Math: Study Skills,
Note Taking Skills, And Test Taking Strategies
Math Study Skill Active Study vs. Passive
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
- 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
- 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
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 School.
- Tests may seem harder just because they cover more material. Study
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
Note Taking Tips for Math
- Write down the "title"
of the lesson. If you don't know, ask the teacher.
- Write down the math problem and each step in the solution using
math symbols. Next to each step write down "in
your own words" exactly what you are doing.
- Write down a "question mark"
next to anything you don't understand. Ask the teacher to explain the parts
where you have written your "question marks". Don't just "let
it go" thinking that you will figure it out later. Many times,
it doesn't happen.
- When you get home, before you start your homework, "highlight
in color" the titles you have written in your notes. The highlighted
information will help to give you the "big picture"
of what you are doing.
- Remember, do all homework problems, not just some of them!
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.
Test Taking Tips for Math
You already have a lot of knowledge stored in your memory. The problem
is pulling out the correct information when you need it. Picture your brain
like a giant filing cabinet full of file folders and the hard part is remembering
the headings on the file folders.
- Know how to distinguish between the various types of problems.
This is the hardest part.
- Most math texts have chapter tests at the end of each chapter.
Try one problem from each section. Make a note of their differences. Write
down the first step to each problem -- this is usually the hardest to remember.
- Go back to the section in the text where you are having difficulty.
Follow the examples making sure you understand each step. This takes time.
- Reading a math book is not like reading a novel. It goes slowly.
It may take you 20 minutes to go through one example problem.
- Don't leave preparing for a test to the last minute. Make sure
you leave time to ask questions in class AFTER you have studied.
- Do as many problems as you can until you feel comfortable with
- In the class session a day or so BEFORE the test, ask the teacher
to please point out any major similarities or differences among the various
types of problems you will encounter on the test.
- Get the phone number of someone in your class who won't mind if
you call them with questions.
- If possible, form a small study group with members from your class
and meet periodically during the semester.
- Math is a cumulative subject. You REALLY need to understand today's
material to understand the material the next day. Ask questions immediately
in class as soon as you don't understand anything. Don't just "let
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
- 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
- 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 a classmate.
- Go to the Math Help Sessions or other tutoring sessions on campus
(The Success Center is a great resource at Florence-Darlington Tech).
- 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
- 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
- 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 thought process.
- Right after you get help with a problem, work another similar
problem by yourself.
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 sessions.
- 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.
Ten Ways To Reduce Math Anxiety
- Overcome negative self-talk.
- Ask questions.
- Consider math a foreign language -- it must be practiced.
- Don't rely on memorization to study mathematics.
- READ your math text.
- Study math according to YOUR LEARNING STYLE.
- Get help the same day you don't understand.
- Be relaxed and comfortable while studying math.
- "TALK" mathematics.
- Develop responsibility for your own successes and failures
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