Involuntarily Conscripted Into The Math Wars

It’s difficult for me to overstate how tedious I find the commenters at Kitchen Table Math, and math warriors more generally. It’s like watching two sides argue whether it’s better to feed children fruits or vegetables. Both sides approach the new and unfamiliar interested foremost in determining to which reductive party it belongs so they can get properly exercised.  This requires a healthy amount of unhealthy inference and I’m not inclined to engage any of it. (ie. “All we need are grocery line problems, apparently.” Have mercy.) 

Skill practice and conceptual development are both essential. I have no interest in any war between them, nor in anyone who suggests they’re enemies. I will put this judgment on the record, though: I have only ever found one of them difficult. Even in my first year, at my worst, I could dip into any number of instructional strategies and problem sets to teach students how to reliably factor, solve, simplify, and evaluate. I have always found it difficult, however, to give my students tools to resolve problems that they haven’t yet seen, to empower their intuition through math, or to convince them to give a damn.

I know I could turn to any one of the KTM pedants at any time to help me improve my skill practice instruction.  (Okay, maybe not after calling them “pedants.”) There are far fewer people who have any help to offer me on the harder challenge of math education. 

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. The mere fact that people feel the need to create ideological “isms” and promote binary thinking suggests that you are right in your assessment of the current math curriculum. The reality is that the world is holistic and it is broken into parts. It’s macro and micro. We learn skills and concepts.

    One of the blog comments really struck me – that you are simply young and new and ignorant because you still have passion. Really? Some of the greatest teachers I know are veterans and they are still innovative, passionate and authentic.

    Keep doing what you are doing. You aren’t fighting a war. You are broadening worldviews. People need your perspective.

  2. I read the kitchen table stuff via your twitter last week and it has bugged me since. Then I saw this video and it struck me. As math educators, we should be making math classes more engaging and enjoyable. If we make math more engaging, more students will want participate because they enjoy mathematics. That is where true learning for all students will begin.

    Many of your critics are educators teaching the highest level of mathematics in their high schools. They think that they are successful because they are showing proofs, giving the hard problems, and “thus” seeing great results from students (i.e. top grades). They would never “waste time” on grocery line problems. However, I feel that these educators are missing the point. The point of teaching mathematics should not only be students “learning the math” and scoring high scores. Just because a student does well in math does not mean they like it. It just means they are high achievers and probably do well in all of their classes. Many of these high level students will even claim that they are not “good” at math, and many more will say they do not like math at all. The end result should be that students not only learn how to do the mathematics, but think mathematically and understand mathematics. Most importantly, students coming away from a great math class should enjoy mathematics. This does not only happen in a dry, proof driven, drill and kill AP Calc class, even if you do score a 5 on the AP Calc exam. This also happens in the grocery line.

    As good educators we should not be doing one or the other, we should be doing both. In fact, we should be doing anything and everything that we can to ensure that students learn mathematics, understand mathematics, enjoy mathematics, and know that they are good at mathematics.

    I hear and I forget. I see and I remember. I do and I understand. Confucius

  3. Dan, Why are you wasting the cpu cycles (your brain’s and your computer’s) reading what those people are saying? It will just P_ss you off.

    Let them home educate their kids and complain about public schools. That is their right and choice. We’ll be here when their kids need math help.

    Keep doing what you’re doing. It is all about thinking. If we can keep our students thinking, they will be able to do the basics.

  4. There’s good reason to be bored with the math wars. They’re over. They’ve been over. Kids need both. KTM just hasn’t gotten the memo, or hasn’t noticed over all the shouting and recriminations.

  5. I think it’s good to see what some people are “thinking.” As an admitted progressive in the Math Wars (though I never think of myself as a warrior; I’m more in the espionage, counter-intelligence end of things, with a lot of my open efforts involved in countering propaganda and disinformation, hopefully in the tradition of Gerald Bracey and others), I don’t think it’s possible to do good work in mathematics education without incurring the wrath of the lunatics. I would call them a fringe, but they aren’t QUITE enough on the fringe for my taste. They tend to be well-connected to powerful and influential and RICH people and organizations who, unlike NCTM and NCSM, know how to win friends, influence people (particularly naive and ignorant ones, along with those easily panicked into reactive behavior), and perhaps most importantly KNOW HOW TO GET THEIR MESSAGE OUT. NCTM never has and likely never will.

