How to FAIL a Math Course

How to FAIL A Math Course
Jeﬀ Suzuki
Department of Mathematics
Brooklyn College
Brooklyn NY 11210
jeff suzuki@yahoo.com
J. Suzuki (CUNY) How to Fail Math 1 / 7

How To Fail Math (the Easy Way)
The easy way to fail a math class:

Not being prepared for the class.

Not being prepared for the class. If you haven’t passed algebra, you probably
shouldn’t take calculus.

Not going to class.

Not going to class. Registering for a course and not showing up to class is
like buying lunch and leaving it on the counter: you’ve paid for it, but it
won’t feed you.

won’t feed you.
Not doing the work.

won’t feed you.
Not doing the work. Since your grade depends on the work you’ve done, not
doing the work is a guaranteed way to fail the course.

How To Fail Math (the Hard way)
The hard way to fail a math class is to

The hard way to fail a math class is to be prepared for the course,

The hard way to fail a math class is to be prepared for the course, go to every
class,

class, and do all the work,

class, and do all the work, then fail the class.

How can you do this?

I’ve been teaching math for 3413yearsfeet15.351 years,

I’ve been teaching math for 3413yearsfeet15.351 years, but I’m still a math student, and still
learning new things in mathematics.

I’ve been teaching math for 3413yearsfeet15.351 years, but I’m still a math student, and still
learning new things in mathematics.
So I know how to fail math.

How To Fail a Math Course: Memorizing Procedures
Procedures are important time savers, and there are a few things that you should
memorize.

memorize. But memorizing a procedure without understanding why you’re doing
it is a fast way to failure.

For example: Solve x2
− x − 6 = 10.

− x − 6 = 10.
Many students are taught that quadratic equations can be solved by factoring, so
they factor:

− x − 6 = 10.
they factor:
x2
− x − 6 = 10

− x − 6 = 10.
they factor:
x2
− x − 6 = 10
(x − 3)(x + 2) = 10

− x − 6 = 10.
they factor:
x2
− x − 6 = 10
(x − 3)(x + 2) = 10
This takes them quickly to the answers x = 3, x = −2.

− x − 6 = 10.
they factor:
x2
− x − 6 = 10
(x − 3)(x + 2) = 10
This takes them quickly to the answers x = 3, x = −2. Unfortunately, these are
the wrong answers.

− x − 6 = 10.
they factor:
x2
− x − 6 = 10
(x − 3)(x + 2) = 10
the wrong answers.
If you don’t know why,

− x − 6 = 10.
they factor:
x2
− x − 6 = 10
(x − 3)(x + 2) = 10
the wrong answers.
If you don’t know why, you shouldn’t use this procedure.

How To Fail a Math Course: Following Examples
Many math teachers (myself included!) give examples of how to solve problems,
then assign problems based on those examples.

This gives the impression that the problems can be solved by following the
examples.

examples.
However, it’s not possible to give examples of every situation that can occur, so
you will ALWAYS encounter problems for which you’ve never seen an exemplar.

examples.
However, it’s not possible to give examples of every situation that can occur, so
you will ALWAYS encounter problems for which you’ve never seen an exemplar.
Focus on the reasoning behind the example, and not the details of the example
itself.

How To Fail a Math Course: Working In Your Head
Many math students (myself included!) practice mathematics by thinking about
what they would do to solve a particular problem.

It’s a great workout, but it’s very easy to convince yourself that you know how to
solve a problem, without actually being able to solve it.

It’s a great workout, but it’s very easy to convince yourself that you know how to
solve a problem, without actually being able to solve it.
This is because actual problems often have unexpected complications that aren’t
apparent until you get to them.

Three Bumper Stickers
Perhaps you don’t want to fail this math course. In that case, here are three
bumper stickers you might take to heart.

Of course, if it can be reduced to a bumper sticker, it’s either very trivial . . . or
very profound.

Of course, if it can be reduced to a bumper sticker, it’s either very trivial . . . or
very profound.
I’m hoping for profound.

Paper is cheap, understanding is priceless.

Paper is cheap, understanding is priceless. Write stuﬀ down. Even if you can
do several steps in your head, write them down one step at a time.

Deﬁnitions are the whole of mathematics; all else is commentary.

Definitions are the whole of mathematics; all else is commentary. You MUST
know the definitions, and understand the difference between definitions,
theorems, and rules.

theorems, and rules. It’s useful to know things besides the deﬁnitions, but if
you don’t know the deﬁnitions, you can’t do mathematics.

It doesn’t matter if you get it right at ﬁrst, as long as you get it right at last.

Once you get past the simplest arithmetic, there’s a lot of trial-and-error in
mathematics, and the most important thing to remember about trial and
error

error is that it involves a lot of errors and trying again.

A little analysis goes a long ways.

A little analysis goes a long ways. Did I say three? I meant four.

Four Bumper Stickers
A little analysis goes a long ways. Analyze the problem before you start to
write things down.

How to FAIL a Math Course

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How to FAIL a Math Course