**Before I get into the tips for how to study math let me first say that everyone studies**

differently and there is no one right way to study for a math class. There are a lot of tips

in this document and there is a pretty good chance that you will not agree with all of them

or find that you can’t do all of them due to time constraints. There is nothing wrong with

that. We all study differently and all that anyone can ask of us is that we do the best that

we can. It is my intent with these tips to help you do the best that you can given the time

that you’ve got to work with.

Now, I figure that there are two groups of people here reading this document, those that

are happy with their grade, but are interested in what I’ve got to say and those that are not

happy with their grade and want some ideas on how to improve. Here are a couple of

quick comments for each of these groups.

If you have a study routine that you are happy with and you are getting the grade you

want from your math class you may find this an interesting read. There is, of course, no

reason to change your study habits if you’ve been successful with them in the past.

However, you might benefit from a comparison of your study habits to the tips presented

here.

If you are not happy with your grade in your math class and you are looking for ways to

improve your grade there are a couple of general comments that I need to get out of the

way before proceeding with the tips. Most people who are doing poorly in a math class

fall into three main categories.

The first category consists of the largest group of students and these are students that just

do not have good study habits and/or don’t really understand how to study for a math

class. Students in this category should find these tips helpful and while you may not be

able to follow all of them hopefully you will be able to follow enough of them to improve

your study skills.

The next category is the people who spend hours each day studying and still don’t do

well. Most of the people in this category suffer from inefficient study habits and

hopefully this set of notes will help you to study more efficiently and not waste time.

The final category is those people who simply aren’t spending enough time studying.

Students are in this category for a variety of reasons. Some students have job and/or

family commitments that prevent them from spending the time needed to be successful in

a math class. To be honest there isn’t a whole lot that I can do for you if that is your case

other than hopefully you will become a more efficient in your studies after you are

through reading this. The vast majority of the students in this category unfortunately,

don’t realize that they are in this category. Many don’t realize how much time you need

to spend on studying in order to be successful in a math class. Hopefully reading this

document will help you to realize that you do need to study more. Many simply aren’twilling to make the time to study as there are other things in their lives that are more

important to them. While that is a decision that you will have to make, realize that

eventually you will have to take the time if you want to pass your math course.

Now, with all of that out of the way let’s get into the tips. I’ve tried to break down the

hints and advice here into specific areas such as general study tips, doing homework,,

studying for exams, etc. However, there are three broad, general areas that all of these

tips will fall into.

Math is Not a Spectator Sport

You cannot learn mathematics by just going to class and watching the instructor

lecture and work problems. In order to learn mathematics you must be actively

involved in the learning process. You’ve got to attend class and pay attention while

in class. You’ve got to take a good set of notes. You’ve got to work homework

problems, even if the instructor doesn’t assign any. You’ve got to study on a regular

schedule, not just the night before exams. In other words you need to be involved in

the learning process.

The reality is that most people really need to work to pass a math class, and in general

they need to work harder at math classes than they do with their other classes. If all

that you’re willing to do is spend a couple of hours studying before each exam then

you will find that passing most math classes will be very difficult.

If you aren’t willing to be actively involved in the process of learning mathematics,

both inside and outside of the class room, then you will have trouble passing any

math class.

Work to Understand the Principles

You can pass a history class by simply memorizing a set of dates, names and events.

You will find, however, that in order to pass a math class you will need to do more

than just memorize a set of formulas. While there is certainly a fair amount of

memorization of formulas in a math class you need to do more. You need to

understand how to USE the formulas and that is often far different from just

memorizing them.

Some formulas have restrictions on them that you need to know in order to correctly

use them. For instance, in order to use the quadratic formula you must have the

quadratic in standard form first. You need to remember this or you will often get the

wrong answer!

Other formulas are very general and require you to identify the parts in the problem

that correspond to parts in the formula. If you don’t understand how the formula

works and the principle behind it, it can often be very difficult to use the formula.

For example, in a calculus course it’s not terribly difficult to memorize the formula

for integration by parts for integrals. However, if you don’t understand how to actually use the formula and identify the appropriate parts of the integral you will find

the memorized formula worthless.

Mathematics is Cumulative

You’ve always got to remember that mathematics courses are cumulative. Almost

everything you do in a math class will depend on subjects that you’ve previously

learned. This goes beyond just knowing the previous sections in your current class to

needing to remember material from previous classes.

You will find a college algebra class to be very difficult without the knowledge that

you learned in your high school algebra class. You can’t do a calculus class without

first taking (and understanding) an Algebra and a Trigonometry class.

So, with these three main ideas in mind let’s proceed with some more specific tips to

studying for a math class. Note as well that several of the tips show up in multiple

sections since they are either super important tips or simply can fall under several general

topics.

General Tips for Studying Mathematics

These are some general tips that where either important enough to single out or just

didn’t seem to fit into any of the other sections.

• Go To Class. Remember that math is cumulative. If you don’t go to class you

will miss important material that will be used in later sections and/or important

announcements.

• Get to Class On Time. Sometime important announcements are only given

during the first few minutes of a class.

• LISTEN During Class. In order to get something out of the class you need to

listen while in class. Often this can be difficult to do but it is very important.

Sometimes important ideas will not be written down on the board, but instead just

spoken by the instructor.

Watch for things the instructor emphasizes, even if just in words. This often

means the instructor thinks it’s important. The more important that an instructor

thinks a topic is, the more likely that it will show up on the exam!

