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.


About educationrealist

21 responses to “Reform Math: An Isolationist’s View

  • Michael Pershan

    As you said, most teachers aren’t especially concerned with policy. And you write that “most teachers aren’t aware of the ideological underpinnings of their chosen method.” And then you write that in your own teaching you employ many non-traditional methods.

    So here’s what I’m gathering: you see teachers as representing certain ideologies, or even reflecting them. So, in your book, I’m a reform teacher, even though the ideological underpinnings that you mention are completely foreign to me, and have never crossed my mind. Unknowingly, I’ve adapted an ideology that as very much to do with race.

    In other words: using certain methods, reading certain people, talking about teaching in a certain way makes me part of an ideological movement and under their sway, to a certain extent. And, whether I know it or not, my teaching has a lot to do with race.

    Did I get that right?

    • educationrealist

      These questions are helpful to see what I need to alter or restate, so thanks.

      None of this is quite right. I don’t see you as a reform teacher. I could be wrong. I see you as wanting to be one, but being distracted by the fact that it doesn’t work as well as it should, and wondering what you do wrong that you can’t be like Dan, Fawn, and the others.

      And, whether I know it or not, my teaching has a lot to do with race.

      Definitely not this. Rather, that the reasons for pushing reform math originally had a lot to do with the achievement gap as it pertains to race. The reform teachers, who talk a good line in social justice, nonetheless don’t have particularly challenging classrooms with wide ability ranges, particularly low abilities.

      using certain methods, reading certain people, talking about teaching in a certain way makes me part of an ideological movement and under their sway, to a certain extent.

      “Under their sway” in one area only—you appear to think that, if you were the teacher you wanted to be, you’d be like them. That they represent the ultimate in teaching. And if you don’t, that’s great, but I think you at least know many of the teachers I’m referring to. They’re in the comments section: “Oh, my god, I’ve been teaching for ten years and I never knew I could think about doing this! Thank you sooooo much!” “I read you, I want to teach like you, but I’m not there yet!” and so on.

      Meanwhile, reformers are jumping all over anyone who points out that this method is hard on kids who don’t like math because how DARE they suggest that a teacher’s job doesn’t involve teaching kids who don’t want to be there!!!

      I see nothing wrong with reading the teachers and commenting. I’d comment more, but they ignore me. (g) And I definitely see you as quite the skeptic.

      So let me be clear: I was not in any way thinking of you as a reform teacher. I do see you as part of the audience. I don’t want to kill their audience or scream “look away!”. I do think there’s a problem in that the audience has a false idea of reform teaching—not about the ideological underpinnings, but about stuff I haven’t mentioned yet. That’s in part two, and I am going to do my damndest to write it up sooner than a week.

  • Justin

    You say, ““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.”

    I always thought explaining served (or at least also served) to (1) assess where the problem solver went wrong (or where they got the right answer even though they didn’t know what they were doing), (2) give some credit to the problem solver who shouldn’t get a very low grade just because he/she didn’t quite grasp one nuance that was being repeatedly tested, and (3) prevent cheating.

    I wouldn’t expect it to harm high achieving kids, but it would create more dispersed grades because of (2) I mentioned above.

    I’m generally dismissive of partial credit for trying or for getting some of the process right, and I get how it allows more subjectivity as to how much partial credit to give and to whom, but is that a problem with “explaining your process” or with the teachers?

  • educationrealist


    Let’s make a distinction between “explaining” and “show your work”.

    What I’m talking about is the insistence on explanation–not a math equation series, but a paragraph or so of analysis of the work. Worse, in many group work tasks, students don’t only have to explain their own work, but everyone else’s, too.

    Check out this teacher blogger on complex instruction ( (also linked in above)

    The onus is on the students to make sure everyone in the group contributes and can explain how to complete the task.

    All solutions are equal. No one is wrong–in fact, complex instruction methods prohibit students from saying “that’s wrong”. They’re required to say “I disagree.”

    It’s all part of the “multiple ways to be smart” or “assigning competence” process of CI. So Juan can’t add, but he can explain the group’s solution. Sally can’t multiply, but she can draw the poster. And so on.

    I probably should have included more source material–here’s a summary of Cohen, who originated CI.

    • Justin

      Thanks for the clarification. I’m not a teacher, just interested in these topics, so the source material helps people like me try to make sense of what is going on in classrooms.

      • Mary Dooms

        Justin, here’s a more fitting quote from my blog (source material) that addresses “quantity”: “understand how one or more solutions to a task are found.” It can be written, it can be oral, it can be one solution, or it can be many solutions. It depends on the student, how much time the teacher wants to spend on the task, etc. Complex Instruction allows students to contribute their individual, intellectual strengths. I wish I could underscore intellectual because it’s not about multiple intelligences—Sally’s a great artist because she draws the picture. Cohen’s research predates Howard Gardner’s multiple intelligences. In fact her book, Designing Groupwork makes no mention of MI or even such characteristics. If you want to learn about group roles go to:

        and click on the complex instruction roles document that’s listed in day 2. I’ve crafted my own version using this document and Cohen’s work, but it’s worth looking at.

        As an aside, I use CI with several tasks but not all. Like everything else a teacher does, any strategy should be implemented purposefully, with intention.

