Is There Room for More Critical Thinking in Math Education? October 21, 2011

Is There Room for More Critical Thinking in Math Education?

At the 2011 Secular Student Alliance conference, I gave a talk about the need for more critical thinking in math education. The video of the talk is finally available so I wanted to share that with you. (Plus, I’m at a math conference this weekend and it seemed like the perfect time to post it.)

Hopefully, it won’t scare you away even if you hate the subject!

(Spoiler: If you’re coming to Skepticon IV next month and you want to be surprised, don’t watch this! I’ll be giving a version of this talk there.)

I owe a lot to Dan Meyer, who’s influenced a lot of my thinking on this subject. I got a number of the examples in the talk from his website. It’s a must-read for any math teacher.

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  • I watched this yesterday. I thought you did great. It was fascinating – especially the odd one out!

  • Trina

    So entertaining & educational! There’s such a need for more of this kind of teaching.   I’m basically a language person, rather than a math/science person, but it held my interest.   I had rather a bad start with math and for years avoided it like the plague, but had helpful  college instructors who got me up to speed on the basics – though they weren’t really teaching critical thinking about it, either. 

  • Great speech, Hemant. What were the two clips you cut out of the video? I assume that was for copyright reasons, but it would be good to know what they were.

  • djinnE

    Precisely.  Thank you.
    I graduated with a relatively useless degree in English and writing and actually did 3-D design for years. In school entering math class was hopeless and the problem wasn’t that I didn’t care about it as much as it was that I wasn’t being taught how to use it.
    I am so interested in science that I feel now that if I had to do it over again, that I would tackle the math and go into…I dunno…planetary biology or some such field. But would I really. Even though I encountered all sorts of mathematical dilemmas in my work, the software really does it for you (though you do shortcut around it often). As an adult, I feel that I could wrap my head around it, but as a young student, it’s such a high wall to scale, especially when you’re not given any sort of context to apply it.
    I am so happy to see that there are some out there who get it. My own math teachers often looked at me with thinly veiled rage at the fact that I was asking them to explain how a formula might be used practically. I thought it was a good question.
    I love my language and the art that is created with it. I just wish that I had had the opportunity to fully grasp the universal language of numbers and appreciate more fully the art of the universe.

  • AJ

    As a homeschooling parent who didn’t get a decent math education, I found this video very interesting. Thanks so much!

  • oambitiousone

    Would you share some favorite math blogs?

    We home-school (secularly).  I’m a recovering mathephobe and am in a rut doing the pencil/paper/workbook routine with my elementary-aged kids.  My spouse is brilliant with numbers but not skilled with making it accessible– all theoretical, not practical.

    I need ideas beyond the obvious cooking math of measuring and weights (your orange peeling project was cool).

    Thank you for speaking at the institution’s failings with math (learning to pass a test, not how to think).  I passed college algebra and trigonometry but don’t recall much; it was plug-and-chug to get a grade, not learning how to think about reality anew.

  • Edward Tarte

    I taught middle school math 17 years, then high school math 20 years, now retired from classroom for 6 years but self-employed as a private math tutor.  I struggled to teach students to think critically.  Prescribed curricula made it extremely difficult. I now have 59 Math Challenges on YouTube, and every one of them requires critical thinking.  I invite you to watch one or more of them.  At YT, search edward tarte math.  Thanks.

  • Edward Tarte

    P.S.  58 of these 59 math videos of mine offer a prize for correct solution, if the solver is interested in getting the prize I offer:) 

  • annette

    I wish you had been my math teacher!  I’m going to try to remember some of these things are I after school my daughter. Do you have any suggestions?  Our system  uses Everyday Mathematics.  What do you think about that program?

  • Haven’t watched the talk yet, but my instant reaction to the title is “Euclid’s Parallel Postulate: Teach the Controversy?”

  • Anonymous

    I, too, would like to see the clips that were not included in this video.

  • Anonymous

    Speaking of 3D design and teaching. That was the problem with the maths course I had to take in computer science. It was extremely dry, theoretical and the professor just read verbatim from her script.

    We did – among other things – vectors, planes and stuff and there are tons of applications for that in 3D computer graphics and/or game engines. Rotating objects, determining when certain things are visible, rendering surface, etc. The basic geometry is all about vectors and similar concepts. Why not have some practical applications that people can actually relate to? Would have been much more helpful.

    I really liked the cryptography and statistics courses though. Yes, much of the maths itself was a lot easier – except group theory. But I also immediately saw what I was actually doing and why

  • Interesting talk there, H. Reminds me actually of when I was a college student way back studying for ONC (That’s the first rung on the post-school science ladder here in the UK. Well, one of them.)  The maths in the course was really hard work but for just one session, a revision session prior to exams, the head of the maths dept gave us a lesson. He began by telling us all to put our pens and notebooks away and just follow what he was doing. His method was similar to what you have described and afterwards quite a few of us remarked that we had learned more maths during that morning than during the whole course until then. I think that guy made the difference between passing and failing for some of us.

  • Hemant,

    I thought you were 100% correct about the need to think mathematically. I learned to think mathematically as a coping mechanism at a young age because I had great difficulty memorizing equations. I would always remember the basic concepts and then derive the more complicated equations as I needed them on tests and homework. It was how I got by with a bad memory in school. It’s great that teachers like you are actually teaching or encouraging that way of thinking. I have friends that could memorize circles around me but could never get past a certain point in mathematics because they never learned how to think mathematically.