• Take Good Notes. Try to write down everything that instructor puts on board. It

may seem easy when watching the instructor, but it often is not so easy when it

comes time for you to do it. A good set of notes will help remind you how to do

these problems. For some instructors writing down everything may be difficult.

In these cases you should try to write down as much as possible.

Note as well that this seems to contradict the previous tip. It is often hard to both

listen and take a good set of notes. This is something that one often only gains

with practice. You need to be able to listen while you are writing down the

important parts of the lecture If you find that are having trouble both listening and taking good notes then you

might consider bringing in a tape recorder and record the lecture.

Note however that prior to doing this you should first speak with your instructor.

There are a few instructors out there in the world that do not like to have their

lectures recorded.

• Ask Questions. If you don’t understand something then ask your instructor.

Chances are you are not the only one who doesn’t understand.

• Listen When Others Ask Questions. When other students ask questions make

sure you listen to both the question and the answer. It may be that the student

asking the question thought of something that you didn’t think of.

• Review Notes After Class. After each class you should review your notes. Note

the topics that you found confusing and formulate questions that you can ask your

instructor or tutor to help you understand the topic.

• Make a Set of Index Cards. Make a set of index cards with important formulas

and concepts on them. You can carry these around with you to look over when

you’ve got a few spare minutes. Use them to help you memorize the important

formulas and concepts.

• Learn The (Proper) Notation. Instructors will assume you know it so you’ll

need to and many instructors will take points off for bad notation.

• Get Into A Study Group. It is often helpful to study in groups. People often

look at things differently so someone else may see how to solve a problem that

can’t do or understand a topic that you find confusing.

• Note Due Dates. Write down the due dates for homework and dates for exams

someplace you’ll see them so you don’t forget about them.

• Budget Adequate Time For Studying/Homework. It often takes more time

studying mathematics to learn the subject than you may require in other classes.

Homework will often take more time than you had originally thought it would.

Keep this in mind as you budget time.

• Do Homework After Each Class. At the end of each class budget some time to

look over the homework from that days lecture and attempt to do it Doing this

will allow you time to really work at understanding the concepts covered that day.

Do not wait until the last minute to do the homework as this often results in an

incomplete homework set and/or an incomplete understanding of the concept.

• Do Homework Without Notes and Book. After the first few homework

problems, put your notes and book up and try to do the remaining problems

without referring to your notes and/or book. In most cases you will not have these

during your exams so get used to doing problems without them.

• Do More Homework. Do not limit yourself to just the homework that your

instructor assigns. The more problems that you work the better off you’ll be.

• Practice, Practice, Practice. Practice as much as possible. The only way to

really learn how to do problems is work lots of them. The more you work, the

better prepared you will be come exam time.

• Persevere. You will not just instantly get every topic that is covered in a math

class. There will be some topics that you will have to work at before you

completely understand. The only way to really grasp some topics is to go home

and think about it and work some problems. You will often find that after a little

work a topic that initially baffled you will all of a sudden make sense.

• Keep Old Homework and Exams. Do not throw away homework and exams

once you get them back. The homework is a good source of study material for

exams and both the homework and exams is a good source of study material for

comprehensive final exams (if you’ve got one).

• Don’t Forget Your Textbook. If you get stuck on a topic that was discussed in

class do not forget that you do have a textbook. Often the text book will contain

examples not worked in class and/or a different approach to a problem.

• Seek Help If You Need It. If you are having trouble with your math class you

have many options open to you and you should take advantage of them. You can

go to your instructor’s office hours, go to the tutoring room or hire a tutor to get

help.

Here at Lamar University we have a free math tutoring room located in Lucas

209. You can get a current list of tutors for hire at

http://www.math.lamar.edu/tutorlist.asp or by visiting the departmental office in

Lucas 200.

• Have the Proper Attitude. Always do the best that you can. Do not do try to do

just enough to get by. Doing this can lead to major problems if you aren’t careful.

If you are trying to do just enough to get by then all it takes is one bad exam and

you are now failing the course.

You should always do the best that you can and strive for the best grade that you

can possible get.

Taking Notes

Here are a couple of tips for taking notes in the class.

• Listen in Class. Do not just write down what you see on the board. No

instructor is going to write down every word they say and sometimes the

important ideas won’t get written down.

• Write Down Explanatory Remarks. Make sure you write down any

explanatory remarks the instructor makes. These often won’t get written down by

the instructor, but can tell you how to work a particular kind of problem or why

the instructor used one formula/method over another for a given problem.

• Note Important Formulas/Concepts. If an instructor emphasizes a particular

formula or concept then make note of it. This probably means the instructor feels

that it’s important and important formulas and concepts are much more likely to

show up on an exam.

• Question Your Instructor. If you are unclear on something ask questions.

• Note Topics You Don’t Understand. If you are having trouble understanding

something being presented note that in the margin and at least write down the key

words. Leave yourself a couple of lines so you can fill in the missing details later

once you’ve gotten help to understand the concept.

Review/Edit Your Notes. As soon you can after class go back over your notes.

Look for any errors and/or omissions. Fill in any information you didn’t have

time to write down in class.

• Review Regularly. At regular intervals sit down and review your notes so that

you can learn and retain the information. Remember, that this information will

probably be required down the road so it’s best to learn it as soon as possible.

Getting Help

Getting help when you are in trouble is one of the most important things that you can do

in a math class. Here are a couple of things that you can do the get help.

• Get Help When You Need It. Do not wait until the last minute to get help.

When you start running into problems it is time to get help. Remember that math

is cumulative. If you don’t get help right away you will only be making it all that

more difficult to understand future material.