        If you are one who enjoys reading research findings and teasing out the strategies that maximize learning I highly recommend reading John Hattie’s works: Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement and Visible Learning for Teachers: Maximizing Impact on Learning.

        There are some real game changers identified that I now implement.

  • Robert Evans

    Training students to be indoctrinated followers.

    Ignoring the philosophy of utilitarianism as a meaningful approach to life.

    Avoiding acknowledging to the students that Life Isn’t Fair, and that bureaucracies are primarily made to make life easier for those at the top (the “decision makers”), and only occasionally work to ameliorate the unintended consequences for those at the bottom.

    Have I got the gist?

    • educationrealist

      No. But then, you know that.

      • Robert Evans

        Sorry, I’m not sure if we’re talking past each other because I phrased my original post not so well.

        I was referring to the reformist/method teaching strategy.

        Training to be followers: “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? ”

        Ignoring utilitarianism: ditto the above, and contradistinction to a statement in your followup post “…but here’s a basic truth: there’s not a single situation in your life that gets worse if you pass algebra. And there’s a whole bunch of things that improve.””

        You’ve got a lot more time on the ground, and from both points of view (teacher and student). I’ve just got the student POV. But it seems to me the gist of things is that the reform method sees their means as making every student and teacher a true believer, regardless of what’s already in the hearts, minds and lives of the individual students and teachers.

      • educationrealist

        Oh my lord. I’m an idiot. I’m in my comments section of the wordpress application, and I mistakenly thought this was a response to my next post, Who I am as a teacher. So I thought you were being sarcastic about my teaching and deliberately misconstruing it (in no way could I be conceived as someone deferential to the man). Sorry about that! I will reread your comments in application to the correct post, and report back.

    • educationrealist

      Okay. Having now read your comments in the context of the CORRECT post (attention to detail is never one of my strong points), yes, you have a lot of it.

      Except one thing: this movement began out of a genuine attempt to improve equity. It is an ideological goal, and it’s never a good idea to use education as a tool to advance ideological goals. But they genuinely believe that they are increasing equity and opportunity. They are aided in this delusion by people like Meyer and Nguyen, both of whom are true mathematicians who love math and adopt their philosophy. Boaler, in my view, doesn’t help the cause at all—it’s not apparent she knows much about math.

      So yes, I see their determination as enforcement of a dogma, but like many zealots, they are seeking to improve the world, not consolidate their own power. But here, I’m talking about the ed schools; reform math teachers at the high school level are usually genuinely convinced that this is the best way to teach math. But they aren’t teaching low ability kids all that often.

      • anonymousskimmer

        I have no words. You have to be right, but I don’t want to accept it. It’s easier to oppose if I believe they are demons, but on the other hand I guess it’s stands a better chance of working if they are opposed as merely being wrong. I hope they are successfully opposed on the ground, because until they are – while true believers like them exist among the teachers – it will be that much harder to convince the legislators of their wrongheadedness.

        Reminds me of my favorite quote (about the Milgram Prison Experiment): “People don’t inflict harm because they are unaware of doing wrong but because they believe what they are doing is right. We should be wary not of zombies, but of zealous followers of an ignoble cause.” — “Stephen Reicher is professor of psychology at the University of St Andrews, Alex Haslam is professor of psychology at the University of Exeter.”

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  • MissDtheTeacher

    Interesting post… It seems a bit like you are making bold generalisations about the ‘reformers’, basing your judgements of their methods on two people alone? You question the ideologies of others but what has informed your ideology?

    What about the work of Slavin et al (2009) in their BES that supports so much of the reform maths? What academic research are you basing your judgements on? I ask because I am interested in challenging every students, the achievers and the non achievers. And I am interested in any research that can help me achieve this.

    Also, I ask because I refuse to be part of your cycle described above… I teach full time and have been studying part time for the past three years. The intention being that I never become the academic who can’t practice what they preach, or the teacher who insists that academic arguments don’t hold true in the classroom.

    You should probably read… Slavin, R. E., Lake, C., & Groff, C. (2009). Effective Programs in Middle and High School Mathematics: A best-Evidence Synthesis. Review of Educational Research, 79(2), 839-911. doi: 10.3102/0034654308330968

    • educationrealist

      I went to an elite ed school that did nothing but preach reform math. I am probably at least as well read as you are on the subject. On this site, there are two in-depth reviews of Jo Boaler’s work. I also state on numerous occasions that my own teaching method is pretty squishy. That, too, you can see on this site. If you’re interested, you can read up in the Encyclopedia of Ed (links on right).

      I try not to have an ideology. I have a reality.

  • gtrmath

    I ended up on your page as a result of looking up stuff on Jo Boaler – who is teaching a class for teachers in my state (NH). After reading up on the Boaler/Milgram controversy; I got a pretty good idea of where she is coming from. You write very eloquently about the political hoax that is “Reform Math”. I come from a very different place: AP Teacher(Calculus and Statistics), ARML coach, and Math Team Adviser. The Reform Movement is in opposition to excellence. Social justice and “equity” means bringing down the top- even if that includes poor kids who excel. I’ve a had a student who had free lunch in high school who is now a Phd from MIT. Opportunity is there for all; we don’t need educational Marxism to make everyone’s outcomes the same.

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