    I know Dan is uncomfortable being labeled “Math Education Future” (a reference to what Jon Landau, I think, once called Bruce Springsteen), but he is. He’s also not alone, but from what I’ve seen of his work, he’s one of the absolute best we’ve got. It’s not necessary, however, for him to take sides openly. All he needs to do is to do what he does. People like me will happily take on the ass-hats, nay-sayers, and Grumpy Old Men (including the 23 year old Grumpy Old Men).

    It’s what I do extremely well. If I were as innovative as Dan, I’d be doing what he does instead. But the trick is to learn where one is most effective and not be afraid to commit to building on that. I’m a synthesizer, as well as someone who knows something great when I see it. But I never worship blindly and always question, probe, and push at the edges of the envelope.

    Don’t fret, Dan. You don’t have to invest too much thought or energy in these people. But do be aware of them. It’s silly to pretend that they don’t exist or underestimate (as NCTM has tried to do for nearly two decades), their willingness and ability to do harm or try to do it.

  6. “…the harder challenge of math education.” It’s harder for the teacher because it’s harder for the kids.

    Teachers are traditionally paid and handled like petty civil servants. But that’s not what they are. They’re managers. A worker is someone who does work. A manager is someone who gets others to do work, wielding whatever incentives are at hand. That’s what teachers do.

    Whatever the curriculum is, a teacher’s job is to get kids to do things most of them would never do if left to themselves. We know that the best incentive is for the teacher to set goals and model the enthusiasm–the passion–for them that we want the kids to share. It’s hard work. That’s why managers outside of schools get paid so much and get to ride in limousines.

    Modeling enthusiasm is especially difficult if you don’t happen to feel it at the moment. As the great philosopher George Burns said, “Honesty and sincerity is the key, and if you can fake that, you’ve got it made.”

  7. So I thought it was cool that KTM featured your TED video, and there are many positive and encouraging comments there. But, as in all groups, there are some grumps who try to shout down & poo-poo all new ideas.

    I think it’s fantastic that your ideas caused so much disequilibrium! Even if they’re just arguing against them, at least they’re thinking about them, and if they’re thinking, maybe a little spark may tweak a nerve and they’ll think “y’know, this guy is nuts, but even in my perfect classroom/homeschool where we always Do The Work and schlog through tons of Practice Problems and have great Fact Fluency, sometimes I have a student who is just not interested or not successful despite my best efforts. I wonder if I should try something new or different” and maybe teacher will grow just a little bit because they saw your video and were bothered by it.

  8. Amber Caldwell

    May 9, 2010 - 9:03 am -

    While basic skills are necessary, who cares if my students can factor trinomials if they don’t know how much to tip a waiter without an app? I have Algebra II students who can not compare cell phone plans, but can simplify radicals with the best of them.

    I am a math person so I am always first to run to the appropriate equation and solve it showing all of my steps, but I am often humbled when a student suggests a quicker method that often involves critical thinking and did not require the creation of a variable named x. This is what I want to foster in my students. I will be successful in my classroom when my students can think through a problem and share possible solutions, even if they didn’t do it like the sample problem in the text. Our classrooms must be a balance of skills and relevant problems that necessitate those skills. Please continue with your plight in math education. There are many of us out there who appreciate and even rely on your work to inspire us.

  9. I agree that, at high school level and above, both (skills and concepts) are important. I’m not so sure if that’s the right outlook for elementary school. I think ‘playing around’ is incredibly valuable (at all levels, but especially for the little ones).

    I guess that makes me a number one suspect on the KTM list, but I bet we could find some values we hold in common. ;^)

  10. It’s not news that there are educational conservatives in mathematics all over the world. The English and Australians have them and no translator is needed. Israel is fairly rife with them. I’ve found them in Holland, too. I have little doubt they are universal and that like the poor, they will always be among us.

    The difference for me is that I don’t blame poor people for their circumstances unless I have a lot of evidence that a given individual is utterly responsible for his/her own sorry state. With educational conservatives facing innovative ideas, it’s hard not to blame them for their head-in-the-sand, hold-back-the-ocean-with-a-broom attitudes, however. To quote a variation that frequently appears on math-teach, a list I finally left after about 15 years of arguing with such people because the list-moderator and list owners had clearly changed the rules in ways that overly-favored their own worst enemies (can you say, “Liberals love to shoot themselves in the feet and then wonder why they limp”?), “There’s nothing that’s good that’s new and nothing new that’s good.” This is said in relation to math teaching, teaching, and much else. And Dan’s work is a constant thorn in the side of people with that viewpoint.

