"Why/when should Johnny factor?"
"Why does Johnny spend 80% or more of his/her mathematical studies on the
factorable function when one is hard-pressed to come up with a real-life
non-contrived use for the factorable function?"
"Why does Johnny (even in calculus) not know the relative size between 1
million and 1 trillion dollars--thereby does not have the number sense
necessary to make informed political judgements?"
"Why doesn't Johnny know what rate of change of rate of change means. In
practical terms, why doesn't Johnny understand increase or decrease in the
rate of inflation? I'll bet that most Johnny's who can factor think that
'a reduced rate of growth in federal budget/deficit' means that the
budget/deficit is decreasing."
"Why can Johnny only minimally attack word problems by following a cookbook
example with a few numbers changed and he/she can do this only if he/she is
told which recipe to follow? Why does Johnny think that math problems have
one correct answer? Why does Johnny think that math applications are word
problems that can be solved by following a particular recipe?"
"Why does Johnny think that fractions are arithmetic processes, not concepts?"
One of the big ironies in all of this controversy surfaces in topics like
simplifying radicals. Historically, the fine points of
simplifying/rationalizing/combining radicals were important because people
needed every trick possible to arrive at an accurate decimal approximation
to a numeric problem in the shortest amount of time possible--given that
the computational tools were logarithms and tables.
Now that a student can arrive at that decimal approximation in a very short
amount of time using a calculator, we do not generally let him/her use the
calculator for that purpose. However, somehow we think it mathematical
heracy to skip those endless problems that pull out perfect squares, cubes,
etc from radicalls and magically end up like terms that can be collected or
factors that can be cancelled/multiplied. Imagine the shame of failing to
write 1/(square root(2)) as (Square root(2))/2 (although the calculator
will give you the same decimal approximation for either form and the
historical rationalle was numerical approximation accuracy.)
My thought for today: "The rate in which bureaucracies change approaches
zero as time goes to infinity."
Martha
Martha Haehl
Maple Woods Community College
2601 N. E. Barry Rd.
Kansas City, Missouri 64156
(816)437-3147
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