Sunday, February 28, 2016

The Wrong Way to Target Math (Part I)

If you know me (or follow me on Twitter), you know I have a few choice words for people like Andrew Hacker, with his anti-math stance and negative opinions on math education. I wasn't going to write anything because I didn't want to lend credibility to him or his agenda, but I can't contain myself any longer. He's really pissed me off with his most recent NY Times OpEd "The Wrong Way to Teach Math" by taking aim directly at AP Statistics. Don't worry, I promise I did not use profane language.  I used as little profane language as I could.

First and foremost, take a deep breath and pull up a comfy chair. Your Andrew Hacker required reading:

  1. 2012 NY Times OpEd: "Is Algebra Necessary?"
  2. NY Times interview by Jane Karr earlier this month, in which we also get a glimpse at Hacker's ideas about gender differences in learning to boot: "Who Needs Advanced Math? Not Everybody"
  3. Chronicle article (now locked), previewing Andrew Hacker's book coming out next month: "The Case Against Mandating Math for Students"
  4. The most recent NY Times OpEd: "The Wrong Way to Teach Math"
Got all that? I know, it's a bit much. Let's break it down, shall we?

First, a little sidebar, if you will, so that we can discuss the general philosophies of Andrew Hacker. One of his big issues with math education in general is that higher-level math is unnecessary for most 'citizens' and, in fact, prevents them from obtaining things like high school diplomas. As a Professor Emeritus of Political Science at Queens College, who I guess was allowed to teach some applied math/stats classes along the way, he has inexplicably acquired the skills to become an expert in math education. By the way, in general, let's all be skeptical of a person who decrees themselves an expert in anything, okay?

Anyway, Hacker's argument is that most 'theoretical' math, like Algebra and Geometry, is unnecessary for people who think they use very little of it in their lives. Quoted in the NYTimes interview earlier this month: "The number of people who use either in their jobs is tiny, at most 5 percent. You don’t need that kind of math for coding. It’s not a building block." First of all, WTF, is he serious?! No math, even in computer programming? Does he know most computer science courses are taught in math departments? I'm glad that even a ninth grade Geometry student knew this was bullsh!t.

Secondly, how did he get that estimate of 5%? No, I'm not worried so much about the lack of a good citation here, although that would be nice. My concern lies with the inherent fact that he (or at least someone else) would need some advanced math to be able to accurately make that statistical claim. [More about that advanced math stuff later.]

My grandmother's dress form. Those curves are screaming out for Calculus.

Furthermore, Hacker argues, it's wholly impractical for a person to be held back from his/her success by having to pass math classes. We should stop mandated math classes from ruining people's lives! From the Chronicle article: "Typical math requirements... unnecessarily trip up students who plan to major in dance or fashion design." Um, ok. Thankfully for all us, I'm guessing Andrew Hacker has never designed fashion. If he had, he'd know that it requires a lot of math skill.

I used to watch my maternal grandmother, you know... a professional seamstress, expertly lay patterns in ways that maximized expensive textiles, minimized the number of cuts, acknowledged fabric grains, and matched pattern repeats. She knew how much fabric an item would take, how to create a garment that would flatter the curves of the body, and how to make clothing that comfortably moved with the wearer. I am sure she didn't think about it explicitly as being math. No. I'm sure she might have even told you that she wasn't very good at math. And, yet, despite never having the ability to finish high school, what my grandmother did was deeply mathematical.

Interestingly, in terms of his examples of dance and fashion design, Andrew Hacker has picked two majors that are far more popular for women than men... but I won't try to read into the subtext on that one. I'll let someone else deal with that nonsense. Sigh.

Stay tuned for the next installment of my rant against Andrew Hacker: The Wrong Way to Target Math (Part II)

Until then, enjoy this beautiful take on the "Waltz of the Snowflakes" by Mark Morris in The Hard Nut, which artfully employs the use of Geometry skills many students learn in high school.