    Long my he wave.

  11. Just posted this on KTM:

    It can’t be easy to find this many wrong-headed people (though a few with their blinders off), though I should remember this is “Math Wars” and ‘math warrior’ turf and not be quite so surprised. SteveH appears to be the blindest of the bunch, not able to get anything right about what Dan Meyer is saying even in a short 12 minute talk.

    Mr. Meyer is likely one of the more interesting people teaching K-12 math out there, and while no one, least of all Mr. Meyer, is calling out “Dan, Dan, Be Like Him,” he certainly is offering lots of ideas worth thinking about. It looks like, however, thinking about things without having to judge them instantly in “Math Warrior-Speak” is not the long suit of some folks. Nothing new there, but always so sad when a really interesting person like Dan Meyer comes along.

    Nothing Dan does or talks about is offered as a panacea. Nor is he ever suggesting that any particular thing he does or talks about is even something he has “perfected” (as if that were ever really possible to begin with, outside the weird imaginations of, well, self-appointed math warriors and their dupes).

    What he does show is that we need not settle for business as usual, need not pretend that new technology doesn’t exist or can’t be applied to teaching, that old technology and resources and everyday objects can be used in remarkably innovative ways to make things INTERESTING (perish the thought, eh, math warriors?) and that in general there are many more ways through the woods than one.

    This is terribly threatening to people who want to keep everyone firmly rooted in about the 13th century, give or take. Luckily for most of us, Dan Meyer and others like him really don’t give a fig for all the nay-saying. As someone pointed out on his blog today, the perfect image for SteveH, as well as many more nationally-known math warriors like Wayne Bishop, James Milgram, and David Klein, is Dana Carvey’s character on SNL, “The Grumpy Old Man. Doesn’t matter if you’re old or young, male or female: anyone can be a grumpy old man, and we’ve got some beauts in the comments above. Holding back the sea with a broom, are ya? Lots of luck with that.

  12. Bill Bradley

    May 9, 2010 - 1:41 pm -

    My one comment as to the various “reform” movements in education is the problem with pendulums is that they spend so much time at the extremes, and so little in the middle.

    I teach both Science and Mathematics and am amazed at the insanity that is the mantra “We need to teach problem solving and higher order thinking skills so that the students can succeed in today’s world” compared to the reality “So we’re going to assessment using multiple choice bubble sheets”

  13. Good teaching is hard. I appreciate you working on it, and sharing your process with us. (As do so many of these commenters so far!)

    Please keep doing so. I guess the good side of being noticed is that it means you’re being read, which is good reason to keep writing. Or videoing.

  14. Wow, Dan. Have to say I disagree with you on this one. It’s clear that the problem with math education in America today is that we’re not giving enough worksheets… I mean skills practices. My heart goes out to all those poor souls in remedial classes who clearly are there because their teachers in previous years didn’t give enough homework. What a disservice you are doing to your children by taking a small portion of time trying to get them to think about math in the world around them. What are they going to do when their future employers give them job application questions where they have to solve compound inequalities? or complete the square? Seriously have you even *considered* what will happen to the children of America when they grow up and can’t remember the Trig product to sum identities? You haven’t and that is appalling, sir, downright appalling! With teachers like you, we’ll have people running around trying to creatively think their way through life problems instead of thinking inside the box! Why don’t you take the time you use on these silly lessons and spend it on something productive like finding a way to fit a worksheet INSIDE another worksheet, so that teachers can give homework *while* they’re giving homework.

  15. Dan-

    The people who comment at KTM strike me as being genuinely concerned about kids’ mathematical knowledge, and yet so indescribably burned by something bad that happened either to them or to their kids by way of modern pedagogy that their concern has mostly sublimated into shrillness and alarm-sounding. It’s like the voices of people who once would have said, “Math education needs fixing; what can we do to make it better?” and now can only say, “Math worked for me and let’s hunt down the people who do it differently”.

    I think your time is better spent on continuing to care about kids, how they learn math, and how best to prepare them for college and the real world — as you are already doing — than to engage in the math wars with people who are verifiably not interested in changing their minds about anything.

