
Other useless school trivia: the quadratic formula - platz
http://lemire.me/blog/archives/2015/03/16/other-useless-school-trivia-the-quadratic-formula/
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mixedmath
As an aspiring mathematician and current math grad student, I am often
confronted by students facing existential questions about life and the role
mathematics plays in it. [For that matter, I also face these questions, just
pitched a little differently]

I think I can summarize the existential angst into a single question: does
everyone need to learn mathematics?

I waver on how I feel about this. On the one hand, the answer is clearly _no._
Not everyone needs to learn mathematics.

Recently, there was a post on HN that prompted discussion about whether or not
going to college was necessary to achieve "the American Dream." One of the
higher comments also said _no._ But not going to college limits the paths one
can take forward. This is parallel to my current thinking about general
mathematics education.

Being innumerate is bad for personal development. Numeracy is required for
many professions while innumeracy is targeted and taken advantage of by news
makers and, for lack of a better word, propagandists.

That aside, this doesn't actually answer the question of whether or not
everyone should learn math. I suggest that there are reasons for everyone to
become numerate. Becoming numerate in the American education system is thought
of as a byproduct of the mathematical system. Learning the quadratic formula
by rote does not contribute to numeracy. It seems plausible that having the
mental faculty to understand its derivation does.

But I would also argue that becoming good at programming, physics, or
chemistry (among others) also develops good numeracy. [I have thought about
how "critical thinking skills," to use a buzzword, relates to basic numeracy.
There are many studies, and the Math Wars is a battlefield]. In physics and
chemistry, the quadratic formula might arise in the process of understanding
something else. It doesn't bother me if a student sees a quadratic, knows
there exists a formula to compute its roots, and then proceeds to look up/use
this black box formula -- if the quadratic arose from good reasoning about
some physical phenomenon (like finding orbits, or kinematics, or even making
plans in games like KSP). To this, the author would reply that such a student
is capable of understanding and perhaps even rederiving the quadratic formula
on his or her own.

I suppose I could summarize my view by saying that I have conflicting thoughts
on the merits for or against rote memorization in early mathematics... or for
that matter calculus (which I'm currently teaching).

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beeworker
It's really easy to memorize if your teacher presents it to the tune of _pop
goes the weasel_... Whether it's worthwhile to memorize or not, use a computer
or not, the valuable conceptual struggle teachers need to focus in on is in
what the answer _means_ , and when to apply it, not in deriving the formula,
though that can be a useful struggle if you doubt the power of proof or the
rules of algebraic manipulation.

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arikrak
The reason there's little point in memorizing these formulas is that it's
easier to use a computer. If you don't understand it anyways, why not just
plug it into a computer? How is it plugging it into a paper formula any
better?

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itazula
Solving it by hand gives an exact answer, which in some contexts, might be
preferable. Forman Acton, in his classic book, Numerical Methods That Work,
uses the quadratic formula as an example to illustrate how a computer can give
a wildly incorrect solution.

~~~
gizmo686
Computer algebra systems can symbolicly solve quadratics precisly (think
Mathematica).

~~~
arikrak
Right. Anything that a human can solve by following simple mechanical steps
can be easily done by a computer. (See Turing's definition of computability.)
Many people now are just following simple mechanical steps without
understanding. They may as well use Mathematica or Wolfram|Alpha for such
simple problems
[http://www.wolframalpha.com/input/?i=12x%5E2%2B2x-30%3D0](http://www.wolframalpha.com/input/?i=12x%5E2%2B2x-30%3D0)
They should focus on learning how to convert real problems into a format
Wolfram|Alpha can understand.

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tomrod
I disagree with the author. I've found that rote memorization (especially in
quantitative endeavors) gives one a foundation from which creativity can
spring.