• Ask Questions in Class. This way you get the help you need AND stay actively

involved in the class.

• Visit the Instructor’s Office Hours. The instructor has office hours for a reason,

so use them!

• Form a Study Group. Many people find it convenient to study in a group.

Different people will see things differently and may see a way to work a problem

that you don’t know how to do.

• Go to the Tutor Lab. If your school has a free math tutoring lab (many do and

many don’t) then make use of it! That’s what it’s there for.

Here at Lamar University the free math tutoring lab located in Lucas 209.

• Get a Private Tutor. You can always hire a private tutor for some help. In

almost every school you will find people who are willing to tutor you for a fee.

Most math departments keep a list of tutors or can tell you where you might be

able to find one.

If you are here at Lamar University you can access a list of current tutors at

http://www.math.lamar.edu/turorlist.asp or stop by the Math Departments office

in Lucas 200 for a list.

• Ask Good Questions. Saying “I don’t understand this section.” or “I don’t get

it.” is not the best way to seek help. It just doesn’t imply what you’re having

trouble with and so will probably not get your questions answered. Be specific

with your questions. What exactly is it about this section don’t you understand?

Many instructors won’t help you unless you do have specific questions and/or can

articulate exactly what it is that you don’t understand and/or “get”. If you really

don’t understand a given section that is okay, but be prepared to tell your

instructor just what is causing the problems. Do you not understand the concept?

Are you having trouble getting the problems started? Are you having trouble

identifying that the problems use the ideas in the given section?

Have Attempted Work With You. When you get help make sure and bring the

attempts that you’ve made on the problem. This will help the person helping you

to understand just where you’re having problem.

Again, many instructors won’t help you unless you’ve got something to show that

you’ve at least attempted a problem. If you really don’t understand how to even

start the problem then bring in work for other problems in that section that you

have done. This accomplishes two things. First, it shows the instructor that you

have been working and second, it gives the instructor something to look at to see

just where you’re having trouble understanding the problem you’re trying to

work.

Homework

Note that this section contains some general tips on making the most out of your

homework. The next section contains tips on actually working homework problems.

• Understand the Purpose of Homework. Instructors do not give you homework

assignments to make your life miserable (well some might, but most don’t!).

Homework assignments are given to help you to learn the material in the class and

to develop good reasoning and problems solving skills.

Mathematics is just not a subject that most people will instantly understand every

single topic after hearing the instructors lecture. Most people need to work on

some problems in order to really start to understand the topic. That is the point of

the homework. It gives you a set of problems that will help you to understand the

topics.

Remember that it almost always seems easier to watch an instructor doing

problems on the board than it actually is. You won’t know if you truly understand

the material and can do the problem if you don’t attempt the homework.

• Have The Actual Assignment. This may seem like a silly tip, but make sure

that you accurately write down the assignment and due date. This is one of the

more common mistakes that students make with homework.

• Do the Assignment Promptly. You should always do the assignment as soon

after the lecture as possible while the lecture is still fresh in your mind. Do not

wait until the last minute to do the whole assignment when comments made by

the instructor are no longer fresh in your mind. Often these little asides that an

instructor makes won’t seem important at the time, but when it comes time to

doing the homework the reason for making the comment will become clear.

• Be Organized. When you start working on homework make sure that you’ve got

all the materials that you’ll need to do the homework such as notes and textbook.

• Review. Go back over the lecture for each section and review any examples that

the instructor worked to make sure that you understand the ideas from that

section. Make note of any common errors that your instructor may have

mentioned. Do the same with the text book. Read the section and note examples

worked and common errors mentioned in the text book

One of the biggest roadblocks in doing homework that I’ve seen in many students

is that they completely ignore the notes and/or text. They look at a problem and if

they can’t see how to do it they give up and go to the next problem. Often there

will be a similar problem in the notes and/or text that can help you to get started!

• Read/Follow the Directions. Make sure that you read and follow all the

directions for both the homework set and the individual problems.

• Be Neat. Make sure that you write neatly. This will help the instructor as he/she

is grading the assignment and you when you are going over the assignment in

preparation for an exam.

• Show All Work. Make sure that you show all of your work. Do not just give the

answer. Many instructors will not accept homework that consists only of answers

and no work. Also, do not skip large chunks of the work. Instructors aren’t mind

readers and so they won’t know how you got from Step 1 to Step 3 unless you

also show Step 2. This is also important if you made a mistake in Step 2. If the

instructor can’t determine how you got from Step 1 to Step 3 you’re liable to lose

far more points than you would have lost for the error in Step 2 had you shown it.

Showing your work will also help you when you are reviewing for the exam.

• Check Your Work. Always go back over your work and make sure that you’ve

not made any simple arithmetic/sign errors.

Problem Solving

In the previous section there were some general tips in regards to homework sets as a

whole. Here are some tips to help you actually work the problems. Note that some of the

ideas were important enough that they are actually in both sections.

• Read the Problem. Read the problem to get an idea of what you’re being asked

to do. This one of the biggest sources of point loss that I’ve seen in grading. Too

many students just skim the problem and assume they know what’s going on and

what they are being asked to do.

• Read the Problem Again. Now that you know what you’re being asked to do,

read the problem again. This time around make note of what you are given and

what you need to find. Also make sure that you understand just what you’re

being asked to do.

• Clearly Note What You Are Asked to Find. Clearly write down somewhere

what you’re being asked to find.

• Clearly Note What You Know. Clearly write down somewhere all the

information you’ve been given.

