

Dan Meyer dissects the flaws of math textbooks (video) - anuleczka
http://www.youtube.com/watch?v=BlvKWEvKSi8

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yequalsx
I'm a teacher of mathematics at a community college.

It appears to me that the crux of the problem is that people, including the
guy in the video, confuse problem solving with mathematics. The utility of
mathematics comes in the remarkable fact that a great deal of phenomena can be
adequately modeled mathematically. The focus of an algebra class ought to be
in learning the language of algebra. That is, in manipulating numbers in the
abstract. The application problems ought to be saved for physics, biology,
economics, etc. The result of an emphasis on so called real world problems in
high school mathematics is a generation of students who are incapable of
correctly manipulating algebraic expressions and equations.

I recently gave my college algebra class an equation. It was a simple equation
and all of them could solve it. I then asked them for an example of an
equation that had no solution. Not a single person could provide an answer.
They can solve the word problems in the textbook but don't have the slightest
clue about what these mathematical concepts actually mean.

Perhaps it isn't important that one need to manipulate algebraic objects. I
won't argue with this. But let's not call solving word problems mathematics.
If you want to learn mathematics then grinding through the minutia and having
the patience to understand the symbols is necessary. You can't get around
this. If the goal is to solve word problems then....go ahead and change
things.

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anuleczka
In a world where Wolfram Alpha can do all the algebraic calculations for you,
isn't learning to solve problems more relevant? I'd say that problem solving
is the core of mathematics. Am I wrong?

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flatline
The conceptual understanding is certainly essential, but if you want to use a
computer to do symbolic/algebraic manipulation, how could you be sure to
understand the results or even properly phrase the question without a thorough
understanding of the symbols and the rules for their manipulation? The best I
think that something like Alpha could do is to help elucidate the underlying
principles or give you a quick answer for guesswork or estimation, like a
calculator.

~~~
jey
You contradict yourself. As you said, one does not need to be skilled in
combinatorial _search_ , er I mean, algebraic manipulations to be able to
solve problems; one only needs a solid conceptual grounding and understand the
symbols and the _rules_ for their manipulation. I wouldn't be surprised if
most students who pass college calculus courses with good grades are entirely
unable to recognize the situations where calculus is applicable.

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lotharbot
tl;dw summary:

you know you're doing math wrong if students display (1) a lack of initiative,
(2) lack of perspective, (3) lack of retention, (4) aversion to word problems,
and (5) the few who understand the math just want to jump to a formula.

Math textbooks encourage teachers to teach math wrong. The way they present
problems is with a complex visual with mathematical structure already imposed,
step-by-step handholding through the problem, and asking a question at the end
(a question that can often be solved just by figuring out which number to plug
into which part of the formula, without necessarily understanding why.)

Suggested method for teaching right: (1) use multimedia. (2) encourage student
intuition. Students will argue with each other about what they see and buy in
to the problem. (3) ask the shortest possible question. Don't begin with a
page full of numbers, measurements, and individual steps. Let the detailed
questions come out through discussion. (4) Let the students build the problem.
Students will recognize the need for mathematical structure (labels,
coordinates, measurements, etc.) as they decide what information they will
need to answer the question. They'll go through the steps on their own. (5) Be
less helpful. The textbook helps in all the wrong ways, taking you away from
your obligation for developing patient problem solving and mathematical
reasoning.

Example: he completely rewrites a question from a math book about filling a
water tank. He produces a video of a water tank being filled from a garden
hose, which takes excruciatingly long to complete. Students get uncomfortable,
complain about how long it's taking, and then put in their guesses as to how
long it will take. Then they decide what information they'd need to calculate
the end result, ask for the measurements they think are important, do the
calculations, and watch the rest of the video to see if their calculation was
right and how close their initial guesses were.

~~~
Estragon
Central soundbite: "The way our mass-adopted textbooks teach math reasoning
and patient problem solving is functionally equivalent to turning on [a TV
sitcom] and calling it a day."

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snowbird122
I love the fresh thought here on how to best present problems to students. I
wonder how much work it takes to redefine each problem in the textbook.

~~~
yequalsx
A great deal of work.

Some problems won't be easily changed to suit his paradigm. For instance, how
does one go about redefining an equation like, sqrt(2x+1) = sqrt(x) + 1? I'd
like to know what this guy does for these types of problems.

I've been teaching community college mathematics for 10 years and we simply
don't have the time to do what he says. Maybe I'm bad at motivating students
but my anecdotal experience is that most of the students are solely interested
in getting a degree and not in learning. It's understandable that their focus
is no getting a degree but focusing on learning makes it easier to get the
degree. It's very hard to get this point across.

While I see many problems with the current system of teaching mathematics
there simply is no cure to apathy. At some point one has to be willing to sit
down and learn to solve problems like, sqrt(2x+1) = sqrt(x) + 1.

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bshep
This doesnt make any sense: sqrt(2x+1) = sqrt(x) + 1

EDIT: Ahh I thought he was saying that he had factorized/simplified the left
side into the right and it wasnt making any sense.

~~~
SlyShy
Solve for x: sqrt(2x + 1) = sqrt(x) + 1

    
    
      2x + 1 = x + 2sqrt(x) + 1
      x = 2sqrt(x)
      x^2 = 4x
      x^2 - 4x = 0
      x(x - 4) = 0
      x = 0 or 4

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sketerpot
Keep in mind that if you're posting on Hacker News then you're probably better
at math than, say, 90% of the population. It's hard to come up with ideas for
teaching math to people who are profoundly different from you.