(Graphic from via


  1. Preach it, Amy! Scream it loud and proud.

  2. A former geometry student from my first year of teaching stopped by for a visit. She is now a professional ballerina with the Béjart Ballet Lausanne based in Switzerland. (Here's a neat little video of her dancing: )

    She told me how important geometry is in her work, both in doing choreography and in dancing. She said you can easily tell the difference between a dancer who understands the geometry of the whole dance and one who just learns their part of the dance. I found that very powerful.

    1. I always love hearing about these connections too.

  3. As a former teacher, and a math-phobe, I beg the schools to please, please bring in the math wizards. The lack of confidence in maneuvering life problems has been beyond crippling. I, too, didn't realize I was a mathematician till I found contra dancing and realized we were dancing equations, though I could never tell you what they were. Thank you for speaking up about this. Also, this is the only encounter I've ever had with anyone who knows about the Hard Nut!! Been looking for it for decades!

    1. Yes, I know contra dancing as well.

      I had the pleasure of seeing Hard Nut this past December at BAM. Great experience live if you have the opportunity to see it.

  4. I'm mostly waiting to read his book from the library when its published to make up my mind. But I think the fact Hacker has tested his ideas on students and produced full courses moves his thinking into the realm of a credible proposal. You may still disagree but this is a lot more fully fleshed out than say Wolfram waving his hands and saying we should all just model in Mathematica and skip teaching computation. That means I think its less interesting to attack his credential although it does make for some fun reading.

    Then you reach the meat of your argument there is math everywhere in computer programming or fashion design or ballet dancing. I don't think that Hacker would disagree precisely. His contention is that the high school algebra or geometry curriculum doesn't inform most of these domains. For example, I learned to program prior to knowing Algebra and after twenty years in the field I'm pretty confident saying 95% of practitioners or more don't use it directly. The field is most directly related to logic with some exceptions in computational graphics etc. And those cases would fall into his model under specialties where you would study more advanced math. Implicitly manipulating spacial geometries like your grandmother did is cool but also not directly connected to curriculum. The way I think of it is could it be learned or was it traditionally learned without mathematical formalism. (And this does not contradict the inherent mathematical ideas being used)

    That all said, I mostly feel that when I see the details his proposal is going to look mostly like "let's more intensively teach middle school math."
    There's already a huge push on real world problems going on in pre-algebra. So I'm not seeing yet what's going to new here other than a claim that students are ill-prepared.

    1. You may want to read Part II to see where I'm going with this.

  5. How many math courses did your grandmother have to pass?
    It seems to me that your response supports his point -- that people don't need to pass math classes to learn the math they need.

    1. My grandmother didn't have to pass any courses. There were no schools at the time due to Nazi occupation. I am doubtful that a war refugee's lack of any secondary education is considered a support for Andrew Hacker's point. In fact, if Hacker's philosophies are even remotely equivalent to the systematic suppression and cultural genocide that occurred during the Nazi era, I think that would be a huge reason to oppose it.

    2. First of all, I am sorry that your grandmother lived under Nazi occupation. I work in adult literacy education in New York City, where the children who were left behind sit in classrooms with immigrants and refugees from all around the world. I love math and I love teaching math. But when I see my students unable to get their diplomas and/or get into college because of high stakes math assessments that most of my non-math teacher friends and colleagues, all brilliant and successful, would be hard pressed to pass, my faith is challenged. When I read your brief description of your grandmother I think of all my students who would be able to succeed regardless of their inability to handle/lack of opportunity to learn certain abstract manipulations. Not to mention they could go on to develop all this amazing mathematical knowledge because I think of all the joyful math content rife with productive struggle, estimation, multiple strategies, problem-posing that I want to teach and then the pressures to "waste" precious class focusing on the joyless aspects of math because of the assessments love to out do each other by focusing on the highest levels of the standards du jour. And I wonder if Hacker might not be even part right.

    3. It sounds like your issue, then, is with the tests, not with math. Math doesn't have to be joyless nor a waste of time.