Sunday, March 9, 2008

General Tips for Studying Mathematics: How to Study Math Part 2

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.

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.

How to Study Mathematics Part 1

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’t willing 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.