• Draw a Diagram. If appropriate draw a diagram and label what you know and

what you need to find. Often diagrams will suggest the solution technique, so it’s

a good idea to get into the habit of drawing them.

• Devise a Plan. Try to figure out what you’re going to need to work the problem.

Identify formulas that may help you. See if there are any intermediate

steps/answers that will be needed in order to arrive at the final answer.

Work a Similar Problem. If you can’t figure out how to work the problem find

a similar problem that is simpler. Work this then go back and compare what you

did in the simpler problem to the problem you’re asked to do.

• Work the Plan. Once you’ve got the plan, work it out to get the answer.

• Check Your Solution. Is the answer in proper form? Does your answer make

sense? If possible, plug your answer back into the original problem as a check.

• Go Back Over the Problem. Once you’re satisfied that you’ve got the correct

answer go back over the problem. Identify concepts/methods/formulas that were

used for the problem. Try to understand why these concepts/methods/formulas

were used on this problem. Look for identifying characteristics that will help you

identify this kind of problem in the future.

Studying for Exams

Here are some tips on studying for exams.

• Start on Day One. You should always be studying for the next exam. Do a little

each day, or at the very least start studying 2 – 3 days before the exam. Do NOT

start studying the night before the exam. Cramming, while a time honored

college tradition, just doesn’t work as well as spending time each day studying,

especially with a math class.

• Get a Good Nights Sleep. Get a good nights sleep the night before the exam. It

is important to be well rested and mentally sharp when you take the exam.

• Make a List of Important Concepts/Formulas. Review your notes and make a

concise list of important concepts and formulas. Make sure you know these

formulas and more importantly how to use them!

• Rework Homework Problems. Do not just read over the homework problems.

Actually rework them. Writing down the steps will help you to remember them.

Make sure that you try to do the problems without looking at the solutions.

• Rework Book/Notes Examples. Cover up the solutions to book or note

examples and try to rework them. When looking for problems from the book

don’t forget that most books have a review section at the end of each chapter that

usually contains more problems.

• Look for Identifying Characteristics in Problems. While doing your

homework you knew which section it came out of. This provided some clues as

to the solution process. During an exam you won’t have this to help you. So,

while reviewing your homework look for identifying characteristics that will give

you clues on how to identify that kind of problem.

• Take a Practice Exam. Find some problems and treat them a practice test. Give

yourself a time limit and don’t use your notes or book

Taking an Exam

Taking exams is probably one of the most important things that you’ll do in a math class

and so it’s important to do the best that you can. Here are some ideas that will help you

while you’re taking an exam.

• RELAX!!! This is the first step to successfully taking an exam. Unfortunately,

it’s also one of the hardest things to do. The more worked up and nervous you are

during the exam the more likely you are to forget something or blank out. The

worst thing that you can do in an exam is panic.

• Be Smart. By this I mean be smart as you take the exam. You should go over

the exam three times. First, go over the exam and work all the problems that you

KNOW you can do. Second, work all the problems that you think you can do, but

aren’t sure. Last, go back and work the remaining problems. In this way you will

get all the points that you know you can get.

• Be Time Efficient. Watch the clock. Don’t spend a huge amount of time trying

to get the points for one problem! If you spend too much time trying to get the

points for one problem, you may not be able to finish the exam and lose more

points than you gained by taking all that time for that one problem.

• If You’re Stuck Move On. If you find that you’re stuck on a problem, move on

to a different problem and come back later to finish the problem. Don’t waste

time trying to get 10 points and then not be able to finish and miss 20 points

because you ran out of time.

Note that is really the same as the previous tip, but it was important enough to

make again and in a different way.

• 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.

Don’t leave it to the instructor to read your mind trying to figure out if you knew

what you were doing or not.

• Never Leave a Problem Blank. You should never leave a problem blank. Even

if you don’t know how to finish the problem, write down as much as you do

know. The instructor can only give partial credit if there is something written

down for the problem. Writing something down is not a guarantee of partial

credit, but not writing anything down is a guarantee of no partial credit!

• Read the Problem. Make sure that you read the questions carefully and

completely before you answer the question. If the instructor asks for the answer to

be written in a specific form then make sure that you do that.

• Does Your Answer Make Sense? Make sure you’ve gotten an answer that

makes sense.

• Recheck Your Work. If time permits go back over the exam and check every

problem. This means completely rework the problem from scratch

Learn From Your Errors

This is probably one of the more important sections here and also one of the most over

looked. Learning from your mistakes can only help you.

• Review Homework. When you get your homework back review it looking for

errors that you made.

• Review Exams. Do the same thing with exams.

• Understand the Error. When you find an error in your homework or exams try

to understand what the error is and just what you did wrong. Look for something

about the error that you can remember to help you to avoid making it again.

• Get Help. If you can find the error and/or don’t understand why it was an error

then get help. Ask the instructor, your tutor, or a classmate who got the problem

correct.

• Rushed Errors. If you find yourself continually making silly arithmetic or

notational errors then slow down when you are working the problems. Most of

these types of errors happen because students get in a hurry and don’t pay

attention to what they are doing.

• Repeated Errors. If you find yourself continually making errors on one

particular type of problem then you probably don’t have a really good grasp of the

concept behind that type of problem. Go back and find more examples and really

try to understand just what you are doing wrong or don’t understand.

• Keep a List of Errors. Put errors that you keep making in a “list of errors”.