  • Alexis

    I would discourage the use of multiple guess questions not only in math, but in any subject.

  • Oxymormon

    Wow. That was an incredibly interesting and engaging speech. I don’t teach, but I do tutor my little brother in math from time to time. I will have to start incorporating some of these things into our tutoring sessions. He is definitely a smart kid, but has been trained to plug and chug without really thinking about what is going on.

  • Anonymous

    Having grown up in Ireland and received a really good public education, I am always amazed at the level of math phobia in the US. When I tell people my background is in math, the invariable response is: “Oh god, I hate math! That was my worst subject!” I guess a big reason is that people never see the relevance of it in their daily lives – even though they have to balance their checkbooks, pay interest on credit card debts, etc. Also I think multiple choice is almost a fetish in the US educational system – everything has to be multiple choice. I know it makes it easier to grade exams and homework but it encourages kids to guess blindly or at best to work backwards from the answers, rather than figuring things out. I think multiple choice is harmful.

  • Anonymous

    Hey Hemant, that’s not a frustrum, it’s a frustum.

  • Weird — you’re right. I could’ve sworn I saw it that way elsewhere. A lot of Google image results come up when I search for it, too. But I’ll make the change! Thanks 🙂

  • Anonymous

    I’ve found that most people tend to be either really good in languages or maths, but rarely both. The maths geniuses I went to school with all sucked at languages and the language ones (to which I belong) weren’t that good at math – maybe not bad, but just average

  • Anonymous

    I also see it spelled fustrum a lot – I guess it must be frustrating to remember the correct spelling! 🙂

  • rachel fasiang

    Awesome speech Hemant! 

    I can definitely relate to this…I was an A student in my math classes in high school simply by using the plug and chug method. I was recently studying for the GRE and realized that without having the formulas memorized, I was incapable of doing a lot of the practice problems. Hopefully teachers will start catching on and teach kids how to think mathematically instead. This should be the topic of your next book perhaps?

  • Carl

    Or is that fustrating?

  • I love it. I am also a math teacher, but in the middle grades. I use a curriculum that is designed for critical mathematical thinking, and I haven’t taught from a traditional text in a few years. The kids have had a rough transition, but the conversations about the math are so much richer.

    I’ve been feeling very downtrodden this year, being in Correction Action (dun dun dun), and looking at seemingly impossible percentages. Thirty-two percent of my 8th graders are projected to pass, and 75% must pass in order to make annual yearly progress. I love my lessons (I’m just starting my unit on Pythagoras), but we’re all running scared with these abysmal passing rates.

    I hate those stupid tests. I can think of many problems off the top of my head that a student could get wrong and yet KNOW how to do it if you let them use their own method instead of a perceived ‘right’ way.

    GRRRR. 😉

  • Ashley Will

    I read you had been my math teacher too. I am jealous of all your students! I have a B.A. in English and always thought myself to be horrible at work. My last math I took was freshman year of college and was my worst grade of any college course because I just couldn’t understand it.

  • Laura Lou

    Hemant, I recently graduated from a public high school in Portland, OR and you’ll be happy to hear that my teachers embraced exactly this style of teaching. In fact, everything you said in the video was old hat to me.

    Thank you for sticking up for good math education!

  • Nude0007

    Very relevant speech!  This is the approach we need not only in math, but all subjects. Can we get you to run for whatever the national position is over education?  I have always thought that there should be national standards and texts for all subjects, and that thought like this should go into each program.   This way we wouldn’t have individual states or schools overriding national criteria with creationism, for instance.

  • Pseudonym

    Something that I think is worth pointing out is that it’s not just relevance to everyday life that’s at issue, but also relevance to what mathematicians and mathematical scientists do.

    Imagine if we taught music the way we taught maths. Students would spend all of their time drilling scales and arpeggios. Don’t get me wrong: scales and arpeggios are important. You can’t be a good musician if you can’t do them. But scales and arpeggios aren’t really what a musician does (i.e. it would turn off those who might want to do it professionally), and it’s not really that important for being musically literate (i.e. it would be useless for everyone else).

  • Pseudonym

    I work in a field that has a lot of computational linguists working in it. So maybe I’m biassed, but I know a lot of people who are good at both.

  • Maria

    Wow, this is probably why math stopped being my favorite subject around 9th or 10th grade…..they just weren’t teaching it right!  

    p.s.- Hemant, you’re really cute!

  • Rich Wilson

    Have you read “Surely You’re Joking Mr. Feynman”?  He has some interesting anecdotes about reviewing HS textbooks in CA.

  • Chad Casarotto

    I am not sure if I am agreeing or disagreeing with you, but mathematicians do something that is completely different from high school math. For the most part, stuff like Abstract Algebra and Topology, are barely relevant to reality, and topics like Differential Equations are so far beyond what most high school students are able to do.

    If you get a bachelor’s or master’s degree in Literature, History, Art, Science, etc., you are learning a subject at a deeper level than you do in high school, but the subject is essentially the same. With math, you are learning essentially a new subject, and a subject that is much less relevant and more abstract.

    I agree that what mathematicians do is vastly different from what is being taught in high schools, but I think that for the most part, that is the correct thing to do. The real issue is presenting the material more concrete way not a more abstract way.

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