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Topic: Re: quadratic formula
Replies: 1   Last Post: May 1, 2001 12:42 PM

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Joan Reinthaler

Posts: 110
Registered: 12/6/04
Re: quadratic formula
Posted: May 1, 2001 12:42 PM
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As a teacher of high school kids who study the quadratic formula in
algebra classes, I see all sorts of good reasons to spend time with it.
1. Kids ought to be encouraged to generalize their results at every
oportunity. Programmable calculators make this worth their while when
can use their generalization to write a quadratic equation-solving program
(I know, there is a dedicated function built in to the TI-83 etc. but it's
much nicer for the kids to write their own first - also, the first time
their discriminent is negative and they get an error message is a
wonderful opportunity for further discussion).
2. The understanding about what it means "to be in the form of", as in, to
use the formula, an equation must be in the form of ax^2 + bx + c = 0 is
more sophisticated than most of us recognize, and it is essential.
3. I encourage kids to approximate rational values for the roots they get
when using the quadratic formula - in their head (i.e. "Root of 21 is
about 4 1/2 so 3 +/- root 21 is approx 7.5 or -1.5 and so forth - all
things that contribute to a secure number sense.
4. Why is the sum of the roots rational (given rational
coefficients)? how about the product? The formula leads to discussions
about conjugate pairs.

It seems to me that the quadratic formula offers a lot of opportunity to
be playful with mathematical ideas and the notion that it can be dispensed
with because calculators do it job better is only true if math is
considered only as a bottom line and not as inquiry.

Joan Reinthaler
Sidwell Friends School



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