    The other Dan @4: Please reconsider the remark about home-schooling parents. The homeschooled students I get in my college math classes are far and away better prepared in math than the other young men and women. So these homeschooling parents must be doing something right, and I don’t think there’s any evidence that KTM is representative of the entire homeschooling community.

  16. When reading KTM comments, I felt like it was grad school all over again. I’m going to go on a digression here.

    I was in grad school in history, and we took these seminars where everyone read the same dense books and we got together and we discussed. The one survival strategy in these seminars — the strategy that each of the grad students thought would make them look the smartest/most analytic/most prepared — was to criticize the books. Find weak points in the argument, and really tear ’em a new one. The faux-confidence that students derived from bashing this or that became nauseating.

    It became boring for me. A p*ssing contest. It’s totally easy to find holes, to poke sticks, to find weaknesses. There was a lack of deep engagement or a goal of having meaningful and productive outcomes. *The discussion wasn’t about the book at all, but about the personalities of those discussing — and how they wanted to be perceived.*

    When I read the comments of KTM, I immediately had flashbacks to those seminars.


  17. Sam, I didn’t have quite the same grad school experience, but otherwise that’s exactly what I thought. It seemed like mudslinging because they felt threatened.

    I see it in our faculty meetings or professional development meetings all the time: “What are they going to force on us now?” Everyone goes in to these things very defensive and worried about how we’re going to be forced to change, so they try to pick at something in the hopes that it’ll go away.

    Change is hard.

  18. I know the Math Wars are over, and you know they are over, but many of the combatants won’t let the war end. They feel their side was right and they feel it with a religious fervor. I have seen this on both sides. Some try to bash anything that looks like direct instruction or practice while others bash what they see as watered-down math.

    You can’t convince anyone who is solidly in one camp of the end of the wars any more than you could convince the Pope to convert to Islam. All you can do is try to learn from each perspective and keep doing what works for you. It isn’t about any side in a war. It isn’t about focusing on constructivism or skills or great applications or worksheets. It’s about excellent teaching.


  19. Well Dan, the one thing they all seemed to agree on was the problem started with K-8 math, so let me take that burden off your shoulders, it’s all my fault, lol.

  20. I read KTM, but quit participating in any discussion because of that very tedium. And my respect for you just went up a few notches.

  21. Don’t let the haters get you down!

    I got a 92% in my Grade 12 Algebra class, and I teach science (which requires a passing knowledge of math), but damned if I can remember a single thing I learned. I know there was something on quadratic equations, but I can’t even remember what the formula is nowadays. My science students find it moderately humourous that I can’t help them with their math homework, and they’re fairly scandalized when I tell them that very little of what they’re learning (Grade 10 & 11) will actually be useful to them outside of school.

    By contrast, I remember well many individual lessons of my quirky Gr 10 science teacher, because he always tried to get us to make some connection between what we were doing and the real world.

    Keep doin’ what you’re doin’, and let the response of the students be all the accolades you need.

  22. paul: I don’t know any serious mathematics educators who try to bash anything that looks like direct instruction. What those of us who spend a vast amount of time observing US mathematics education do is despair about how rare it is to find effective instruction of any kind. An eclectic approach that keeps kids thinking and on their toes and gets them to engage in meaningful mathematics is what we ask for. What we generally see is teachers talking to themselves and pretending not to notice (or truly not noticing) that few listen and fewer still hear. And then blaming it all on the kids, the neighborhood, the parents, and everything else. These factors are real, too, but they aren’t an excuse for acting as if direct instruction, tons of homework, lots of drill, and making things as dull and deadly as possible are the answer.

    On the other hand, there is no dearth of web-sites or people on them who are 100% dedicated to attacking anything different. Dan is a real threat to such folks, and the KTM cabal try to denigrate his work and dismiss it by lumping him into the fuzzy math/fuzzy book camp. Since even a blind person can see he’s anything but about books, that bespeaks a fanaticism that is truly evil.

    The Math Wars aren’t over. That doesn’t mean Dan has to waste his time fighting in the war. It suffices for him to develop his practice and share it.

