"Do not worry about your difficulties in mathematics,
I can assure you mine are still greater." - Einstein
MATH SURVIVAL GUIDE FOR FIRST YEAR
STUDENTS
UTSC
MATH & STATS HELP CENTRE
Compiled and edited by Geanina Tudose
CONTENTS
1. What is university math like?
1.
2.
3.
4.
5.
6.
7.
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What is new and different in university? Well, almost
everything: new people (your peers/colleagues, teaching and
lab assistants, instructors, administrators, etc.), new
environment, new social contexts, new norms, and – very
important - new demands and expectations. Think about the
issues raised below. How do you plan to deal with it? Read
tips and suggestions, and try to devise your own strategies.
What is university math like?
How to be a great math student
Problem Solving
Writing mathematics (homework and tests)
Preparing and taking a math test. Dealing with anxiety
Getting Help
Appendices:
FAQ (Common Student Concerns)
TLS Support
Additional Readings
Teaching and Learning Services
Math & Stats Help Centre
University of Toronto at Scarborough
©2004 TLS
First-year lectures are large – you will find yourself in a huge
auditorium, surrounded by 300, 400, or perhaps even more
students. Large classes create intimidating situations. You
listen to a professor lecturing, and hear something that you do
not understand. Do you have enough courage to rise your
hand and ask the lecturer to clarify the point? Keep in mind
that you are not alone – other students feel the same way you
do. It’s hard to break the ice, but you have to try. Other
students will be grateful that you asked the question – you can
be sure that lots of them had exactly the same question in
mind.
Lectures move at a faster pace. Usually, one lecture covers one
section from your textbook. Although lectures provide
necessary theoretical material, they rarely present sufficient
number of worked examples and problems. You have to do
those on your own.
Certain topics (trigonometry, exponential and logarithm
functions, vectors, matrices, etc.) will be reviewed in your
first-year calculus and linear algebra courses. However, the
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time spent reviewing in lectures will not suffice to cover all
details, or to provide sufficient number of routine exercises –
you are expected to do it on your own.
You have to know and be proficient with the material from
 Basic Algebra
 Basic Formulas from Geometry
 Equations and Inequalities
 Elements of Analytic Geometry.
For instance, computing common denominators, solving
equations involving fractions, graphing the parabola y=x2, or
solving a quadratic equation will not be reviewed in lectures.
courses. You will learn how to approach learning ‘theory,’
how to think about proofs, how to use theorems, etc.
Layperson-like attitude towards mathematics (and other
disciplines!) - accepting facts, formulas, statements, etc. at face
value - is no longer acceptable in university. Thinking (critical
thinking!) must be (and will be) integral part of your student
life. In that sense, you must accept the fact that proofs and
definitions are as much parts of mathematics as are
computations of derivatives and operations with matrices.
©Mathematics Review Manual, Miroslav Lovric, McMaster
University, 2003.
In university, there is more emphasis on understanding than
on technical aspects. For instance, your math tests and exams
will include questions that will ask you to quote a definition,
or to explain a theorem, or answer a ‘theoretical question.’
Here is a sample of questions that appeared on past exams and
tests in the first-year calculus course:
 Is it true that f’(x)=g’(x) implies f(x)=g(x)? Answering
‘yes’ or ‘no’ only will not suffice. You must explain
your answer.
 State the definition of a horizontal asymptote.

Given the graph of 1/x, explain how to construct
the graph of 1+1/(x-2).
 Using the definition, compute the derivative of f(x)=(x2)-1.
Mathematics is not just formulas, rules and calculations. In
university courses, you will study definitions, theorems, and
other pieces of ‘theory.’ Proofs are integral parts of
mathematics, and you will meet some in your first-year
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2. How to be great Math Student
These remarks are provided to assist you, the first year
student, in making the transition from high school to
university. For a student with intellectual curiosity who is
determined to work regularly from the beginning of the term,
a first year mathematics course can be remarkably rewarding
and stimulating. However, the unwary student may fall into
difficulties and have a poor experience instead. These
following are intended to help you avoid that.
1. In all mathematics courses, the key to success can be
summarized briefly:
DEVELOP REGULAR WORK HABITS SO YOU DO
NOT FALL BEHIND!
