The intelligent use of technology

The other day a student asked me “why can’t I just punch the whole quadratic formula, with the numbers into it, into my calculator?”.  Of course you can, but there’s some subtle ways that we write mathematical formulas that you have to be very detailed about when you put them in the calculator.

What I’ve seen students do is say out loud “negative b plus or minus the square root of b squared minus four a c all over two a”, and that’s the way they type it into the calculator. So if a is 1, b is -2, and c is 3, they proceed thusly;

-2 + √ -2^2 – 4*1*3 / 2*1 Enter
Then they do it again with a negative in place of the first positive, since they do understand the ± notation.
(Note that ideally they would use (-(-2) + √ ( (-2)^2 – 4*1*3 ) ) / (2*1) Enter.)

I’m trying to come up with a good learning opportunity to address this.

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5 Comments

  1. novice9 said,

    March 17, 2009 at 1:07 pm

    Isn’t the Quadratic formula “negative b plus or minus the square root…” and not “b squared plus or minus the square root of…”?

  2. novice9 said,

    March 17, 2009 at 2:59 pm

    No problem. Umm…if b=-2, then the “negative b” at the beginning of the numerator should be +2, right?

  3. March 17, 2009 at 3:22 pm

    Yes, and that’s one of the problems. If it’s negative already, often they don’t realize they have to make it “negative again”.

  4. novice9 said,

    March 17, 2009 at 3:31 pm

    Ah, okay, I see. Good luck with this. =)


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