  23. Bill Bradley

    May 10, 2010 - 6:12 am -

    @paul thomas It doesn’t help the Constructivist cause that there are many amazing idiots promoting it. Where I got my Masters the Science Education Department were all the worst kind, claiming that you couldn’t teach anything by direct instruction. How where they teaching it? Why lecture of course. When I asked “Are my Physics students supposed to make all of the discoveries from Galileo to Einstein with just some prodding in the right direction?” and got the answer “Yes”… just “Yes” I lost what little respect I had for them. I use exploration, directed inquiry, an projects, but people like them give the whole paradigm a black eye. (Whole Language is a good idea too, but not taken to the extremes that it was)

    The traditional math curriculum and standards do make it difficult to teach connections. I’d disagree on the Geometry bits though…those are all easy to make connections and use, that’s its nature (Geo=Earth, Metry=Measurement, it’s all applied mathematics of measuring) I was given an evaluation copy of what looks to be a wonderful book called _Fundamentals of Algebraic Modeling” by Timmons, Johnson, and McCook. I had to tell the math department that it looks like a great book, and I have no idea how we could use it with our curriculum, so it’s now just on my reference shelf.

  24. I use the word “evil” advisedly and apply it to the conscious adherence to practices that hurt people when such behavior is readily avoidable. I’m not generally applying it to teachers, however, and most of the ideologues in the Math Wars aren’t classroom teachers: they are mathematicians, engineers, pundits, think-tankers, and those that are easily stirred up with rhetoric about “kids today” and “the sky is falling.”

    But some of these people aren’t just evil in thought. They are consciously evil in deed. I can’t speak about anyone on KTM as I don’t spend much time there and haven’t even begun to attempt to sort out the players. I speak from personal experience with people from national anti-progressive groups like Mathematically Correct, people who don’t bat an eye at trying to cost good teachers and others their jobs and careers because they don’t, say, worship at the feet of Saxon or Singapore Math, or say something favorable about some reform text, or dare to suggest that direct instruction isn’t quite the alpha and omega of mathematics pedagogy. When I say personal experience, I mean PERSONAL.

  25. “The homeschooled students I get in my college math classes are far and away better prepared in math than the other young men and women.”

    Interesting point, Talbert. Why do you think this might be?

    What I hear from the many college and university-level math professors I’ve talked to is that their best-prepared students were educated under the Russian, Continental European, and East Asian math systems, which use standardized curricula that have more in common with one another (e.g., the Japanese system compared to the French system) than the myriad of curricula used in the U.S. have amongst themselves (e.g., Saxon compared to Chicago Math).

    Might there be something useful to conclude from this?

    Katharine Beals

  26. Nothing really to add here, though I’d like to highlight Robert’s description of the KTM commenters, which strikes me as both generous and accurate.

    Also this: I’m not immune to criticism but the substance of my talk concerned two propositions, that mathematical applications are important and that we present them poorly to students. If anyone has taken a hatchet to either one of those (as opposed to something I didn’t say) I’d love to hear about and learn from that discussion. I’d love to hear someone argue that we should abandon mathematical application entirely, for example, or that the textbook’s water tank problem is effective.

  27. I used a few of your ideas from the video and elsewhere at my all-day workshop with Detroit h.s. math teachers last Thursday, some of whom had watched the video when I sent it to them. Lots of agreement, lots of rewarding recognition of the wisdom of “Be Less Helpful,” and then trying to figure out how to come to grips with kids who do NO homework EVER, are as likely as not to fall asleep, start singing, or otherwise be way off task seemingly regardless of what is being put forth for them to do or how it’s being offered.

    Of course, that’s not QUITE true in that there is a limit to what has been tried and it’s hard to ignore the contexts in which even the most interesting things tried are placed. Hard to engage students who don’t have any notion of how to listen, speak accountably about mathematics, or a host of other relevant and necessary skills that aren’t strictly academic in nature.

    My teachers are frustrated, but they are (mostly) thinking and listening. My job in part is to keep them from feeling so beaten down from above and below that they give up. Most are still open, when they have five minutes to reflect. Part of what I’ll need to figure out is how to buy them more time to do that.

    As for informed criticism of your ideas? Haven’t seen any. We in Detroit are seeing the need to take problems and strip them down, then figure out how to scaffold them appropriately as we address mainstreaming and differentiated instruction. Every kid is different. Finding powerful, important problems and then toying with them so as to truly give multiple entry points and doing just enough and no more for each student is enormously challenging and time-consuming. Not sure if you have taught classes with such a high percentage of ‘special needs’ students, kids who are in high school operating on average at about a fourth to fifth grade level of mathematical knowledge (if that), or the kinds of inner city culture that informs Detroit schools, one in which the undercurrent of VERBAL violence is one of the most debilitating challenges teachers and students alike must deal with all the time. But I think my teachers are wise enough to see that just stand up and flapping their gums at kids isn’t the way to go. They’re trying to make decent use of the resources and technology they have, to acquire more and better, and to figure out how to be more effective regardless. Perhaps it’s time to bring WCYDWT to the inner city.

