Sunday, November 1, 2009

When Too Much Becomes Too Little

Joseph Ganem wrote a great article for the APS (American Physical Society) News, titled "A Math Paradox: The Widening Gap Between High School and College Math". Ganem is a physics prof at Loyola University Maryland, and works with incoming students at orientation. He's also the father of 3 children (aged 14, 17, and 20), and helps with their math homework.

I want to share 3 quotes from his article, and then encourage you to follow the link to read the whole thing.

He satrts here:
We are in the midst of paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math.

After some examples from his kids' homework, he has these questions:
So if eighth graders are taught math at the level of a college sophomore why are graduating seniors struggling? How can students who have studied college level math for years need remedial math when they finally arrive at college? From my knowledge of both curricula I see three problems.
I'll let him tell you the 3 problems, so I don't steal all his thunder. His conclusion seems just right to me: (President Obama, Secretary of Education Duncan, Are you listening?)
All three of these problems are the result of the adult obsession with testing and the need to show year-to-year improvement in test scores. Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers. But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping.

It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time. To do my job as a physicist I need to know matrix inversion. It didn’t hurt my career that I learned that technique in college rather than in eighth grade. What mattered was that I understood enough about math when I got to college that I could take calculus. Memorizing a long list of advanced techniques to appease test scorers does not constitute an understanding.
Please read his article in all its glory, over at APS.


  1. Thanks for the article recommendation Sue! I really enjoyed it. And I'm glad some folks at the college level are connecting the dots and recognizing that the solution to underprepared entering freshmen is not randomly throwing more standards into the state frameworks.

    It's a fine point but I have one difference with Ganem: the problem isn't that the ideas aren't developmentally appropriate, it's how and why they're being taught. If you teach a procedure with no context, motivation, or understanding, purely for the sake of being able to say your standards include it, it won't be "developmentally appropriate" for a college sophomore any more than it will be for an 8th grader. Conversely, I believe 8-year-olds are ready for algebra - it just has to be taught meaningfully, driven by problems comprehensible to them, and with the focus on the big ideas rather than on all the little skills.

  2. nice find; i'll probably reread it
    a couple times even.

    i do *so* wish he hadn't taken
    freshman calc so for granted
    like some natural law. and
    indeed i quite agree with ben.
    matrix math is one heck
    of lot better intro to
    than any calc ever was;
    "freshman linear algebra"
    could be the beginning
    of the healing if the gods will.

    poor devil probably thinks math
    is for physics or something.
    when of course it's for clarity.
    and schools are run for and
    mostly by *enemies* of clarity:
    sworn liars for example.
    the result follows.

  3. Hmm, can someone teach me how to do the trackback thing? Seems I should alert the author that there are comments over here.

  4. beats me. if they wanted to know
    they'd have a comments feature
    i figure.

  5. Good find, thank you.

    Difficulty vs rigor is indeed, a huge mistake. I think he overstates the process over understanding bit... but that depends on the district, the school, and the teacher.

    And the inclusion of developmentally inappropriate material is huge.

    He missed a huge one: just too many topics. That kills a big chunk of rigor - there's no time for depth. Think of what those matrices are replacing.

    And when we jamb in a whole bunch of stats and probability, um...
    1) have we removed an equal amount of material?
    2) have we provided an incremental development through the grades? (no, they get massively harder in high school, or move directly from topics taught for understanding in 6th grade to topics taught for formula memorization in 8th or 9th)
    3) Have we allowed time for real understanding and appreciation of the topics? (no. just no)


  6. not just "no" but "of course not".
    otherwise... what JD said.

    the stats thing is *transparently*
    an effort by the powers to eliminate
    the last vestiges of "down to the ground"
    understanding in math classes.

    i've been ranting about this for years;
    screaming in pain never convinced anybody
    of anything of course but people in pain *will*
    somehow persist...

    where you at, sue? internet connection ok?

  7. Thanks for your comments, JD. And thanks for your concern, Owen. I still have no internet at home. My mac still has more troubles than I care to describe now. Will tell the saga once it's over.


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