With each error write down the correct method/solution. Review the list after you

complete a problem and see if you’ve made any of your “common” errors.

differently and there is no one right way to study for a math class. There are a lot of tips

in this document and there is a pretty good chance that you will not agree with all of them

or find that you can’t do all of them due to time constraints. There is nothing wrong with

that. We all study differently and all that anyone can ask of us is that we do the best that

we can. It is my intent with these tips to help you do the best that you can given the time

that you’ve got to work with.

Now, I figure that there are two groups of people here reading this document, those that

are happy with their grade, but are interested in what I’ve got to say and those that are not

happy with their grade and want some ideas on how to improve. Here are a couple of

quick comments for each of these groups.

If you have a study routine that you are happy with and you are getting the grade you

want from your math class you may find this an interesting read. There is, of course, no

reason to change your study habits if you’ve been successful with them in the past.

However, you might benefit from a comparison of your study habits to the tips presented

here.

If you are not happy with your grade in your math class and you are looking for ways to

improve your grade there are a couple of general comments that I need to get out of the

way before proceeding with the tips. Most people who are doing poorly in a math class

fall into three main categories.

The first category consists of the largest group of students and these are students that just

do not have good study habits and/or don’t really understand how to study for a math

class. Students in this category should find these tips helpful and while you may not be

able to follow all of them hopefully you will be able to follow enough of them to improve

your study skills.

The next category is the people who spend hours each day studying and still don’t do

well. Most of the people in this category suffer from inefficient study habits and

hopefully this set of notes will help you to study more efficiently and not waste time.

The final category is those people who simply aren’t spending enough time studying.

Students are in this category for a variety of reasons. Some students have job and/or

family commitments that prevent them from spending the time needed to be successful in

a math class. To be honest there isn’t a whole lot that I can do for you if that is your case

other than hopefully you will become a more efficient in your studies after you are

through reading this. The vast majority of the students in this category unfortunately,

don’t realize that they are in this category. Many don’t realize how much time you need

to spend on studying in order to be successful in a math class. Hopefully reading this

document will help you to realize that you do need to study more. Many simply aren’twilling to make the time to study as there are other things in their lives that are more

important to them. While that is a decision that you will have to make, realize that

eventually you will have to take the time if you want to pass your math course.

Now, with all of that out of the way let’s get into the tips. I’ve tried to break down the

hints and advice here into specific areas such as general study tips, doing homework,,

studying for exams, etc. However, there are three broad, general areas that all of these

tips will fall into.

Math is Not a Spectator Sport

You cannot learn mathematics by just going to class and watching the instructor

lecture and work problems. In order to learn mathematics you must be actively

involved in the learning process. You’ve got to attend class and pay attention while

in class. You’ve got to take a good set of notes. You’ve got to work homework

problems, even if the instructor doesn’t assign any. You’ve got to study on a regular

schedule, not just the night before exams. In other words you need to be involved in

the learning process.

The reality is that most people really need to work to pass a math class, and in general

they need to work harder at math classes than they do with their other classes. If all

that you’re willing to do is spend a couple of hours studying before each exam then

you will find that passing most math classes will be very difficult.

If you aren’t willing to be actively involved in the process of learning mathematics,

both inside and outside of the class room, then you will have trouble passing any

math class.

Work to Understand the Principles

You can pass a history class by simply memorizing a set of dates, names and events.

You will find, however, that in order to pass a math class you will need to do more

than just memorize a set of formulas. While there is certainly a fair amount of

memorization of formulas in a math class you need to do more. You need to

understand how to USE the formulas and that is often far different from just

memorizing them.

Some formulas have restrictions on them that you need to know in order to correctly

use them. For instance, in order to use the quadratic formula you must have the

quadratic in standard form first. You need to remember this or you will often get the

wrong answer!

Other formulas are very general and require you to identify the parts in the problem

that correspond to parts in the formula. If you don’t understand how the formula

works and the principle behind it, it can often be very difficult to use the formula.

For example, in a calculus course it’s not terribly difficult to memorize the formula

for integration by parts for integrals. However, if you don’t understand how to actually use the formula and identify the appropriate parts of the integral you will find

the memorized formula worthless.

Mathematics is Cumulative

You’ve always got to remember that mathematics courses are cumulative. Almost

everything you do in a math class will depend on subjects that you’ve previously

learned. This goes beyond just knowing the previous sections in your current class to

needing to remember material from previous classes.

You will find a college algebra class to be very difficult without the knowledge that

you learned in your high school algebra class. You can’t do a calculus class without

first taking (and understanding) an Algebra and a Trigonometry class.

So, with these three main ideas in mind let’s proceed with some more specific tips to

studying for a math class. Note as well that several of the tips show up in multiple

sections since they are either super important tips or simply can fall under several general

topics.

General Tips for Studying Mathematics

These are some general tips that where either important enough to single out or just

didn’t seem to fit into any of the other sections.

• Go To Class. Remember that math is cumulative. If you don’t go to class you

will miss important material that will be used in later sections and/or important

announcements.

• Get to Class On Time. Sometime important announcements are only given

during the first few minutes of a class.

• LISTEN During Class. In order to get something out of the class you need to

listen while in class. Often this can be difficult to do but it is very important.

Sometimes important ideas will not be written down on the board, but instead just

spoken by the instructor.

Watch for things the instructor emphasizes, even if just in words. This often

means the instructor thinks it’s important. The more important that an instructor

thinks a topic is, the more likely that it will show up on the exam!

