Typical Math 1XX syllabus trailer
Prerequisites:
I will presume that you are actually able to do on demand most of the things that are taught in the prerequisite classes.
For example, Math 124, Differential Calculus, requires Math 120 or a B average in 4 years of high school mathematics. The college catalog lists the prerequisites for Math 120 to be Math 105 or a B average in 3.5 years of high school math. Math 105 requires a B- average in Intermediate Algebra, and so on. These classes cover topics often described as "trigonometry" and "algebra." Unfortunately, as with many things in this life, if you don't use it you lose it. Having taken these classes years ago is not necessarily enough. You may need a refresher course before mastery returns. You will find that your plate is quite full enough as is in Math 124. Attempting to refresh trig and college algebra while taking calculus almost always yields a poor result.
Time Pressure and Testing:
My tests are timed and there is a bit of "time pressure" if the student is
uncertain of the material. This is intentional on my part.
One reason is that both you and I need a "reality check" periodically
throughout the quarter. It is very hard for the student (and for me in
conversations with students) to tell the difference between "familiarity" with
the material in the sense of "recognizing" it if someone else does it, and
actual mastery of the material.
I don't want students to be "discovering" how to do the problems on the tests.
I want them to recognize the type of problem and go right to the solution
technique. This math class is part of a sequence leading to calculus and
beyond. If the student is not "fluent" in the techniques of this course, he or
she cannot hope to pass subsequent courses. My usage of the word "fluency" is
the same as if this were a foreign language class, and the reason the student
must be fluent is the same.
Imagine the following scenario:
A student tells me that he or she can read French and I present that student with a copy of "Le Monde" and ask the student to translate the front page. The student replies that this is terribly unfair. The student says that he or she is "left brained" or "right brained" or something and cannot be expected to just sit down and read the paper, even though he or she says "I really do know how to read French. I just can't do it when you ask me like that."
The student claims that to demonstrate reading ability it is sufficient to be able to translate specific articles with much more time. The student claims that it would be more fair to allow the use of a dictionary and a grammar outline, and that this "test" would still demonstrate reading mastery.
After passing this test the student believes that a French literature and a French poetry class should be within reach.
Sound silly? Well this same argument, with "math" substituted for "French," is
used by some, unashamedly and repeatedly, in almost every math class where
tests occur.
The Relevance of Mathematics:
Another issue that comes up from time to time is the issue of "relevance." Some
people would insist that everything in a math class should be built around
something deemed "relevant" by some "relevance authority." This usually means
that the general rules and patterns inherent in the structures we study are
downplayed as being too abstract and the discussion is atomized into a list of
examples in which some math is used to solve a problem in economics or shopping
or carpentry.
However in my view this misses the whole point and beauty of mathematics.
Mathematics is about things that are true and patterns that one can find
REGARDLESS of the application. The same principles can be used in applications
from innumerable areas. Mathematics consists of an incredibly powerful
collection of tools with vast utility and a certain way of thinking.
Mathematics is not about chemistry or economics or carpentry. It is about
unifying principles. These principles and patterns must be emphasized and
examples used to illuminate them, not the other way around if the "way of
thinking" is to be efficiently encouraged.
Learning Styles and Self-Esteem
I have heard worries that the kind of "bottom line" attitude I have about the
study of mathematics doesn't promote the "self-esteem" of students or show
sufficient respect for different learning styles. In my view both these worries
are wrong-headed and show that the worrier doesn't understand the point of math
classes or even the meaning of the words used to describe the worry.
First of all, learning styles are means not ends. Everybody has a
unique and, one hopes, expanding collection of effective learning styles. When
applied to a body of material one achieves a level of mastery of the material
which is measured on tests. It is mastery that is graded, not
learning styles.
Second, real self-esteem in an academic environment can never be founded on
phony back-patting or credits granted for just showing up. It is founded here,
as in other slices of "the world," on hard work and achievement. It is based on
sure knowledge that the material has been mastered and certainty that when
called upon the skills will be there and ready to use.
To organize a grading method that takes inferior work from a student and marks
it "good" indicates a profound disrespect for both the student and the process.
An instructor who does that is saying in effect that students are incapable of
mastering the material and that the process is just a useless hoop through
which students have to jump to get a degree. Why not give away the credits if
they are meaningless and the skills are useless?
I would like to take this opportunity to assure each of you in this class that
I respect both you and the process. I respect you enough to tell you not only
when you have done a great job but also when an idea is just plain wrong or the
level of effort insufficient. I respect the process and the need for general
mathematical competence enough to have high standards.
"Will this be on the test?"
We can save quite a bit of class time by dealing with the repetitive "Will this
be on the test?" question right here in the syllabus. I will respond to the
question "Will this be on the test?" by referring the student to the following
statement:
My feeling on this matter is that if you concentrate on understanding the
material and the ideas in the class the tests will take care of themselves.
I try to telegraph clearly the type of material that will be on tests and
quizzes, but I avoid saying that any particular problem will be on the test.
This is because I want students to learn everything and not focus on a few
trees (at the expense of the forest) too early.
Anything in any text sections we cover before the exam and anything we do in
class before the exam is "fair game" for test questions. Questions that mention
topics from prerequisite algebra (basic polynomial simplification, lines and
linear relationships, rules of exponents etc.) or arithmetic (such as decimals,
rounding, percents, simplifying, adding and multiplying fractions, least common
multiples or greatest common factors, signed numbers, the number line, order of
operations) are always fair.
As a practical matter, the more basic a topic is the more important it is.
Don't spend all your homework time on the really hard problems thinking you
will "get back" to the easier ones later. Do all the easier ones first.
I rarely ask a problem on an exam without doing several problems just like it
on the board. To study for an exam, go over your notes and the assigned
homework problems. (Some of the assigned problems are really hard, involving
several different techniques - synthesis problems. Although these are good for
homework, they don't work well as exam questions.)
During the quarter, exam questions will mostly be on topics studied after the
last test. I recycle quiz problems on the following test. The final is
cumulative. To best prepare for it, go over my tests and the cumulative review
exercises found in the text.
To reiterate:
I know my math tests are fairly hard. That is because I need to find out if you
have learned well the many techniques we study in the course. I need to find
out if you recognize problems right away, or if it takes a long time before you
can dredge something up. This correlates with how much time you have spent on
homework outside of class, and with how well you will be able to use the
techniques in longer problems in later courses. Typically you will need to
spend two to three quality hours of study outside of class for every hour
inside to succeed. It may take some people more, and some less. However much
time it takes you, your grade will be based on your ability to perform on
the exams, and not on whether I like you or "feel" you deserve to pass or
because you really need or want a certain grade or because you like math or
don't like math. Except in the case of a documented disability, that
performance must take place in the class on the day of the test within the time
limits I set.
If my attitude toward these matters does not work for you I strongly encourage
you to shop around for an instructor more amenable to alternative theories of
education.
I can be contacted by phone at Bellevue College at (425) 564-2484 or by e-mail at lsusanka@bellevuecollege.edu .
