The Learning & Advising Centers
Ciletti Memorial Library, Lower Level
570-385-6140
2
Math is different from other subjects!
Math requires different study processes. In other courses, you learn and understand the
material, but you seldom have to actually APPLY IT to learn. You have to DO math problems to
learn math.
Math is a linear learning process. What is used one day is used the next, and so forth. (In history you can learn
chapter 2, skip chapter 3, and still do OK on chapter 4. In math, you must understand the material in chapter 1
before you go on to chapter 2.) You must keep up with the instructor: attend class, read the text and do
homework everyday. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep
trouble.
Math is much like a foreign language. It must be practiced EVERY DAY, and often the vocabulary is unfamiliar.
Math in college is different from math in high school. Instead of going to class everyday, in college you go only
two or three times a week. What took a year to learn in high school is now covered in only fifteen weeks. In
college, tests are probably spaced farther apart and so cover more material than high school tests. College
instructions may not even check your homework. You are responsible for making sure that you understand the
material.
Part I: Math Anxiety
Math is the course that most students have anxiety about. You are not alone. Yes, believe it! Fortunately, there
are several strategies for reducing math anxiety.
1. Overcome negative self-talk.
Self-talk is the things you say to yourself. It has a great effect on your abilities and
motivation. Listen and become consciously aware of the types of things your say to
yourself. Make the decision to replace your negative self-talk with positive self-talk.
Learn to say:


I know I can do this.
I have studied and I know what I’m doing.
 I will not give up until I’ve answered every question.
 I believe that I will be able to remember what I’ve studied.
 Oh, seeing that makes me remember what else I studied about this idea.
2. Ask questions! If anything is unclear, or even if you want to confirm what your think is correct, ASK!
Besides, there are usually other students wanting to know the answers to the same questions you
have.
3. Consider math a foreign language – it must be practiced.
4. Don’t rely on memorization to study mathematics. Math is learned by DOING problems, not trying to
memorize them. Each problem is different. Solving ability must be learned by doing.
5. READ your math text book. Yes, actually read it! The text will give you another perspective on the
material and may even offer tips which were not covered in class. Additionally, it is a great way to
reinforce what you are learning in class.
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6. Get help the same day that you find you don’t understand something.
7. Be relaxed and comfortable while studying math.
8. Develop responsibility for your own successes and failures. You found the correct answer because YOU
know how to do the problem, not because it was just an easy one. You had an answer wrong because
YOU need more practice with that type of problem.
Do You Have Math Anxiety?
A Self Test
Rate your answers from 1 to 5; add them up and check your score below.
(1) = Disagree, (5) = Agree.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
I cringe when I have to go to math class. 1 2 3 4 5
I am uneasy about going to the board in a math class. 1 2 3 4 5
I am afraid to ask questions in math class. 1 2 3 4 5
I am always worried about being called on in math class. 1 2 3 4 5
I understand math now, but I worry that it's going to get really difficult soon.1 2 3 4 5
I tend to zone out in math class. 1 2 3 4 5
I fear math tests more than any other kind. 1 2 3 4 5
I don't know how to study for math tests. 1 2 3 4 5
It's clear to me in math class, but when I go home it's like I was never there. 1 2 3 4 5
I'm afraid I won't be able to keep up with the rest of the class. 1 2 3 4 5
CHECK YOUR SCORE
40-50 Sure thing, you have math anxiety.
30-39 No doubt! You're still fearful about math.
20-29 On the fence!.
10-19 Wow! Loose as a goose!
Math anxiety is an emotional reaction to mathematics based on a past unpleasant experience which harms
future learning. A good experience learning mathematics can overcome these past feelings and success
and future achievement in math can be attained.
-Ellen Freedman
Part II : Before, During, and After Math Class
A.
Before Math Class
1.
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Familiarize yourself with the instructor before signing up for the course. If you have a choice of
math classes and the professor which teaches them, preview the course before you decide
which one to register for. Most professors will allow you to “sit-in” on a class to preview it.
Previewing the course will help you to make a more informed decision about such things as
the compatibility of the professors’ teaching styles and your learning style.
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TIP If your math anxiety is high and you want more assurance about a math course, give auditing a course
a try. When auditing a course, you are a full participant in the course, however, the grade you receive does not
affect your G.P.A. and you do not receive credit for the course. It is an excellent opportunity for you to practice
and familiarize yourself with the material before you enroll in the course for credit. Check with your advisor or
the registrar for further information on course auditing.
2.
B.
C.
Read your textbook before class to become familiar with new terms, formulas, and concepts.
For each chapter, prepare your own list of math vocabulary words. For a better understanding
of the material, recite back the materials you have read. Mark any trouble spots that you
might want the instructor’s help in clearing up.
During Math Class
1.
Come to class on time and sit as close to the front as possible.
2.
Exchange phone numbers with someone in class. When you are working on math and hit a
problem you just do not get, you will have someone to call for help.
3.
Make sure you attend every class. If you miss a class, ask your instructor for permission to
attend the same course that is taught at a different time or day. Remember: you are
responsible for material covered in a class that you missed.
4.
Note-taking:
a.
Use a good math note-taking system (see note-taking strategies handout).
b.
Don’t photocopy someone else’s notes. It is important to attend class and hear
everything for yourself. You may not understand what someone else wrote or deem
things important which someone else may leave out.
c.
Take notes on how to solve problems. Don’t just record the problem itself. When you
look at the problem later, you may not be able to recall how it was solved.
d.
Copy all information that is written on the board. It is important, otherwise the
instructor would not have taken the time to write it.
e.
Verbalize (silently) problems the instructor writes on the board. Solve the problem or
silently verbalize each solution step.
f.
Ask questions, ask questions, ask questions! You are paying for the course, make sure
you get your monies worth. Chances are, that many other students in the class have
the same question and will be relieved you asked.
g.
Get help early in the semester before you get too lost in the course. You know the old
saying, “a stitch in time saves nine” Get help figuring out the small stuff before it
grows into a huge dilemma!
After Class
1.
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Find a study buddy and set up group study times.
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2.
Schedule a review period after every class, even if it’s only ten minutes. Work through
examples again on a scrap piece of paper.
3.
Make note cards or a “math dictionary” to remind you how to solve various types of math
problems.
a. -Put each concept on a 3”X5” note card with an example on the back.
b. List all new math terms with their definitions in a separate notebook. Review these at least
once a week.
4.
Take full advantage of all the math resources in the Center for Academic Achievement! It’s
FREE.
a. math tutoring
b. -math resource texts
c. -math sample tests
d. -on-line math aids in the CAA computer lab
5.
Read your text and do all the examples.
6.
Do a bit of math review, homework, studying and practice everyday. Increase or decrease the
time you spend daily on math with respect to your mastery of the material. Remember to
practice working the type of problems you may be having difficulty with until you master
them.
Part III: Getting Assistance, Problem Solving, and Homework Tips
Getting Assistance
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
1.
Asking the right question
a. 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.
Examples:
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
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 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.
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
Good question: “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.
TIP
Right after you get help with a problem, work another similar problem by yourself.
2.
You control the help you get
a. 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.
b. 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.
c. 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.
d. 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.
Problem Solving Skills (homework and tests)
1.
General Problem Solving
A. 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!
B. 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.
C. The practice you get doing homework and reviewing will make test problems easier to
tackle.
D. 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
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(make sure you read the whole problem). Understand all words, phrases, terms, and
symbols. Draw a figure, if needed.
2. Next you need to devise a plan, that is, identify which skills and techniques you have
learned can be applied to solve the problems at hand.

