Tag Archives: constructivism

Reform Math: An Isolationist’s View

For my sins, I periodically peruse the Method Math teacher blogs. I call them Method Math teachers because, much like those self-important thespians in the Actors Studio can’t just act, these guys can’t just teach. Not for them the order of a structured curriculum; no, they want “meaningful math”. They don’t want their kids to do well unless it’s the right kind of doing well. Do they love math? Do they have the proper respect and curiosity for math? What’s the student’s motivation?

They are correctly described as reform math teachers. In math, “reform” refers to the “progressive” side of the debate, in which math is not so much a field of study as it is an ideological value system. Discovery and complex instruction are the guiding lights of their lesson planning. However, since they are teachers, and most teachers don’t really care about education policy in any coherent sense, many teachers who embrace the tenets may not be aware of the ideological underpinnings of their chosen Method. They Like or Don’t Like, without much sense of anything beyond their classroom. (and in that, they are like most teachers).

Reform math is all about social justice, enabling blacks, Hispanics, and girls to “feel successful” about learning math. Actually being successful at learning math is a whole different thing; certainly these demographic categories are successful with their teachers, but when it comes to outside assessments, not so much—which is why reformers don’t much care for standardized tests. But in the classroom, constructivists and discovery-based lessons can accept multiple methods, which means no one method is wrong. And explaining! Explaining is vital. “Explaining your process” is the way that the “procedurally competent” kids (only in reform math is this a bad thing) can be flunked or at least marked down for not explaining their work, while other kids can find “other ways to be smart”. Convenient for grading, this value system allows teachers to dream up all sorts of ways for top kids to fail with the right answer, while tolerating all sorts of other ways for low ability kids to succeed with the wrong one.

(Ironically, these same people who focus on the importance of explaining the “why” are always insisting that teachers reduce the literacy demand of word problems, for kids who can’t read. That’s because the explaining aspect is meant to assist white girls weak on math but strong on literacy, whereas literacy reduction is all about making the problem set up easier for blacks and Hispanics to interpret.)

Reform math practitioners enthuse about this “open-ended discourse”, which avoids calculations and algorithms and, you know, answers. At least definitively right answers. Which teachers don’t give. Teacher explanations = failure. Hence Dan Meyer, the Lee Strasberg of the math blogosphere, famous for his Ted talk, has a blog that proudly bears the label “less helpful”.

Open-ended discourse requires curiosity and ability, which some might deem a feature, but the knowledgeable understand is a bug. Inquiry teaching deliberately eschews algorithms or process or anything resembling a structured approach (while allowing that “blind memorization” might occasionally be useful). Few reform teachers understand the underlying rationale for this method, which lies in the hope that open-ended problems will narrow the achievement gap—not by improving achievement of the lower half, but by narrowing all achievement into a much thinner band. Hence the importance of grading down the top students, and slowing (well, they call it deepening) instruction to be sure that no one is pulling too far ahead.

Ed schools ferociously pretend that all but a few racist fuddy-duddies teach using constructivist methods, but out in the real world, reform math is mostly fringe. The greatest penetration is at the suburban elementary school level, which has a teaching population disproportionately comprised of cheery young women who care more about their students’ interpersonal skills than intellectual development (a feature, not a bug). Complex instruction requires students to “share ideas and knowledge” and the strongest students are responsible for the weakest students’ learning, entrancing elementary school teachers with the delusion that math lessons can enhance social justice. Besides, elementary school teachers aren’t terribly strong at math to begin with, so a method that de-emphasizes algorithms reinforces their own preferences.

Since elementary school teachers rarely have the math chops to develop their own lessons, most reform curriculum development is found in middle school, where kids don’t stay long enough for the parents to complain and the teachers are knowledgeable—and teaching the subjects most attended to by reformers (pre-algebra, algebra, and geometry). So there’s a big support group and lots of material to build on.

Few high school math teachers embrace reform; those who are committed to the Method don’t have a long shelf-life. Most give it up after a few years, the rest show up at grad school where they can pretend that constructivism and complex instruction are valid, proven methods. They get a Phd and demand conformity from prospective teachers in ed school, successfully selling their dogma to a few eager apostles. These converts, alas, ultimately abandon the method or return to grad school where the cycle begins again. Thus Dan Meyer is no longer teaching math but getting his PhD at Stanford with Jo Boaler, Queen Mother of Reform Math. (Understand, however, that reformers do not practice what they preach in ed school. There aren’t multiple ways and many right answers when training new teachers. Heavens, no.)

