More Old Lecture Notes. Whee!

Here’s a little eight-pager I like to call “Counting Heads” (PDF): deriving the formula for expanding the n^th power of a binomial, from first principles, and applying it to “coin toss” problems. (Not to be confused with D. Marusek’s outstanding novel.)


  1. xxx xxy xyx xyy yxx yxy yyx yyy is crucial to linking together different kinds of counting. I am amazed that students routinely reach the binomial theorem without this.

    “First principles” sounds scary – but it really just means that the students have a window into what is going on, and an opportunity to achieve much more real understanding than usual.


  2. peter ford

    “But what if the suppression of mathematical thinking is actually deliberate? Mathematics is characterised by its intolerance of nonsense; it’s not surprising that such an attitude should meet with hostility from those in the business of pushing people around.”

    I am new to your blog/posts; upon reading this statement in your Education ‘Reform’ post I was jumping out of my chair in jubilation from hearing from someone else what I’ve felt for years!

    Count me as a regular reader!

  3. wow. thanks … here’s my day made
    and it’s only 7:30 AM.

    other potential new readers might want to know
    that the quoted passage is found here
    (a talk i gave at the annual joint AMS/MAA meeting
    almost exactly ten years ago). there’s some discussion
    of the *same passage* in the comments …
    i must of been unusually eloquent that day …

  4. pdexiii

    as a math teacher who leaped into the profession from military acquisition and engineering school, the edu-babble I hear from the education ‘intelligentsia’ is infuriating and sometimes just silly. Am I the only one who thinks we harm urban students with calculators and ‘projects’? urrrgh.

  5. you bring up an interesting point.
    my blogroll includes a goodly handful
    of explicitly “counter-reform” pages …
    and at least a few that are explicitly
    working the “urban” beat (innercitymathteacher
    comes to mind immediately for some reason …).
    but, anyway offhand, i can’t think of
    a point in the intersection.

    the interesting-though-frequently-infuriating
    kitchen table math is run by (and mostly for)
    well-off suburbanites. now that i think of it,
    this is quite typical. very likely the rest of the world
    is concerned with resisting other, even more brutal,
    oppressions than the pedagogy of lowered expectations.

    my recent remarks on the “math wars”
    may be pertinent here.

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