• Take Good Notes. Try to write down everything that instructor puts on board. It

may seem easy when watching the instructor, but it often is not so easy when it

comes time for you to do it. A good set of notes will help remind you how to do

these problems. For some instructors writing down everything may be difficult.

In these cases you should try to write down as much as possible.

Note as well that this seems to contradict the previous tip. It is often hard to both

listen and take a good set of notes. This is something that one often only gains

with practice. You need to be able to listen while you are writing down the

important parts of the lecture If you find that are having trouble both listening and taking good notes then you

might consider bringing in a tape recorder and record the lecture.

Note however that prior to doing this you should first speak with your instructor.

There are a few instructors out there in the world that do not like to have their

lectures recorded.

• Ask Questions. If you don’t understand something then ask your instructor.

Chances are you are not the only one who doesn’t understand.

• Listen When Others Ask Questions. When other students ask questions make

sure you listen to both the question and the answer. It may be that the student

asking the question thought of something that you didn’t think of.

• Review Notes After Class. After each class you should review your notes. Note

the topics that you found confusing and formulate questions that you can ask your

instructor or tutor to help you understand the topic.

• Make a Set of Index Cards. Make a set of index cards with important formulas

and concepts on them. You can carry these around with you to look over when

you’ve got a few spare minutes. Use them to help you memorize the important

formulas and concepts.

• Learn The (Proper) Notation. Instructors will assume you know it so you’ll

need to and many instructors will take points off for bad notation.

• Get Into A Study Group. It is often helpful to study in groups. People often

look at things differently so someone else may see how to solve a problem that

can’t do or understand a topic that you find confusing.

• Note Due Dates. Write down the due dates for homework and dates for exams

someplace you’ll see them so you don’t forget about them.

• Budget Adequate Time For Studying/Homework. It often takes more time

studying mathematics to learn the subject than you may require in other classes.

Homework will often take more time than you had originally thought it would.

Keep this in mind as you budget time.

• Do Homework After Each Class. At the end of each class budget some time to

look over the homework from that days lecture and attempt to do it Doing this

will allow you time to really work at understanding the concepts covered that day.

Do not wait until the last minute to do the homework as this often results in an

incomplete homework set and/or an incomplete understanding of the concept.

• Do Homework Without Notes and Book. After the first few homework

problems, put your notes and book up and try to do the remaining problems

without referring to your notes and/or book. In most cases you will not have these

during your exams so get used to doing problems without them.

• Do More Homework. Do not limit yourself to just the homework that your

instructor assigns. The more problems that you work the better off you’ll be.

• Practice, Practice, Practice. Practice as much as possible. The only way to

really learn how to do problems is work lots of them. The more you work, the

better prepared you will be come exam time.

• Persevere. You will not just instantly get every topic that is covered in a math

class. There will be some topics that you will have to work at before you

completely understand. The only way to really grasp some topics is to go home

and think about it and work some problems. You will often find that after a little

work a topic that initially baffled you will all of a sudden make sense.

• Keep Old Homework and Exams. Do not throw away homework and exams

once you get them back. The homework is a good source of study material for

exams and both the homework and exams is a good source of study material for

comprehensive final exams (if you’ve got one).

• Don’t Forget Your Textbook. If you get stuck on a topic that was discussed in

class do not forget that you do have a textbook. Often the text book will contain

examples not worked in class and/or a different approach to a problem.

• Seek Help If You Need It. If you are having trouble with your math class you

have many options open to you and you should take advantage of them. You can

go to your instructor’s office hours, go to the tutoring room or hire a tutor to get

help.

Here at Lamar University we have a free math tutoring room located in Lucas

209. You can get a current list of tutors for hire at

http://www.math.lamar.edu/tutorlist.asp or by visiting the departmental office in

Lucas 200.

• Have the Proper Attitude. Always do the best that you can. Do not do try to do

just enough to get by. Doing this can lead to major problems if you aren’t careful.

If you are trying to do just enough to get by then all it takes is one bad exam and

you are now failing the course.

You should always do the best that you can and strive for the best grade that you

can possible get.

Taking Notes

Here are a couple of tips for taking notes in the class.

• Listen in Class. Do not just write down what you see on the board. No

instructor is going to write down every word they say and sometimes the

important ideas won’t get written down.

• Write Down Explanatory Remarks. Make sure you write down any

explanatory remarks the instructor makes. These often won’t get written down by

the instructor, but can tell you how to work a particular kind of problem or why

the instructor used one formula/method over another for a given problem.

• Note Important Formulas/Concepts. If an instructor emphasizes a particular

formula or concept then make note of it. This probably means the instructor feels

that it’s important and important formulas and concepts are much more likely to

show up on an exam.

• Question Your Instructor. If you are unclear on something ask questions.

• Note Topics You Don’t Understand. If you are having trouble understanding

something being presented note that in the margin and at least write down the key

words. Leave yourself a couple of lines so you can fill in the missing details later

once you’ve gotten help to understand the concept.

Review/Edit Your Notes. As soon you can after class go back over your notes.

Look for any errors and/or omissions. Fill in any information you didn’t have

time to write down in class.

• Review Regularly. At regular intervals sit down and review your notes so that

you can learn and retain the information. Remember, that this information will

probably be required down the road so it’s best to learn it as soon as possible.

Getting Help

Getting help when you are in trouble is one of the most important things that you can do

in a math class. Here are a couple of things that you can do the get help.

• Get Help When You Need It. Do not wait until the last minute to get help.

When you start running into problems it is time to get help. Remember that math

is cumulative. If you don’t get help right away you will only be making it all that

more difficult to understand future material.

