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Success in Mathematic Tips
Math Study Skills
Studying for a Math Test
Taking a Math Test
Math Study Skills
Active Study vs. Passive Study
Be actively involved in managing the learning process, the
mathematics and your study time:
Take responsibility for studying, recognizing what you do and don't know,
and knowing how to get your Instructor to help you with what you don't know.
Attend class every day and take complete notes. Instructors formulate test
questions based on material and examples covered in class as well as on those
in the text.
Be an active participant in the classroom. Get ahead in the book; try to
work some of the problems before they are covered in class. Anticipate what
the Instructor's next step will be.
Ask questions in class! There are usually other students wanting to know
the answers to the same questions you have.
Go to office hours and ask questions. The Instructor will be pleased to see
that you are interested, and you will be actively helping yourself.
Good study habits throughout the semester make it easier to study for tests.
Studying Math is Different from Studying Other Subjects
Math is learned by doing problems. Do the homework. The
problems help you learn the formulas and techniques you do need to know,
as well as improve your problem-solving prowess.
A word of warning: Each class builds on the previous ones, all semester long.
You must keep up with the Instructor: attend class, read the text and do
homework every day. Falling a day behind puts you at a disadvantage. Falling
a week behind puts you in deep trouble.
A word of encouragement: Each class builds on the previous ones, all semester
long. You're always reviewing previous material as you do new material. Many
of the ideas hang together. Identifying and learning the key concepts means
you don't have to memorize as much.
College Math is Different from High School Math
A College math class meets less often and covers material at about twice
the pace that a High School course does. You are expected to absorb new material
much more quickly. Tests are probably spaced farther apart and so cover more
material than before. The Instructor may not even check your homework.
Take responsibility for keeping up with the homework. Make sure
you find out how to do it.
You probably need to spend more time studying per week -
you do more of the learning outside of class than in High
Tests may seem harder just because they cover more material.
You may know a rule of thumb about math (and other) classes: at least 2 hours
of study time per class hour. But this may not be enough!
Take as much time as you need to do all the homework and to get complete
understanding of the material.
Form a study group. Meet once or twice a week (also use
the phone). Go over problems you've had trouble with. Either someone else
in the group will help you, or you will discover you're all stuck on the
same problems. Then it's time to get help from your Instructor.
The more challenging the material, the more time you should spend on it.
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!
Problems testing memorization ("drill"),
Problems testing skills ("drill"),
Problems requiring application of skills to familiar situations ("template"
Problems requiring application of skills to unfamiliar situations (you develop
a strategy for a new problem type),
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.
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.
Tips on Problem Solving
Apply Pólya's four-step process:
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).
Next you need to devise a plan, that is, identify which
skills and techniques you have learned can be applied to solve the problem
Carry out the plan.
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.
"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.
Solving an Applied Problem
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
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.
Studying for a Math Test
Everyday Study is a Big Part of Test Preparation
Good study habits throughout the semester make it easier to study for tests.
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
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.
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 problem; on a
test the problems from different sections are all together.
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.
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 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
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 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
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).
Get help as soon as you need it. Don't wait until a test
is near. The new material builds on the previous sections, so anything you
don't understand now will make future material difficult to understand.
Use the Resources You Have Available
Ask questions in class. You get help and
stay actively involved in the class.
Visit the Instructor's Office Hours. Instructors like to
see students who want to help themselves.
Ask friends, members of your study group, or anyone else
who can help. The classmate who explains something to you learns just as
much as you do, for he/she must think carefully about how to explain the
particular concept or solution in a clear way. So don't be reluctant to ask
Go to the Math Help Sessions or other tutoring sessions
Find a private tutor if you can't get enough help from other sources.
All students need help at some point, so be sure to get
the help you need.
Don't be afraid to ask questions. Any question is better
than no question at all (at least your Instructor/tutor will know you are
confused). But a good question will allow your helper to
quickly identify exactly what you don't understand.
Not too helpful comment: "I don't understand this section." The best you
can expect in reply to such a remark is a brief review of the section, and
this will likely overlook the particular thing(s) which you don't understand.
Good comment: "I don't understand why f(x + h) doesn't equal f(x) + f(h)."
This is a very specific remark that will get a very specific response and
hopefully clear up your difficulty.
Good question: "How can you tell the difference between the equation of a
circle and the equation of a line?"
Okay question: "How do you do #17?"
Better question: "Can you show me how to set up #17?" (the Instructor can
let you try to finish the problem on your own), or "This is how I tried to
do #17. What went wrong?" The focus of attention is on your
Right after you get help with a problem, work another similar problem by
You Control the Help You Get
Helpers should be coaches, not crutches. They should encourage
you, give you hints as you need them, and sometimes show you how to do problems.
But they should not, nor be expected to, actually do the
work you need to do. They are there to help you figure out
how to learn math for yourself.
When you go to office hours, your study group or a tutor, have a specific
list of questions prepared in advance. You should run the
session as much as possible.
Do not allow yourself to become dependent on a tutor. The tutor cannot take
the exams for you. You must take care to be the one in control of tutoring
You must recognize that sometimes you do need some coaching to help you through,
and it is up to you to seek out that coaching.
By Saint Louis University
Since December 1999 - last modified: February 22, 2012