Math by Hand, Math by Calculator

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The purpose
of this article is to point out the procedural cobwebs within our
mathematics classrooms, both within our institutions of higher learning
and within our public schools.

It's always
the same. Whenever and wherever math teachers gather, the conversation
is of student deficiencies and who's to blame. Professors blame
adjuncts, adjuncts blame high school teachers, who blame middle
school teachers, who blame elementary school teachers, who blame
parents and nearly everyone blames calculators. Why? Why are these
supposed deficiencies of millennium-old mathematics of concern to
anyone? Is there really a dearth of unsolved circumferences and
areas? Is there really a shortage of algebraic equations that go
unsolved?

Certainly one
could argue there is a labor shortage of individuals who are proficient
in secondary mathematics (algebra, geometry, consumer math, statistics,
etc.) but we can hardly argue there is a shortage of answers. From
the comforts of my TI 89 calculator, I may input sets of data, acquire
all needed measures of central tendency and standard deviations,
run a regression analysis, formulate an equation, run various derivative
and integrals, plot my data, upload it to my laptop and e-mail anyone
I would like while drinking an overpriced white chocolate mocha
from my local coffee shop. I could spend a few hours teaching any
competent teenager to mimic my button inputs, and send them off
with their final exam thus saving them a semester worth of work.

Certainly this
wouldn't be within my interests as a professor and most likely wouldn't
be within the interests of the student, but we have to agree that
a small investment in technology and training could provide all
required solutions that are asked of them. In fact, these secondary
mathematics problems are so easily solvable with technology, and
said technology is so prolific, that we may safely say that there
is no demand for these skills by hand – aside from the actual
signal to employers they reveal by passing my coursework.

Yet, this simply
begs the question, what is so special about the process of deriving
solutions? Surely we would all be better spellers with the elimination
of spell check and may possibly be better writers with the elimination
of the backspace key and eraser, but exactly how would this benefit
production and consumption?

Clearly we
cannot churn out engineers and scientists by increasing the production
of Texas Instrument calculators but then again, no engineering firm
on the planet would trust their scientists or engineers without
these calculating devices. A stubborn mathematician who refuses
to employ calculating technology would be hard pressed to find work
in the fast-paced world of consulting. Simply, he is a relic; delegated
to the classroom to grade papers.

So why are
we still educating math like we did in the pre-calculator revolution
of the 1980's? I'm not sure I can provide a legitimate answer to
this question, and there is still much to debate within this topic,
but I think an extract from a favorite economist of mine (Steven
Landsburg) about quality today versus quality of the recent past
may offer some insight:

"As
far as quality of the goods we buy [today versus the past], try
picking up an electronics catalogue from oh, say, 2001 and ask
yourself whether there's anything there you'd consider owning…or,
if you prefer, take a product like health care. Would you rather
purchase today's health care at today's prices, or the health
care of say, 1970 at 1970 prices?"

Nevertheless,
as forward as I am on this topic, I would not dare call myself a
professional mathematician, as it would be an injustice to the mathematicians
I studied under as well as those I work alongside. Simply, I just
imagine a society who embraces answers instead of worshiping processes.

For more traditional
educational criticism and help/advice for educators see my Hands-on
Math website
or my book "Surviving
the Trenches of Education: Unorthodox Advice from the Proudly Self-proclaimed
Worst Teacher to Ever Enter the Classroom
"

October
5, 2010

Jeremiah
Dyke [send him mail]
is a professor of mathematics and author of Surviving
the Trenches of Education.
He invites you to brainstorm with him via his
website
.

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