This will ensure that you develop the depth, breadth
and maturity of your knowledge. It means: attend
lectures and tutorials, do assignments and enough
extra problems to master the material. If you attend
lectures, but don't do exercises, you may get lulled into
a false sense of accomplishment and can expect a rude
shock. In mathematics a thorough knowledge of the
previous material is essential to reach an
understanding of new material. Hence, falling behind
tends to be cumulative and is one of the most frequent
causes of failure. Understanding grows with time and
experience. Do not expect to follow the mathematics
completely, right away; you will have to think about it,
and it may not be until later work is covered that you
can appreciate the full significance of earlier material.
2. Some of the ideas in many first year courses, such as
differentiation, have been introduced in high school.
This does not mean the course is a review. New and
more sophisticated concepts will be introduced and
must be mastered at a new and higher level of
thoroughness and understanding.
3. Learn from doing badly. If you receive a poor grade
on early tests or assignments, that is an important
signal that you are not mastering the material at an
appropriate level. You can deal with this by working
harder and consulting about problems with your TA or
instructor.
4. If you are having difficulty, first consult your TA;
then if the problems persist, your instructor. Professors
have regular office hours and are generally willing to
meeting with students outside these times by
appointment. It should be emphasized that it is your
responsibility to seek help if difficulties arise.
5. The Math & Stats Help Centre AC320 and the Math
Aid Room S506F is open for extended periods and
staffed by faculty and TAs who will assist you. The
Math & Stats Help Centre offers tutoring, study
groups, and workshops on study techniques and
seminars on various mathematics topics. More detailed
information can be found on the centre’s website.
6. Do not delay asking for assistance until the day before
the exam. It is impossible to cram mathematics at the
last minute. Just as with playing a musical instrument,
learning mathematics involves a development of skills
and understanding that must be consolidated over a
period of time.
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7. One of the main differences between high school and
university is that, at the university, you are expected to
be responsible for mastering course material.
Considerable help is offered--lectures, tutorials,
mathematics assistance centres and personal help--but
it's your responsibility to utilize it.
8. If, nevertheless, you find that you have fallen behind in
your coursework, speak with your instructor. He or
she can advise you on what to do next.
3. Problem Solving
Problem Solving (Homework and Tests)
The higher the math class, the more types of problems: in
earlier classes, problems often required just one step to find a
solution. Increasingly, you will tackle problems which require
several steps to solve them. Break these problems down into
smaller pieces and solve each piece divide and conquer!

Problem types:
1. Problems testing memorization ("drill"),
2. Problems testing skills ("drill"),
3. Problems requiring application of skills to
familiar situations ("template" problems),
4. Problems requiring application of skills to
unfamiliar situations (you develop a strategy
for a new problem type),
5. Problems requiring that you extend the skills or
theory you know before applying them to an
unfamiliar situation.
In early courses, you solved problems of types 1, 2 and
3. By College Algebra you expect to do mostly
problems of types 2 and 3 and sometimes of type 4.
Later courses expect you to tackle more and more
problems of types 3 and 4, and (eventually) of type 5.
Each problem of types 4 or 5 usually requires you to
use a multi-step approach, and may involve several
different math skills and techniques.
5
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When you work problems on homework, write out
complete solutions, as if you were taking a test. Don't
just scratch out a few lines and check the answer in the
back of the book. If your answer is not right, rework
the problem; don't just do some mental gymnastics to
convince yourself that you could get the correct
answer. If you can't get the answer, get help.
The practice you get doing homework and reviewing
will make test problems easier to tackle.
"Word" Problems are Really "Applied" Problems
The term "word problem" has only negative connotations. It's
better to think of them as "applied problems". These problems
should be the most interesting ones to solve. Sometimes the
"applied" problems don't appear very realistic, but that's
usually because the corresponding real applied problems are
too hard or complicated to solve at your current level. But at
least you get an idea of how the math you are learning can
help solve actual real-world problems.
Tips on Problem Solving
Solving an Applied Problem
Apply Pólya's four-step process:

1. The first and most important step in solving a problem
is to understand the problem, that is, identify exactly
which quantity the problem is asking you to find or
solve for (make sure you read the whole problem).