To the extent reform math survives for any length of time, it does so in white, suburban elementary schools, although not without a struggle. Elementary teachers’ support is counterbalanced by well-educated parents who generally despise it. Parental protests have killed reform math programs at all levels for decades throughout the country. Districts have to balance happy teachers with howlingly angry parents. The high school battles ended over a decade ago, but elementary school parents have to deal with teachers who actually like the program.

But reform math wars are mostly a tale of suburban woes, as parents push back on well-meaning districts hoping to close the achievement gap of their bottom 10-20% by depressing their top performers. It stresses the parents out, but the kids will catch up. For all that reform math propagandists want to change the world for black and Hispanic kids, the techniques are abandoned quickly in high poverty, low ability schools, particularly at the high school level. The story goes like this: a complex instruction curriculum is introduced with great fanfare, math teachers complain, the complainers that can’t be fired are transferred, cue the fawning news coverage with much noise about “equity” and “access”, a few beaming parents who barely speak English talking about their children’s newfound love of math, clips of young black teens and Hispanic girls talking about how they like this math sooooo much better than “just being told what to do”…..and then the dismal state test scores come rolling in and all the canny zealots who once exhorted the grunts to be guides standing to the side are now publicly championing sage on the stage. Back comes explicit direct instruction and the cycle begins again.

The Jo Boaler brouhaha contains one such example, as James Milgram points out:

Indeed, a high official in the district where Railside is located called and updated me on the situation there in May, 2010. One of that person’s remarks is especially relevant. It was stated that as bad as [our work] indicated the situation was at Railside, the school district’s internal data actually showed it was even worse. Consequently, they had to step in and change the math curriculum at Railside to a more traditional approach. Changing the curriculum seems to have had some effect. This year (2012) there was a very large (27 point) increase in Railside’s API score and an even larger (28 point) increase for socioeconomically disadvantaged students, where the target had been 7 points in each case.

Railside High is San Lorenzo High School, in California. As Milgram says, its 2010 scores are dismal, while 2012 scores are improved. Not substantially—ain’t no getting around basic cognitive ability coupled with absurdly unrealistic expectations. But improved.

So I began this post to explain the tiny twitter tempest I began last week, and I’m not there yet. And to get there would take the post into specifics when thus far it’s been general. Sigh. For some reason, I’m writing very slowly this summer. But I didn’t have any clear description of reform math that I could link to in order to explain reform math as I see it, which is not quite as most critics see it.

If the Method teachers out there in the blogosphere do read this, they may confuse me for a traditionalist and, uh, no. My ed school is committed to complex instruction and inquiry-based learning, and I am very fond of my ed school. It’s not fond of me, of course, but then who is?

At that ed school, my all-discovery, all-inquiry, all-complex-instruction master teacher provided me with the best learning experience of my life, adopting effortlessly to my strengths and skepticisms to give me fantastic advice that I hark back to this day. I am, to put it mildly, Not Easy to Teach. That I got six months of valuable education counts for a lot. Thanks to that teacher’s willingness to focus on goals, not methods, I learned to do the same. I can find a lot of good in reform objectives, and steal interesting concepts in their lessons. I might think reform methods are awful but, like progressive educators in general, reformers are thinking about how to teach math, which as it happens is a subject much on my mind.

I am not and never will be a member of the Method group. I am Switzerland, or the US between world wars. Ignore the fact that my first year out I put my students in rows for three weeks until I couldn’t stand it anymore and put them in groups. Second year out I lasted 10 days. Third year out and beyond, I gave into the inevitable and just put the kids in groups from the start. I use manipulatives, introduce units not with facts but with activities that illustrate facts, minimize my use of algorithms, and always remind students that I’ll take a good estimate in lieu of a calculation (and give most of the credit). Anyone evaluating my teaching practice would conclude I have much more in common with the Method crew than I have with traditionalists.

Still, they are profoundly wrong, and their nonsense grates on me much more than the many ways in which the traditionalists err. That’s what led to my tweet, which yes, I still haven’t explained. But I’m ready to start explaining now, so that’s a step up.

Edited later to add:

A couple points. First, I welcome comments on this much because it will help me determine whether I’m getting the right ideas across. I know I can be tough on commenters who misinterpret me, much as I try not to, but I will really try not to if you want to complain about something you’ve misinterpreted on this particular post.

Second, I paint in broad brushes. Keep that in mind!

I’m going to try hard to get the second part of this up faster than normal, for me. I’m hoping for a couple days, but if I fail, know that I tried.