Have you seen a similar problem before?

Break the problem into parts.

Draw on prior knowledge.

Spell out relationships carefully.

Look for related unknowns.
3. Carry out the plan. If you get stuck, reorganize the elements of the problem in a new
way. Check the problem to be sure a simple mistake wasn’t made. If you are still
having difficulty, try taking a small break.
4. Look back: Check all your work. 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.
TIPS 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.
.
Solving Word 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 Applied Problem Steps:
1. 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.
2. Solve the math problem you have generated, using whatever skills and techniques you need (refer
to the four-step process above).
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3. 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. (further help: George Pólya, How to Solve it,
Princeton University Press, Princeton (1945).
.
Some errors in reasoning to avoid:
1. Failing to observe and use all relevant facts of a problem.
2. Failing to approach the problem in a systematic step-by-step manner.
3. Jumping to conclusions or using leaps in logic without thoroughly checking them.
4. Failing to spell out relationships fully.
5. Being sloppy and inaccurate in collecting information and carrying out mental activities.
Homework Tips

Do math homework every day!

Start your assignment as soon after your math class as you can. If you cannot begin working on your
assignment right after class, take a moment to look it over. Try to make some connections between
what you just learned in class and the assignment. Jot down reminders of the connections you drew so
you can more easily mind them to mind when you have the first opportunity to work on your
assignment.

Complete your most difficult homework assignments first. Usually this mean your MATH homework!

Copy each problem down carefully.

Think of the steps you will use and the rules you will follow.

Check your notes and examples.

Try every problem. Take a chance! You might be right.

Do not skip steps at first! Even if the problem has a short-cut. Do all the steps until you have perfected
the process.

Write each step below the previous one. Be neat!

Check your work before looking at the answer key.

Arithmetic error? Brush up on the basics.

“Plug in” your answer, or do the problem a different way.

Incorrect? Check your notes and book.