2. Next you need to devise a plan, that is, identify which
skills and techniques you have learned can be applied
to solve the problem at hand.
3. Carry out the plan.
4. Look back: Does the answer you found seem
reasonable? Also review the problem and method of
solution so that you will be able to more easily
recognize and solve a similar problem.


Some problem-solving strategies: use one or more variables,
complete a table, consider a special case, look for a pattern,
guess and test, draw a picture or diagram, make a list, solve a
simpler related problem, use reasoning, work backward, solve
an equation, look for a formula, use coordinates.
First convert the problem into mathematics. This step
is (usually) the most challenging part of an applied
problem. If possible, start by drawing a picture. Label
it with all the quantities mentioned in the problem. If a
quantity in the problem is not a fixed number, name it
by a variable. Identify the goal of the problem. Then
complete the conversion of the problem into math, i.e.,
find equations which describe relationships among the
variables, and describe the goal of the problem
mathematically.
Solve the math problem you have generated, using
whatever skills and techniques you need (refer to the
four-step process above).
As a final step, you should convert the answer of your
math problem back into words, so that you have now
solved the original applied problem.
©Source: Department of Mathematics and Computer Science
SAINT LOUIS UNIVERSITY
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4. Writing Mathematics
Mathematics is a language, and as such has standards of
writing which should be observed. In a writing class, one must
respect the rules of grammar and punctuation, one must write
in organized paragraphs built with complete sentences, and
the final draft must be a neat paper with a title. Similarly, there
are certain standards for mathematics assignments.
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Write your name and class number clearly at the top
of at least the first page, along with the assignment
number, the section number(s), or the page number(s).
Use standard-sized paper (8.5" x 11"), with no "fringe"
running down the side as a result of the paper’s having
been torn out of a spiral notebook.
Attach your pages with a paper clip or staple. Do not
fold, tear, or otherwise "dog-ear" the pages
Clearly indicate the number of the exercise you are
doing. If you accidentally do a problem out of order,
or separate part of the problem from the rest, then
include a note to the grader, referring the grader to the
missed problem or work.
Write out the problems (except in the case of word
problems, which are too long).
Do your work in pencil, with mistakes cleanly erased,
not crossed or scratched out. If you work in ink, use
"white-out" to correct mistakes.
Write legibly (suitably large and suitably dark); if the
grader can't read your answer, it's wrong. Write neatly
across the page, with each succeeding problem below
the preceding one, not off to the right. Please do not
work in multiple columns down the page (like a
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newspaper); your page should contain only one
column.
Keep work within the margins. If you run out of room
at the end of a problem, please continue onto the next
page; do not try to squeeze lines together at the bottom
of the sheet. Do not lap over the margins on the left or
right; do not wrap writing around the notebook holes.
Do not squeeze the problems together, with one
problem running into the next. Use sufficient space for
each problem, with at least one blank line between one
problem and the next.
Do "scratch work," but do it on scratch paper; hand in
only the "final draft." Show your steps, but any work
that is scribbled in the margins belongs on scratch
paper, not on your homework.
Show your work. This means showing your steps, not
just copying the question from the assignment, and
then the answer from the back of the book. Show
everything in between the question and the answer.
Use complete English sentences if the meaning of the
mathematical sentences is not otherwise clear. For your
work to be complete, you need to explain your
reasoning and make your computations clear.
Do not invent your own notation and abbreviations,
and then expect the grader to figure out what you
meant. For instance, do not use "#" in your sentence if
you mean "pounds" or "numbers". Do not use the
"equals" sign ("=") to mean "indicates", "is", "leads to",
"is related to", or anything else in a sentence; use actual
words. The equals sign should be used only in
equations, and only to mean "is equal to".
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Do not do magic. Plus/minus signs, "= 0", radicals,
and denominators should not disappear in the middle
of your calculations, only to mysteriously reappear at
the end. Each step should be complete.
If the problem is of the "Explain" or "Write in your own
words" type, then copying the answer from the back of
the book, or the definition from the chapter, is
unacceptable. Write the answer in your words, not the
text's.
Remember to put your final answer at the end of your
work, and mark it clearly by, for example, underlining
it. Label your answer appropriately. If the answer is
to a word problem, make sure to put appropriate
units on the answer.