  28. Dan, I read about a third of the page of comments you linked before running out of emotional resources I summarily call “mana.” I found there, and then transformed, a useful idea: focus on students.

    How can we invite students to take leadership and initiative in the two tasks of learning: craft (skills) and art (concepts)?

    As yourself, I find the second part harder. I see kids finding and giving help about the skill part all the time, and there are huge robust online communities for that. I don’t see kids’ autonomy in conceptual learning nearly as much.

    How can you teach kids to do what YOU do?

  29. My two cents, Dan, as maybe one of the KTM “pedants” : ) Well, maybe one cent.

    The substance of my talk concerned two propositions, that mathematical applications are important and that we present them poorly to students.

    I agree.

    If anyone has taken a hatchet to either one of those (as opposed to something I didn’t say) I’d love to hear about and learn from that discussion.

    Wouldn’t you think that the authors and editors of (and teachers who successfully used) the textbook problems you display in that talk might have something to say about their “poor” presentation of “mathematical applications”? It’s not terribly difficult to imagine some kind of rebuttal and address it in the actual talk, is it?

  30. Kilian: Not even Singaporeans are satisfied with Singapore Math. Why are Americans so enamored of it, I wonder? Nothing is “4Eva” and nothing “Rulz” as you put it, for everyone in every circumstance. That’s why teaching math isn’t a programmable activity.

  31. MPG: Not sure if you have taught classes with such a high percentage of ‘special needs’ students, kids who are in high school operating on average at about a fourth to fifth grade level of mathematical knowledge (if that)…

    Maybe not that bad, but I dealt with some pretty rough inner-city populations in Sacramento when I first came on the scene. I turned a lot of bad situations to really bad situations because I was tone-deaf in setting up a classroom ethos. Some of my kids thought I hated them, which wasn’t true. I aimed actively at indifference though. “The mailman doesn’t allow himself to get agitated by the mail.” I really told myself that.

    Assuming your preservice teachers know how to actively aim the class ethos at respect and care (while still falling short of that goal four days out of five and only really reaching it the last week in May) they have to start aiming at a curricular ethos.

    I’m getting preachy here and talking out of turn but this really excites me. My curricular ethos is this: My students are all mathematical. They are all intuitive. Their intuition can lead them to mathematical confidence and then to mathematical competence.

    Sometimes I’m not sure I believe myself there but then I open a WCYDWT question with some kind of intuitive question that anyone can access – even someone with a fourth-grade understanding of math – and then we build the problem together. And the curricular ethos and the classroom ethos are insufficient on their own but, man, do those two start to compound each other quickly.

    Joshua: Wouldn’t you think that the authors and editors of (and teachers who successfully used) the textbook problems you display in that talk might have something to say about their “poor” presentation of “mathematical applications”? It’s not terribly difficult to imagine some kind of rebuttal and address it in the actual talk, is it?

    Hi Joshua, certainly there are enormous practical considerations that I blow merrily past in my talk. I’m advocating a graduated structure to problem solving that jumps off of full color multimedia – a video or a photo. I realize this is a structure you can’t just print on a page. I understand that. Maybe twenty years ago I’d have to settle the issue there but I’m too intrigued by the Internet as a channel for curriculum distribution to let it go just yet.

    Am I missing something else? I can imagine a lot of teachers, editors, and publishers conceding the point but rebutting it with those practical considerations. I can’t imagine the ideological argument for the textbook’s water tank problem, unless we’re operating under very different assumptions about the point of math applications.

    Maria: I don’t see kids’ autonomy in conceptual learning nearly as much. How can you teach kids to do what YOU do?

    This is such a confounding question. I don’t do enough — I know that — but I don’t know what to do. I read an interesting article recently (and shame on me for not storing it somewhere), something about a particular math circle in the classroom where you have an inner circle of students discussing a math problem and an outer circle of students grading the inner circle exclusively on their contribution to problem solving. I can’t recall the exact criteria but it seemed promising.

