A Mathematician's Lament — an Indictment of US Math Education

[furrbear]

via SlashDot:

Scott Aaronson recently had "A Mathematician's Lament" [PDF], Paul Lockhardt's indictment of K-12 math education in the US, pointed out to him and takes some time to examine the finer points.

"Lockhardt says pretty much everything I've wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet. If you like math, and more so if you think you don't like math, I implore you to read his essay with every atom of my being. Which is not to say I don't have a few quibbles [...] In the end, Lockhardt's lament is subversive, angry, and radical ... but if you know anything about math and anything about K-12 'education' (at least in the United States), I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."

Curious what the mathematicians and educators think.

Comments

[dakoopst.livejournal.com]

I like this. A lot.

It says some things that I already say and challenges what I do at the same time.

And I'm only a fourth of the way through this.

Thank you for sending it. I think I'll share it with my colleagues.

[furrbear.livejournal.com]

You were one of the first people I thought of when I read the abstract.

Getting into reading it, I amused myself by how reflexive the answers to his example problems came. Area of triangle inside box, 1/2 without even thinking about it. Diagonal of a cube? beat-beat √3. The funny part was catching myself re-squaring √2 when adding in the z-axis after doing the diagonal on the x-y plane.

[cipherpunk.livejournal.com]

ObDisclosure for people who don't know me: I'm a thesis away from a Ph.D. in computer science, which basically means I'm a mathematician specializing in theoretical discrete mathematics. I've also volunteered to teach fourth-grade math classes at a local school that had to axe their talented and gifted program for budget reasons.

I first read the Lament a few years ago. In the main, I agree with it heartily; the few areas where I do not are so small as to not warrant much discussion. Almost all of what he's complained about I have experienced myself, whether as a student or as an instructor. In high school a particularly sadistic math teacher convinced me that I hated math; it wasn't until well after undergrad that I discovered I loved it. His principal weapon was to punish any and all forms of inquiry and discovery. When I independently rediscovered calculus and used it on an exam, he failed me because it was an algebra exam, not a calculus exam. When he gave us a geometry theorem and asked us to prove it, I instead disproved it by assuming the points could be in three-dimensional space instead of a two-dimensional plane: I was savaged on that one, too. If every time a kid shows inquiry and enthusiasm and drive they are punished, then soon you'll get a kid who shows no inquiry, no enthusiasm, and no drive -- and that's exactly what we're producing in our math classes.

Teaching fourth-graders, I told them they were probably better at long division than I was. They found that hard to believe, up until I told them the truth: I didn't even remember how to do it anymore. (A withering of basic arithmetical skills seems to be common in grad school.) They asked me how I did long division problems, and I told them: I find a prime factorization for each side, cancel out terms, and it usually gets me close enough for government work. They were intrigued by this, so I showed it to them -- and then I stood up there and we re-derived long division. Before they knew that long division worked. Armed with prime factors they understood why it worked.

Their regular math teacher complained to the principal about me, since they weren't going to be covering prime factors until much later in the year, and relating prime factors to long division wasn't in the lesson plan provided by the textbook.

There is rampant — rampant — sexism in elementary schools when it comes to math. My heart damn near broke when Kayla asked me if I knew any girls who were good at math. I told her there were, and the next question she asked me — she was shy about it, I knew this was really important to her — was whether they were pretty. I told her about my officemate Lucena ("Lucy"), a Venezuelan–American computational statistician who could've been a cover model for a fitness magazine. I told her about Heather, who was this blisteringly brilliant drop–dead gorgeous redhead in the math department. I showed her a photo of Elaine, a stunning brunette Ph.D. candidate in virology with whom I was attending a Nobel Laureate lecture in a couple of weeks.

She listened, she nodded. "The boys, they all ... they say girls and math ... you know."

My heart just broke. I spent a lot of time talking to her about the Admiral Grace Murray Hopper, about the Lady Ada Augusta, Countess Lovelace, about Barbara Liskov, about Emmy Noether, about Rosalind Franklin, about Vera Rubin, about Fotini Markopoulous, about Lisa Randall, about Marie Curie. Hell, I even talked about Danica McKellar, Mayim Bialik and Natalie Portman. (And if any of you can get me a date with Markopoulos, Randall, McKellar, Bialik or Portman, I will give you the entire contents of my 401K.)

I don't know if I made an impact on her. She was smiling when we parted company. But ... she's got a long road ahead of her.

I think about her every time the subject of math education comes up. We have got to do better. We've simply got to.

[blt4success66.livejournal.com]

The problem with math education (it was 5 a.m. when I started reading the "Lament" so I was easily bored and being tired, it didn't make sense, but I WILL read it) is that we no longer have time for the creativity the author wishes we had.

We have sold our educational system out to testing and requiring kids to be at a certain level at a certain time and if they're not performing, we blackmail the schools and threaten them with the possible loss of students/staff/funding.

While Lockhardt is focusing in on math, the same could be said for any other discipline. Slowly and very sadly, PE, Music, and Art have given way to testing and lack of funding. Schools are blackmailed into just pushing the basics so that students can pass their tests.

I appreciate Lockhardt's postion (for what I read...and I will read further when I'm rested) but to be honest, it's a "pie in the sky" dream that may never see it's realization.

You know I hate math. I have made not secret of it. Complex formulas and idiotic examples did nothing but to confuse and frustrate me. I would much rather see math become more a practical application and for those children identified as having a potential for advanced math concepts, they should be separated and moved to a class to help them blossom as Lockhardt would suggest.

Just my two cents...

[delko.livejournal.com]

In a couple of months, I will celebrate ten years of living with a mathematician. And he has a MS in applied statistics (and a JD, LLM & MPP).
I gave up trying to even pretend to understand what he does a while back.