Still wrong? Ask the instructor, a tutor, classmate or friend.
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
Do the problem from scratch until you get it right.

Do an extra set – practice pays off!

Spend as much time on homework as needed. Don’t limit yourself. When your taking your math test
you will be more confident.
Part IV
General and Exam Study Skills
Good study habits throughout the semester make it easier to study for tests. How are your study habits? Take
the following inventory to find out how your study skills rate.
Math Study Skills Inventory
Rate your achievement of the following statements by placing a 3 for almost always, 2 for sometimes,
and 1 for almost never. If you have never even thought about doing what the statement says, put a 0.
Selecting a math class
I schedule my math class at a time when I am mentally sharp.
When I register for a math class, I choose the best instructor for me.
If I have a choice, I select a math class that meets three or four days a week instead of one or two.
I schedule the next math class as soon as possible after I have completed the current course.
I am sure that I have signed up for the correct level math course.
Time and place for studying math
I study math every day.
I try to get my math homework immediately after math class.
I have a specific time to study math.
I have a specific place with few distractions to study math
I get my math homework in the lab where I can get help.
I am careful to keep up to date with math homework.
I study math at least 8 to 10 hours a week.
Study strategies for math class
I read my textbook before I come to class.
If I have trouble understanding the text, I find an alternate text.
I take notes in math class.
I am careful to copy all the steps of math problems in my notes.
I ask questions when I am confused.
I go to the instructor or lab when I am confused.
I try to determine exactly when I got confused and exactly what confused me.
I review my notes and text before beginning homework.
I work problems until I understand them, not just until I get the right answer for homework.
I use flashcards for formulas and vocabulary.
I develop memory techniques to remember math concepts.
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Math tests
I preview the test before I begin.
Before I begin the test, I make notes on things such as formulas that I might need.
I begin with the easy questions first.
I take the full amount of time allotted for the test.
I carefully check or rework as many problems that I have time to before I turn in my test.
When tests are returned, I keep a log of the types of mistakes I make on tests: concept errors,
application errors, or careless errors.
I keep up to date so that I don't have to cram the night before a test.
Anxiety
I believe that I can succeed in math class.
I have study partners in my math class.
I take practice tests.
I know several good relaxation techniques.
______ TOTAL SCORE
Scoring:
Total the scores from all 34 statements.
If your score is 90 - 103, give yourself an A. You are using the study skill you need in order to be
successful in math.
If your score is 80 - 89, give yourself a B. You are using good math study skills. Choose a few
strategies to work on each day, and you are well on your way to an A.
If your score is 70 - 79, give yourself a C. Your study skills are average. If you want an A, choose one
or two strategies in each category to work on until you are using most of the strategies described
above.
If you score is below 70, you are probably having a difficult time in math class. Math may not be your
trouble! More than likely, your main problem is the study strategies you are using (or not using). Make
yourself do the things on the list above.
This information can be found on page 117 of The Study Skills Workbook, third edition, by Dr. Carolyn H. Hopper.
General Studying
If your study skills need improvement (and even if they don’t) here are a few tips:

Keep up! You need to review your notes after every class and 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
right before the exam.

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.
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
To memorize formulas, make up flashcards.

Get a study friend and set study times. When someone else is there, you are more likely to follow
through with studying math. Also, you may be able to answer questions for each other.

Rework problems that you missed on your homework.

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
to do 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 it 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
“instructions”. Check your verbal explanations with a friend during a study session (its 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 (in the Center for Academic Achievement). It’s important to keep working
problems the whole time you’re studying.

Get lots of sleep the night before the test. Math tests are easier when you are mentally sharp.
Part V
The Math Test!
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!
1. Learn how to relax before tests are taken. Take a few deep breaths, do some stretches, and if you
need it, take a nice, slow walk to the pencil sharpener to clear your head. If you think the level of
distress you feel over a math test is affecting your grades, make an appointment with the campus
counselor for some stress/anxiety management sessions.
2. Be aware of the time allotted while taking the math test. 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.
3. Don’t panic over being able to remembering tricky formulas while taking the test. Use flash cards to
memorize the formulas. Then as soon as you are handing your math test, write them down in the
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margin or on scrap paper. Then, your mind will be at ease about remembering them, and you can
focus on the problems.
4. 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.
5. 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 to try.
6. 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.
7. 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.
8. In a multiple-step problem outline the steps before actually working the problem.
9. 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, as least explain how you would do it.
10. Make sure you read the questions carefully, and do all parts of each problem.
11. Verify your answers – does each answer make sense given the context of the problem?
12. If you finish early, check every problem (that means rework everything from scratch).
After the Test

Immediately look up questions that caused you problems.

Go over test and correct missed problems (this will strengthen your skills for the next test).

Check with the instructor if you cannot figure out why the problem was wrong.
Remember, be positive. You can do it!
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