    MPG: Nothing is “4Eva” and nothing “Rulz” as you put it, for everyone in every circumstance.

    I’m not sure what makes me sadder here: that MPG seems immune to the sarcasm or that he isn’t acquainted with Kilian, who ran one of the best edublogs around before he decided to trade it all in for what had freaking well better be an amazing administrative position.

  32. I really wish I had had a math teacher like you Dan. Instead, I was stuck with math teachers who are a lot like several of the commenters at KTM.

    This is not to say that there is anything wrong with being a math teacher like they are. There are a lot of kids who do really well with that kind of teaching, some who move on to do great things in math or math heavy fields. But those are not all kids and teaching like that leaves too many of us behind. There is an assumption that because a kid like I was doesn’t hack it in a classroom like theirs, we are just not capable of learning it.

    Nothing could be further from the truth.

    The biggest problem I had as a math student wasn’t getting the right answer – for lower level math I rarely had any trouble getting the right answer. I just had serious problems with following the proper road map to the correct solution. Moreover, I really didn’t understand why those roadmaps were so very important. I just knew that I could sit there, rumble the numbers around in my head and generally from a completely backwards method get the correct answers.

    When I would try to challenge my middle school pre-algebra instructor to explain why the proper roadmap was so important, I was seen as interfering with his instructional time. Because he had already written me off as someone who was ever going to succeed in math or math heavy fields, he really wasn’t interested in wasting his time on me. What he failed to understand about me, was that I have neurological issues that make it very difficult for me to apply myself to things I don’t understand. Being told that I need to do something a certain way because that is the way it needs to be done, when I can get the right solution my way, is not going to get anywhere.

    What really bothers me about this experience, is that I ended up going into contracting and quite often had to do rather complicated math – mostly geometry – on a near daily basis. And for the most part I had to do it in my head. While I did have the benefit of only having to estimate most of the time, I still had to make sure my figures were extremely close. We always hated having to return materials and even worse was disrupting a job to compensate for insufficient supplies.

    And now, eighteen years after dropping out of high school, I am studying neuropsychology and linguistics. While I still have a great deal of trouble with math – still have a lot to pick up on, I am finding that when things are explained reasonably I really get it. Reasonable in this context means taking a very similar approach to what you describe in your TED talk. I am not deficient, nor am I incapable (though I sometimes complain that algebra just isn’t logical) – I just don’t learn the way kids who can pick it up from standard practices and retain it do. I need to see the problem.

    Two semesters ago I had to deal with some math for statistical analysis that I was completely unfamiliar with. The problems were laid out in the context of a particular study – it explained what we were looking for from the data and it provided the raw data set. Now I will grant that what I picked up in last semester’s algebra class taught me a much easier way to solve that very problem, I was actually able to figure it out. Yes, it took me several hours more than it would have, had I attempted to take that class after my algebra class. But I worked it out.

    This si really just my long winded way of saying that while your critics at KTM are certainly teaching many kids the way those kids should be taught, they are also leaving a lot of kids behind. And I am more than a little bitter about my own experience with teachers like that. I cannot begin to express how refreshing it is to run across teachers like you.

  33. One thing I have noticed is that nearly everyone who is for the old-fashioned, rigor and repetition style of teaching is coming from a usually very anecdotal perspective of what worked for them. The trouble is, most of the people who are teaching/using math today are people who were successful under that system and it does work for SOME people. But how many adults do you know personally who have a negative feeling about math, insist they just couldn’t do it or if they could, they just thought it was tedious and boring. All except the ones who grew up to be engineers, accountants and math teachers, give or take.

    If you think about the ways that our brains learn and remember things, there are different ways to make something become a long-term memory. The first is through repetition, assuming you are practicing correctly, and assuming you are disciplined enough to practice it repeatedly, you can create a neural pathway (like wagon ruts in a grassy field) for that piece of knowledge. Another way is if there is a significant emotion attached to it – like how we remember everything about where we were when a loved one died, etc. The more modalities you use to learn something (listening, writing, seeing, thinking, touching, moving, etc) the more likely you are to have it go to long-term memory.

    Copy, practice, repeat is probably the least efficient and most boring way to learn something, although it can work. It’s a great way to kill motivation and take all the beauty, wonder and fun out of what should be a fascinating subject. Some kids still need this, while some kids, we know, absolutely do not and we are holding them back from reaching their full potential if we force it on them.

