Written by Paul Dawkins
I’ve tried to break down the hints and advice here into specific areas such as general study tips, working homework problems, studying for tests, 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 teacher 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 work homework problems, even if the teacher doesn’t assign any. You’ve got to study on a regular schedule, not just the night before tests. If you aren’t willing to be actively involved in the process of learning mathematics 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. 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. In a calculus course it’s not terribly difficult to memorize a formula for the substitution rule 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 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.
General Tips for Studying Mathematics
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.
Get to Class On Time. Sometime important notices are only given during the first few minutes of a class.
LISTEN During Class. You’ve got to pay attention in class. Sometimes important ideas will not be written down on the board. Watch for things the teacher emphasizes, even if just in words. This often means the teacher thinks it’s important. The more important that a teacher thinks a topic is, the more likely that it will show up on the test!
Take Good Notes. Try to write down everything that teacher puts on board. It may seem easy when watching the teacher, 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.
Ask Questions. If you don’t understand something then ask your teacher. Chances are you are not the only one who doesn’t understand.
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 teacher 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. Teachers will assume you know it so you’ll need to and many teachers 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 tests 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.
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 tests so get used to doing problems without them.
Do More Homework. Do not limit yourself to just the homework that your teacher 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 test time.
Persevere. You will not just instantly get every topic that is covered in a class. There will 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.
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 teacher’s office hours, go to the NHS after-school tutoring program or hire a tutor to get help.
Taking Notes
Listen in Class. Do not just write down what you see on the board. No teacher 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 teacher makes. These often won’t get written down, but can tell you how to work a particular kind of problem or why the teacher used one formula/method over another for a given problem.
Note Important Formulas/Concepts. If a teacher emphasizes a particular formula or concept then make note of it. This probably means the teacher feels that it’s important and important formulas and concepts are much more likely to show up on an test.
Question Your Teacher. 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
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 Teacher’s Office Hours. The teacher 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 you need help make use of the free NHS after-school tutoring. Get a Private Tutor. You can always hire a private tutor for some help. You can access a list in the Guidance
Office. Ask Good Questions. Saying “I don’t understand this section” 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?
Problem Solving
Read the Problem. Read the problem to get an idea of what you’re 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.
Clearly Note What You’re 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 Tests
Start on Day One. You should always be studying for the next test. Do a little each day, or at the very least start studying 2 – 3 days before the test. Do NOT start studying the night before the tes. Cramming, while a time honored high school tradition, just doesn’t work as well as spending time each day studying.
Get a Good Night Sleep. Get a good night sleep the night before the test. It is important to be well rested and mentally sharp when you take the test.
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.
Rework Book/Notes Examples. Cover up the solutions to book or note examples and try to rework them.
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 a test 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 Test. Find some problems and treat them a practice test. Give yourself a time limit and don’t use your notes or book.
Taking a Test
RELAX!!! This is the first step to successfully taking a test. Unfortunately, it’s also one of the hardest things to do. The more worked up and nervous you are during the test the more likely you are to forget something or blank out.
Be Smart. By this I mean be smart as you take the test. You should go over the test three times. First, go over the test 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 test 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.
Show All Your Work. Make it as easy as possible for the teacher to see how much you do know. Try to write a well-reasoned solution. If your answer is incorrect, the teacher will assign partial credit based on the work you show. Don’t leave it to the teacher 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 teacher can only give partial credit if there is something wrote 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 teacher 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 test and check every problem. This means completely rework the problem from scratch.