• Ask Questions in Class. This way you get the help you need AND stay actively

involved in the class.

• Visit the Instructor’s Office Hours. The instructor has office hours for a reason,

so use them!

• Form a Study Group. Many people find it convenient to study in a group.

Different people will see things differently and may see a way to work a problem

that you don’t know how to do.

• Go to the Tutor Lab. If your school has a free math tutoring lab (many do and

many don’t) then make use of it! That’s what it’s there for.

Here at Lamar University the free math tutoring lab located in Lucas 209.

• Get a Private Tutor. You can always hire a private tutor for some help. In

almost every school you will find people who are willing to tutor you for a fee.

Most math departments keep a list of tutors or can tell you where you might be

able to find one.

If you are here at Lamar University you can access a list of current tutors at

http://www.math.lamar.edu/turorlist.asp or stop by the Math Departments office

in Lucas 200 for a list.

• Ask Good Questions. Saying “I don’t understand this section.” or “I don’t get

it.” is not the best way to seek help. It just doesn’t imply what you’re having

trouble with and so will probably not get your questions answered. Be specific

with your questions. What exactly is it about this section don’t you understand?

Many instructors won’t help you unless you do have specific questions and/or can

articulate exactly what it is that you don’t understand and/or “get”. If you really

don’t understand a given section that is okay, but be prepared to tell your

instructor just what is causing the problems. Do you not understand the concept?

Are you having trouble getting the problems started? Are you having trouble

identifying that the problems use the ideas in the given section?

Have Attempted Work With You. When you get help make sure and bring the

attempts that you’ve made on the problem. This will help the person helping you

to understand just where you’re having problem.

Again, many instructors won’t help you unless you’ve got something to show that

you’ve at least attempted a problem. If you really don’t understand how to even

start the problem then bring in work for other problems in that section that you

have done. This accomplishes two things. First, it shows the instructor that you

have been working and second, it gives the instructor something to look at to see

just where you’re having trouble understanding the problem you’re trying to

work.

Homework

Note that this section contains some general tips on making the most out of your

homework. The next section contains tips on actually working homework problems.

• Understand the Purpose of Homework. Instructors do not give you homework

assignments to make your life miserable (well some might, but most don’t!).

Homework assignments are given to help you to learn the material in the class and

to develop good reasoning and problems solving skills.

Mathematics is just not a subject that most people will instantly understand every

single topic after hearing the instructors lecture. Most people need to work on

some problems in order to really start to understand the topic. That is the point of

the homework. It gives you a set of problems that will help you to understand the

topics.

Remember that it almost always seems easier to watch an instructor doing

problems on the board than it actually is. You won’t know if you truly understand

the material and can do the problem if you don’t attempt the homework.

• Have The Actual Assignment. This may seem like a silly tip, but make sure

that you accurately write down the assignment and due date. This is one of the

more common mistakes that students make with homework.

• Do the Assignment Promptly. You should always do the assignment as soon

after the lecture as possible while the lecture is still fresh in your mind. Do not

wait until the last minute to do the whole assignment when comments made by

the instructor are no longer fresh in your mind. Often these little asides that an

instructor makes won’t seem important at the time, but when it comes time to

doing the homework the reason for making the comment will become clear.

• Be Organized. When you start working on homework make sure that you’ve got

all the materials that you’ll need to do the homework such as notes and textbook.

• Review. Go back over the lecture for each section and review any examples that

the instructor worked to make sure that you understand the ideas from that

section. Make note of any common errors that your instructor may have

mentioned. Do the same with the text book. Read the section and note examples

worked and common errors mentioned in the text book

One of the biggest roadblocks in doing homework that I’ve seen in many students

is that they completely ignore the notes and/or text. They look at a problem and if

they can’t see how to do it they give up and go to the next problem. Often there

will be a similar problem in the notes and/or text that can help you to get started!

• Read/Follow the Directions. Make sure that you read and follow all the

directions for both the homework set and the individual problems.

• Be Neat. Make sure that you write neatly. This will help the instructor as he/she

is grading the assignment and you when you are going over the assignment in

preparation for an exam.

• Show All Work. Make sure that you show all of your work. Do not just give the

answer. Many instructors will not accept homework that consists only of answers

and no work. Also, do not skip large chunks of the work. Instructors aren’t mind

readers and so they won’t know how you got from Step 1 to Step 3 unless you

also show Step 2. This is also important if you made a mistake in Step 2. If the

instructor can’t determine how you got from Step 1 to Step 3 you’re liable to lose

far more points than you would have lost for the error in Step 2 had you shown it.

Showing your work will also help you when you are reviewing for the exam.

• Check Your Work. Always go back over your work and make sure that you’ve

not made any simple arithmetic/sign errors.

Problem Solving

In the previous section there were some general tips in regards to homework sets as a

whole. Here are some tips to help you actually work the problems. Note that some of the

ideas were important enough that they are actually in both sections.

• Read the Problem. Read the problem to get an idea of what you’re being asked

to do. This one of the biggest sources of point loss that I’ve seen in grading. Too

many students just skim the problem and assume they know what’s going on and

what they are being asked to do.

• Read the Problem Again. Now that you know what you’re being asked to do,

read the problem again. This time around make note of what you are given and

what you need to find. Also make sure that you understand just what you’re

being asked to do.

• Clearly Note What You Are Asked to Find. Clearly write down somewhere

what you’re being asked to find.

• Clearly Note What You Know. Clearly write down somewhere all the

information you’ve been given.