In general, write your homework as though you're trying to
convince someone that you know what you're talking about.
http://www.purplemath.com/guidline.htm
Copyright © 1990-2004 Elizabeth Stapel, Used By Permission
5. Preparing and taking a math test.
Dealing with anxiety
Everyday Study is a Big Part of Test Preparation
Good study habits throughout the semester make it easier to
study for tests.

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
Do the homework when it is assigned. You cannot
hope to cram 3 or 4 weeks worth of learning into a
couple of days of study.
On tests you have to solve problems; homework
problems are the only way to get practice. As you do
homework, make lists of formulas and techniques to
use later when you study for tests.
Ask your Instructor questions as they arise; don't wait
until the day or two before a test. The questions you
ask right before a test should be to clear up minor
details.
Studying for a Test
1. Start by going over each section, reviewing your notes and
checking that you can still do the homework problems
(actually work the problems again). Use the worked examples
in the text and notes - cover up the solutions and work the
problems yourself. Check your work against the solutions
given.
2. You're not ready yet! In the book each problem appears at
the end of the section in which you learned how do to that
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problem; on a test the problems from different sections are all
together.
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
Step back and ask yourself what kind of problems you
have learned how to solve, what techniques of solution
you have learned, and how to tell which techniques go
with which problems.
Try to explain out loud, in your own words, how each
solution strategy is used (e.g. how to solve a quadratic
equation). If you get confused during a test, you can
mentally return to your verbal "capsule instructions".
Check your verbal explanations with a friend during a
study session (it's more fun than talking to yourself!).
Put yourself in a test-like situation: work problems
from review sections at the end of chapters, and work
old tests if you can find some. It's important to keep
working problems the whole time you're studying.
important to think about what strategies you will use when
you take a test (in addition to actually doing the problems on
the test). Good test-taking strategy can make a big difference
to your grade!
Taking a Test
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
3. Also:

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Start studying early. Several days to a week before the
test (longer for the final), begin to allot time in your
schedule to reviewing for the test.
Get lots of sleep the night before the test. Math tests are
easier when you are mentally sharp.

TAKING A MATH TEST
Test-Taking Strategy Matters
Just as it is important to think about how you spend your
study time (in addition to actually doing the studying), it is

First look over the entire test. You'll get a sense of its
length. Try to identify those problems you definitely
know how to do right away, and those you expect to
have to think about.
Do the problems in the order that suits you! Start with
the problems that you know for sure you can do. This
builds confidence and means you don't miss any sure
points just because you run out of time. Then try the
problems you think you can figure out; then finally try
the ones you are least sure about.
Time is of the essence - work as quickly and
continuously as you can while still writing legibly and
showing all your work. If you get stuck on a problem,
move on to another one - you can come back later.
Work by the clock. On a 50 minute, 100 point test, you
have about 5 minutes for a 10 point question. Starting
with the easy questions will probably put you ahead of
the clock. When you work on a harder problem, spend
the allotted time (e.g., 5 minutes) on that question, and
if you have not almost finished it, go on to another
problem. Do not spend 20 minutes on a problem which
will yield few or no points when there are other
problems still to try.
Show all your work: make it as easy as possible for the
Instructor to see how much you do know. Try to write
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a well-reasoned solution. If your answer is incorrect,
the Instructor will assign partial credit based on the
work you show.
Never waste time erasing! Just draw a line through the
work you want ignored and move on. Not only does
erasing waste precious time, but you may discover
later that you erased something useful (and/or maybe
worth partial credit if you cannot complete the
problem). You are (usually) not required to fit your
answer in the space provided - you can put your
answer on another sheet to avoid needing to erase.
In a multiple-step problem outline the steps before
actually working the problem.
Don't give up on a several-part problem just because
you can't do the first part. Attempt the other part(s) - if
the actual solution depends on the first part, at least
explain how you would do it.
Make sure you read the questions carefully, and do all
parts of each problem.
Verify your answers - does each answer make sense
given the context of the problem?
If you finish early, check every problem (that means
rework everything from scratch).
