Review: The Case of Mrs. Oublier

California Math Reform, 1985 Edition

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 and her math teaching, at a time (the 80s) when California lawmakers sought to radically transform math teaching in the state through curriculum reform.

Mrs. Oublier is a pseudonym, oublier meaning “forgotten” in French. She’s earned this title for thinking her teaching had undergone a revolution, though in the eyes of Cohen she hardly changed any of the important stuff. Cohen reports that she is well-liked by her students, colleagues, and that her administration thinks she is doing a swell job.

As a student, Mrs. O hadn’t liked math much, and 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 that a change has occurred, even if he thinks this “revolution” isn’t worth very much at all.

II.

In the centerpiece episode of the paper, Cohen catches Oublier in the midst of what he feels is 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 many 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?

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. The whole text has been posted online, including the lesson that Mrs. O was teaching. I notice that it recommends cubes instead of beans:

Once 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…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.

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 Cohen has more to say about her teaching in the piece. According to Cohen, Oublier generally seemed to adopt only the most obvious external features of cutting-edge 1980s math teaching. She asks kids to estimate, but doesn’t give them chances to think or share their thinking. 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?

Cohen provides a helpful summary of the aims and methods of the 1985 math reforms. At their center was a document, the California Math Framework. This 1985 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 forever.

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.

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.

This is why Cohen dwells so much on Oublier’s textbook choice. Oublier’s favored Math Their Way 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, their beliefs, abilities, and preferences.

Cohen published this article in 1990, just after NCTM published its Principles and Standards for School Mathematics in 1989. The NCTM document 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. The math education establishment generally considers the results mixed. 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, and it can only somewhat impact their teaching.

IV.

Everything above is a lightly reworked version of something I published back in 2017 on a previous blog. I’ve been thinking about it again because education reformers are currently circling back to curriculum as a “the one approach that hasn’t yet been tried to break out of an exhausting cycle of failures,” as the headline to a Robert Pondiscio piece puts it.

Well, it has been tried.

There is a certain amount of soft influence that you can exert with curriculum. What if you took every text currently in use and made it 20% better? Better practice questions? Uncontroversial improvements? Clearer instructions? There is a certain amount of curriculum quality that is just quality, and shouldn’t make anybody particularly angry. I think that would be good!

But what if you gave Mrs. Oublier a textbook that she didn’t like? And what if, instead of 1985, it was 2024, and she had an internet connection?

The question is whether Oublier’s administrators are going to not just mandate a textbook but police her use of it. Is she going to be allowed to make modifications? Some schools and districts, I know, have barred their teachers from choosing problems or revising materials. I get it, they’re worried that teachers will water everything down. But teachers, quite reasonably, know that sometimes the kids in their room need something different from what the text is giving.

So, you make a decision. Either teachers can’t modify things, or they can. And if they can…

Curriculum reform, then and now, is attractive to education reformers because it seems like a way to impact teaching without changing teachers. Every reform along these lines has met a similar fate in the past idk 60 years. I’m not saying curriculum reform is a bad idea, but if it has any chance of changing teaching, it won’t do it by ignoring the people in the classroom.