How to Do Homework
B
and WHY!
INSTRUCTOR: DOUG JONES
GENERAL NOTES
YOUR NAME
_______________________
[Rev. 08.09.10 Mon.]
hw_instructions-ver04_20100809mon_f10.docx
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INTRODUCTION
Practice makes perfect
1
is an old, tried-and-true saying. However, in a math class at the college or university
level, there is not much time during the class period
for you, the student, to practice
math. The number of
required topics and the essentially lecture-type atmosphere do not leave time for in-class practice. Thus
math must be practiced outside the classroom
. Now, I
=
ll try set aside some time each class period to show
you how to work homework problems on which you're "stuck," but in reality this work does not constitute
"practice" for you; it is really just practice for me. And, hopefully, I don't need too much practice.
What does it mean
to practice math?
I suggest that at the college level it means to actually work problems
.
And what does it mean to work problems
?
I believe that there are two types of problems to be worked –
routine problems
and
learning problems
.
And, consequently, there are two approaches to be used in working problems. For each type problem there
is a correct approach
to be used in working the problem.
For the
routine problem
the correct approach is to work fast, do as much mentally as possible, and “master
the
moves.
” It’s like shooting free-throws in basketball – you are supposed to make the free-throw; you are
supposed to get the problem right. And at the end of every basketball practice you have to shoot 10 in a row
before you can leave the court. Repetition! That’s the name of this game! If you don’t do the reps in practice
(homework), then you’ll probably miss the shot (problem) in the game (test). So – when you are doing the
homework you must recognize which problems are the routine problems and practice them accordingly. In
my own case, sometimes I’ll do
the same problem over-and-over
just to make sure that I can get it right.
On a more mundane level,
to practice routine math
is to exercise your basic set of mathematical tools: to
simplify expressions
,
to solve equations
,
to calculate, and
to graph. In solving routine problems there is
seldom a question of which tools to use – my only question is can I correctly use the tools!
What about
learning problems?
These problems are meant to
teach me
. They are meant for me to
study.
I
must ponder them and figure out what I’m supposed to
learn
from them – and
learn it
. I do not try to do these
problems fast. I do not try to do these problems mindlessly. I think a lot. I write a lot. I make notes to myself. I
use the techniques of
Polya
2
. What does it mean for me to study problems? It means
B
to read problems
carefully,
to decide
which mathematical
tools
3
to use, to properly use those mathematical tools
4
, to analyze
the results, and to interpret those results in a written style which is understandable even to an average,
educated person.
And what do we call both these types of practice? We call them