TEN WAYS TO REDUCE MATH ANXIETY
1. You are not alone! Relax. Many people dislike and are
nervous about math. Even mathematicians are unsure of
themselves and get that sinking, panicky feeling called "math
anxiety" when they first confront a new problem.
2. If you have math anxiety, admit it. If you pretend not to
have it, you will not learn to overcome it or manage it.
3. If you're having math trouble, practice a little math each
day.
4. Ask questions. Some people think asking questions is a sign
of weakness. It's not. It's a sign of strength. In fact, other
students will be glad. (They have questions, too.)
5. Do math in a way that's natural for you. There's often more
than one way to work a math problem. Maybe the instructor's
way stumps you at first. Don't give up. Work to understand it
your way. Then it will be easier to understand it the
instructor's way. Remember, "each mind has it's own method."
6. Notice your handwriting when you do math. The sloppier
it gets, the more confused or angry you probably are. When it
gets really sloppy, STOP. Look away for a few seconds. Then
erase the messy parts. Start again. Try not to let your attitude
interfere with learning math.
7. Know the basics. Be sure you know your math from earlier
grades. Maybe you missed something when you moved to a
new high school. Face it: Math builds on itself. You have to go
back and relearn that stuff.
8. Don't go by memory alone. Try to understand your math.
Memorizing is a real trap. When you're nervous, memory is
the first thing to go.
©Source: Department of Mathematics and Computer Science SAINT LOUIS
UNIVERSITY
10
6. Getting Help
Get help as soon as you need it. Do not wait until the test is near.
The new material builds upon the previous one, so anything
that you do not understand will make future material even
harder.
Resources:
1. Ask questions in class. Do not be intimidated by the
size of the class, many students will be grateful you
ask.
2. Visit your Professor’s office hours. We love to see
students and talk to them.
3. Go to your tutorial and ask your Teaching Assistant
(TA) questions.
4. Come to the Math & Stats Help Centre AC 217 and
Math Aid Room S506F. The schedule is listed at
http://tls.utsc.utoronto.ca/data_interpretation/default.htm
5. Come to the regular Math Workshops we offer.
6.
7. Form a Study Group and regularly meet. There are
many places on campus where you can do that: the
Math Help Centres, Study Rooms, Booked Rooms in
the ARC, other classrooms not in sessions, etc.
8. Find a private Tutor. Check for ads in the student
union area.
APPENDIX 1
FAQ
1.``I really know this material, but I just don't do well on
tests.''
This is a common complaint. But there is a distinction between
knowing something and having seen it before. Sometimes you
may recognize the correct answer; but with real knowledge,
you can construct solutions and even reconstruct the theory
with your pencil. While most instructors will say that students
eventually mature into effective ways of learning, we have
very little to guide students in this direction, particularly as
reading texts, listening to lectures, and reading notes may tend
to reinforce that learning is recognition. To get to the bottom of
the problem you may have to reconsider how you study, and
find more ways to make studying active rather than passive.
Just as sports or music or theater performance require lots of
practice before you can ``pull it off under the gun'',
mathematics takes a lot of practice and drill -- and adrenalin is
not beneficial on mathematics tests. On a practical level, one
can, with experience, learn how to anticipate tests. Rewrite
your notes, make up review sheets, join a study group, and
really study for tests (even if you didn't have to in high
school). Your instructor teaches what is important and tests on
it; but you must come to tests over-prepared. If you have a
serious anxiety problem, discuss it with your instructor; there
may be anxiety workshops and specially trained counselors
who can help, or your instructor may suggest another
solution.
11
2. ``The test is too long; if I'd had more time I could have
done really well.''
Speed in mathematics is actually an important measure of how
well we understand the subject. In the working world, doctors,
police officers, and airplane pilots all have to make fast,
accurate decisions. The writing you did on the test probably
did not take more than about ten minutes, so we have to ask
how the rest of the time was spent. Perhaps you are still
feeling your way over subject matter that requires a quick
reaction. Do you write a lot in hopes of partial credit? A
practical suggestion is to browse through the test, allot your
time, and simplify answers last. Read the directions carefully,
limit answers to precisely what is asked, and always check
your work line by line, to avoid going off in disastrously
wrong directions.
3. ``The tests aren't like the homework.''