    Teachers, in a perfect world, would have small classes and plenty of planning time to be able to meet the individual learning needs of all their students.

  34. I can’t imagine the ideological argument for the textbook’s water tank problem, unless we’re operating under very different assumptions about the point of math applications.

    Boy, I can imagine arguments for it. They may not be very good ones, and they may not be “ideological,” but I can certainly think of them.

    What if the stepped-out water tank problem comes after a more open-ended introductory problem like the one you created? How about before? Still bad? Does the textbook specify that thou shalt only give students the problems written in the textbook?

  35. Arlo Guthrie taught “The Garden Song” using “The BOring Method.” (“Repeat after me. Inch by Inch. Row by Row. Gonna Make This Garden Grow.”) GOt a lot of laughs, but it worked. However, there were already all kinds of connections between the song and the real world and the lives of the people at the concert. You have to have both.
    I had the same impression as Robert about the commenters — they’ve been burned. I had low expectations from the video and really cringed at the “be less helpful.” I work with adults on basic arithmetic and algebra skills, and many of them have had teachers who used that philosophy, were generous with “partial credit,” and passed students through courses without ’em knowing much of anything. Teachers can, and do, find vague ways of measuring achievement so they can tell themselves the students learned something. THe teachers who are, themselves, afraid of the math do it; teachers who are skillful in math do it, too, convincing themselves that the student really did “have the concept.” I’m amazed at many of the “concepts” students have, such as that “X stands for 1, right?”
    However, with that example of the ski slope problem, I saw that the “being less helpful” was a lot like what I do when students need to set up problems. (Happily, our texts *do* give ‘extra’ information) The students still had to think and talk.
    I’ve been reading about The Algebra Project and a couple of other programs, and including working with “my language” and then translating that into “math language” and then translating that into symbols keeps coming up. I also identified with the thought if you’re talking math, certain students won’t talk at all – but if you’re just talking, they’ll think and talk.

  36. @ Eileen: “Copy, practice, repeat is probably the least efficient and most boring way to learn something, although it can work. It’s a great way to kill motivation and take all the beauty, wonder and fun out of what should be a fascinating subject.”

    While copy, practice, repeat is not always (ever?) fun, it has a place. What I heard in Dan’s original post is that both skill practice and conceptual understanding are essential, and neither should be sacrificed on the altar of the other.

    Even Michael Jordan and Tiger Woods spent countless boring, repetitive, hours practicing their skills so that we can/could enjoy the beauty and wonder of their performances.

  37. @James – MJ and Tiger were both practicing something they saw as (a) valuable, (b) useful for the rest of their lives, and (c) enjoyable. I’d argue that schools have done a poor job of demonstrating how most subjects are any of those…

  38. Bill Bradley

    May 21, 2010 - 5:40 am -

    The other point is that their practice has a purpose. How many people truly appreciate Calculus before taking a Physics class? Newton came up with Calculus to solve those problems, not because he was interested in describing the slope of functions! Asking students to understand or be interested in Pure Mathematics is like trying to start teaching Art with abstract art or Music with Varese and Steve Reich or Architecture with Gaudi! A few may be fascinated, but the majority will be bored, confused, or turned off to the subject entirely. We had a rule at college that the Mathematics Majors were not allowed to split checks when we ate somewhere because they got so distracted being interested in the numbers that they took forever. It’s not a bad thing to be interested in Mathematics for its own sake, but it’s ridiculous to expect everyone to share your level of interest or particular interests.

  39. I don’t think rational people who have nothing better to do with their time, than explore the nuances of building math curriculum should be referred to as ‘crazies.’ I have observed nothing in the news, other than what the publisher’s could come up with, that ever described student math achievement going up (although I know by now that it can’t go down any further, why am I not cheering) and I’ve been in this business for too long to not understand what’s actually been happenning. When educational research? overlooks some obvious facts, then I am disappointed and so are many others. The New Math Standard will in time be called the Obama Standard and then we can all hunt for an eighth grader that can add two numbers correctly together. Have a nice day gents.

  40. Bill Bradley

    July 31, 2010 - 8:56 am -

    Ah, some Obama Derangement Syndrome. To point out the obvious, math standards are set at the state, not Federal Level, so you’re not only barking at the wrong tree, but the wrong forest.
    If you have something actually positive to contribute, the Common Core STATE Curriculum is still taking comments at