• Draw a Diagram. If appropriate draw a diagram and label what you know and

what you need to find. Often diagrams will suggest the solution technique, so it’s

a good idea to get into the habit of drawing them.

• Devise a Plan. Try to figure out what you’re going to need to work the problem.

Identify formulas that may help you. See if there are any intermediate

steps/answers that will be needed in order to arrive at the final answer.

Work a Similar Problem. If you can’t figure out how to work the problem find

a similar problem that is simpler. Work this then go back and compare what you

did in the simpler problem to the problem you’re asked to do.

• Work the Plan. Once you’ve got the plan, work it out to get the answer.

• Check Your Solution. Is the answer in proper form? Does your answer make

sense? If possible, plug your answer back into the original problem as a check.

• Go Back Over the Problem. Once you’re satisfied that you’ve got the correct

answer go back over the problem. Identify concepts/methods/formulas that were

used for the problem. Try to understand why these concepts/methods/formulas

were used on this problem. Look for identifying characteristics that will help you

identify this kind of problem in the future.

Studying for Exams

Here are some tips on studying for exams.

• Start on Day One. You should always be studying for the next exam. Do a little

each day, or at the very least start studying 2 – 3 days before the exam. Do NOT

start studying the night before the exam. Cramming, while a time honored

college tradition, just doesn’t work as well as spending time each day studying,

especially with a math class.

• Get a Good Nights Sleep. Get a good nights sleep the night before the exam. It

is important to be well rested and mentally sharp when you take the exam.

• Make a List of Important Concepts/Formulas. Review your notes and make a

concise list of important concepts and formulas. Make sure you know these

formulas and more importantly how to use them!

• Rework Homework Problems. Do not just read over the homework problems.

Actually rework them. Writing down the steps will help you to remember them.

Make sure that you try to do the problems without looking at the solutions.

• Rework Book/Notes Examples. Cover up the solutions to book or note

examples and try to rework them. When looking for problems from the book

don’t forget that most books have a review section at the end of each chapter that

usually contains more problems.

• Look for Identifying Characteristics in Problems. While doing your

homework you knew which section it came out of. This provided some clues as

to the solution process. During an exam you won’t have this to help you. So,

while reviewing your homework look for identifying characteristics that will give

you clues on how to identify that kind of problem.

• Take a Practice Exam. Find some problems and treat them a practice test. Give

yourself a time limit and don’t use your notes or book

Taking an Exam

Taking exams is probably one of the most important things that you’ll do in a math class

and so it’s important to do the best that you can. Here are some ideas that will help you

while you’re taking an exam.

• RELAX!!! This is the first step to successfully taking an exam. Unfortunately,

it’s also one of the hardest things to do. The more worked up and nervous you are

during the exam the more likely you are to forget something or blank out. The

worst thing that you can do in an exam is panic.

• Be Smart. By this I mean be smart as you take the exam. You should go over

the exam three times. First, go over the exam and work all the problems that you

KNOW you can do. Second, work all the problems that you think you can do, but

aren’t sure. Last, go back and work the remaining problems. In this way you will

get all the points that you know you can get.

• Be Time Efficient. Watch the clock. Don’t spend a huge amount of time trying

to get the points for one problem! If you spend too much time trying to get the

points for one problem, you may not be able to finish the exam and lose more

points than you gained by taking all that time for that one problem.

• If You’re Stuck Move On. If you find that you’re stuck on a problem, move on

to a different problem and come back later to finish the problem. Don’t waste

time trying to get 10 points and then not be able to finish and miss 20 points

because you ran out of time.

Note that is really the same as the previous tip, but it was important enough to

make again and in a different way.

• 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.

Don’t leave it to the instructor to read your mind trying to figure out if you knew

what you were doing or not.

• Never Leave a Problem Blank. You should never leave a problem blank. Even

if you don’t know how to finish the problem, write down as much as you do

know. The instructor can only give partial credit if there is something written

down for the problem. Writing something down is not a guarantee of partial

credit, but not writing anything down is a guarantee of no partial credit!

• Read the Problem. Make sure that you read the questions carefully and

completely before you answer the question. If the instructor asks for the answer to

be written in a specific form then make sure that you do that.

• Does Your Answer Make Sense? Make sure you’ve gotten an answer that

makes sense.

• Recheck Your Work. If time permits go back over the exam and check every

problem. This means completely rework the problem from scratch

Learn From Your Errors

This is probably one of the more important sections here and also one of the most over

looked. Learning from your mistakes can only help you.

• Review Homework. When you get your homework back review it looking for

errors that you made.

• Review Exams. Do the same thing with exams.

• Understand the Error. When you find an error in your homework or exams try

to understand what the error is and just what you did wrong. Look for something

about the error that you can remember to help you to avoid making it again.

• Get Help. If you can find the error and/or don’t understand why it was an error

then get help. Ask the instructor, your tutor, or a classmate who got the problem

correct.

• Rushed Errors. If you find yourself continually making silly arithmetic or

notational errors then slow down when you are working the problems. Most of

these types of errors happen because students get in a hurry and don’t pay

attention to what they are doing.

• Repeated Errors. If you find yourself continually making errors on one

particular type of problem then you probably don’t have a really good grasp of the

concept behind that type of problem. Go back and find more examples and really

try to understand just what you are doing wrong or don’t understand.

• Keep a List of Errors. Put errors that you keep making in a “list of errors”.

With each error write down the correct method/solution. Review the list after you

complete a problem and see if you’ve made any of your “common” errors.