We do feel a definite security in seeing problems identical to
what we did before, but to emphasize these problems would
be to validate rote learning alone. In mathematics, we do
homework for the purpose of learning the material, not the
other way around. Use the class period as a guide to what
your instructor thinks is important, and be sure to read the
text. As you work homework problems, try to see the bigger
picture: why am I being given this problem, and how does it
reinforce and relate to the theory? Also, the test problems may
be closer to the homework than you recognize, but you may be
falling into a rote mode as you do the homework. If your
instructor does not use the precise wording of the book, or
blends several problems, you may then feel lost. Scramble the
order of the problems you work as you study for tests. And
browse through other books in your library, and study with
friends so you can verbalize the material as much as possible,
in many different ways.
4. ``Careless mistakes keep killing me. I make a lot of stupid
mistakes''
If this is a chronic problem, your mistakes may not be careless.
There is a type of mistake that will disappear and a type that is
related to more fundamental problems of understanding. But
careless mistakes are nevertheless a problem; for example,
careless mistakes are not permitted of bank tellers,
construction workers, airplane pilots, or neurosurgeons.
Check all answers for accuracy and reasonability, backtracking
line by line; and reserve time on tests for a final check. If you
practice being careful as you work homework problems, you
can overcome the problem of ``careless'' or ``stupid'' mistakes.
But it is interesting that many students would prefer to blame
their intelligence or their carelessness before their effort
becomes the variable.
5. ``Why didn't I get more partial credit?''
Sometimes students see knowledge as something that
generates grades, and feel that their partial knowledge should
be rewarded accordingly. However, a lot of partial knowledge
on many topics does not add up to real knowledge, and to
learn for partial knowledge can eventually lead to a
``mathematical shut-down'' in understanding. An instructor
naturally does not want to encourage learning for partial
knowledge. What may seem to you a halfway answer would
probably not be accepted in most careers in the real world
where small errors could send an astronaut on the wrong orbit
or produce other disasters. On a practical level, neater, more
organized work will help you stay under control while
working a problem. An instructor is more likely to assign
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partial credit if you appear to be in control of the problem,
rather than flailing; and the way you present the mathematics
on your test (do you work down the page or scribble all over?)
may affect this perception more than you realize.
6. ``I didn't know what you wanted'', or ``What do you want
here?''
This question can cause an instructor to feel put in the role of a
demagogue whose ``wants'' are mysterious to you. They may
answer, ``I want the correct answer!'' If the question is
incomplete or ambiguous, your instructor will not mind
clarifying the question, and you should make it your
responsibility to come forward (but don't ask this question if
you only want to know if your solution is correct). You may
have a better understanding of the question than you say, but
you may just not be able to solve the problem. Sometimes you
can explain on your test how you are interpreting the
question, and respond accordingly
``I just don't use the book; I can't understand it at all.''
The text is definitely necessary for this subject, just as a
racquet is to a game of tennis or a violin to a violinist; the text
is the main tool for the course! But we can't expect simply to
read, track, and understand a mathematics text. Skim the
book, look at the problems. and see what is needed for a good
understanding. This decoding process does not happen in one
pass; you may need to reread some sections many times. You
can learn to make a text work for you, especially if you read it
before coming to class and then again, after class. Try
rewriting sections of the text, synopsizing it in your own
words. And there are many other texts in the library that you
can refer to. Frequently rereading a particular passage simply
is no help to us, while all we need is another author's
language.
7. ``Why do I have to memorize this? Memorization isn't
learning. Besides I know I'm going to forget it anyway.''
We memorize in order to facilitate learning, so we can
function with the demands of the field. Memorization is not an
end in itself, and it does not constitute learning. But when you
use this information, you won't forget it. Every field requires
memorization, and most fields -- biology, history, physics,
political science, languages -- require far more. We are only
able to solve problems if we are familiar with the necessary
terms and laws. To improve your memory, don't trust your
recognition memory when it comes to a test. Practice writing
out the definitions and theorems, and make outlines of the
major points of the theory. Check back to your text for
accuracy. It is easy to think we know something until we
attempt to put it in writing. By practicing studying
continuously in this way, rather than cramming at the last
minute, you will find memorization will feel more naturally
like part of the learning process.
