each state’s individual standards, at least for states with reasonably large populations. (I suppose Rhode Island is probably still out of luck.)

    Like

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