8. ``Why should we do these long problems -- they won't be
on the test away''
These problems are useful because they synthesize the
material and get us beyond rote skills. In track, for example,
runners may lift weights in practice, although they won't be
doing this in the tournament. These problems push your
ability to manipulate and control the mathematics by engaging
you in multi-step reasoning, and they train you to recognize
where the skills you are learning can be useful.
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``I've always been good at mathematics until this course.''
Mathematics courses are built on previous courses, but
unfortunately, our performance in one course does not
guarantee our success in another. Mathematics is an extremely
complex field, and every mathematics course has new
challenges and introduces new ways of thinking. There are
things that are important that we aren't learning in this course,
but what we are learning is important. Also, different
instructors of mathematics may stress different things.
Perhaps you should discuss with your instructor what it is
that is not meeting the instructor's standards.
9. ``I can never understand my class notes; I don't read them.
I didn't follow you that day.''
Sometimes students write down material they don't
understand, feeling that in writing it down, understanding
will come. But in class, instructors may present the theory,
work examples, go over troublesome homework problems,
give insights into the material, respond to questions or ask
probing questions. With all this on an instructor's agenda,
your notes indeed may not seem too clear! Ask for
clarifications in class at the time. If you read the text before
class, you may recognize material from the book, and where
you do not need to take notes; but jot down what topics the
instructor discussed. Reading the text beforehand will also
help you focus your questions in class in ways that your
instructor will probably appreciate. Bring your text to class.
And rewrite your notes, incorporating material from the book
and problems. You will have created an excellent study guide
for your use.
10. ``I couldn't make it to class yesterday; did I miss anything
important?''
You may be asking if you missed something with a grade
attached. But in any case, the particular information is indeed
important (or we might have been tempted to miss ourselves!),
but the most important thing you missed is the practice of
seeing and doing things with new material.
11. ``Where are we ever going to use this stuff?''
People who don't learn or understand this material probably
won't use it, but people who do may be surprised to find
where it is useful. This applies not just to the content of the
course, but to its association with careful, creative thinking. It
will probably be up to you to find places where you can use
this mathematics. But depending on your career, you may find
that things that are now obvious to you are not known to
others; or on the other hand, you may find it taken for granted
that you know this material and much more. But most likely,
you may actually use the subject of this course and the skills
you've gained, without even realizing it.
In reality, the questions and complaints mentioned above are
all too frequently tacit, and it may be that much more difficult
to bring these issues to a point of real discussion. Sometimes
these complaints only show up on instructors' end-of-term
evaluations. There are certainly more useful responses for
individual students in individual situations than those offered
here.
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APPENDIX 2 Teaching and Learning Services Support
http://tls.utsc.utoronto.ca/
1. Math and Statistics Help Centre
Geanina Tudose, Coordinator 287.5667
2. Academic Learning Services for Students
Martha Young, Coordinator 287.7557
3. English Language Development
Elaine Khoo, 287.7562
4. The Writing Centre
Sarah King, Coordinator 287.7480
5. Presentation Skills Instruction
Saira Mall, 287.5666
6. Research Skills Instruction
Frances Sardone, 287.7502
APPENDIX 3 Additional Readings
1.
2.
3.
4.
5.
6.
7.
8.
9.
What is Mathematics?, R. Courant and H. Robbins; Oxford,
1941.
Number, The Language of Science, T. Dantzig; Anchor, 1956.
The Mathematical Experience, Davis, P.J. and R. Hirsch;
Birkhauser, Boston, 1981.
Art and Science, Escher, M.C.; (H.S.M. Coxeter, M. Emmer, R.
Penrose and M.L. Trewber, Editors); North Holland, 1985.
Great Moments in Mathematics (2 vols.), H. Eves;
Mathematical Association of America, 1983.
A Mathematician's Apology, G.H. Hardy; Cambridge, 1940.
Geometry and the Imagination, D. Hilbert and S. Cohn-Vossin;
Chelsea, 1952.
Godel, Escher, Bach, D. Hofstader; Basic Books, New York,
1979.
The World of Mathematics (4 vols.), J.R. Newman; Simon and
Schuster, New York, 1956.
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