Paul's Online Notes
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1. General Errors

I do not want to leave people with the feeling that I’m trying to imply that math is easy and that everyone should just “get it”! For many people math is a very difficult subject and they will struggle with it. So please do not leave with the impression that I’m trying to imply that math is easy for everyone. The intent of this section is to address certain attitudes and preconceptions many students have that can make a math class very difficult to successfully complete.

Putting off math requirements

I don’t know how many students have come up to me and said something along the lines of :

“I’ve been putting this off for a while now because math is so hard for me and now I’ve got to have it in order to graduate this semester.”

This has got to be one of the strangest attitudes that I’ve ever run across. If math is hard for you, putting off your math requirements is one of the worst things that you can do! You should take your math requirements as soon as you can. There are several reasons for this.

The first reason can be stated in the following way : MATH IS CUMULATIVE. In other words, most math classes build on knowledge you’ve gotten in previous math classes, including your high school math classes. So, the only real effect of putting off your math requirement is that you forget the knowledge that you once had. It will be assumed that you’ve still got this knowledge when you finally do take your math requirement!

If you put off your math requirement you will be faced with the unpleasant situation of having to learn new material AND relearn all the forgotten material at the same time. In most cases, this means that you will struggle in the class far more than if you had just taken it right away!

The second reason has nothing to do with knowledge (or the loss of knowledge), but instead has everything to do with reality. If math is hard for you and you struggle to pass a math course, then you really should take the course at a time that allows for the unfortunate possibility that you don’t pass. In other words, to put it bluntly, if you wait until your last semester to take your required math course and fail you won’t be graduating! Take it right away so if you do unfortunately fail the course you can retake it the next semester.

This leads to the third reason. Too many students wait until the last semester to take their math class in the hopes that their instructor will take pity on them and not fail them because they’re graduating. To be honest the only thing that I, and many other instructors, feel in these cases is irritation at being put into the position at having to be the bad guy and failing a graduating senior. Not a situation where you can expect much in the way of sympathy!

Doing the bare minimum

I see far too many students trying to do the bare minimum required to pass the class, or at least what they feel is the bare minimum required. The problem with this is they often underestimate the amount of work required early in the class, get behind, and then spend the rest of the semester playing catch up and having to do far more than just the bare minimum.

You should always try to get the best grade possible! You might be surprised and do better than you expected. At the very least you will lessen the chances of underestimating the amount of work required and getting behind.

Remember that math is NOT a spectator sport! You must be actively involved in the learning process if you want to do well in the class.

A good/bad first exam score doesn’t translate into a course grade

Another heading here could be : “Don’t get cocky and don’t despair”. If you get a good score on the first exam do not decide that means that you don’t need to work hard for the rest of the semester. All the good score means is that you’re doing the proper amount of for studying for the class! Almost every semester I have a student get an A on the first exam and end up with a C (or less) for the class because he/she got cocky and decided to not study as much and promptly started getting behind and doing poorly on exams.

Likewise, if you get a bad score on the first exam do not despair! All the bad score means is that you need to do a little more work for the next exam. Work more problems, join a study group, or get a tutor to help you. Just as I have someone go downhill almost every semester I also have at least one student who fails the first exam and yet passes the class, often with a B and occasionally an A!

Your score on the first exam simply doesn’t translate into a course grade. There is a whole semester in front of you and lots of opportunities to improve your grade so don’t despair if you didn’t do as well as you wanted to on the first exam.

Expecting to instantly understand a concept/topic/section
Assuming that if it’s “easy” in class it will be “easy” on the exam
Don’t know how to study mathematics

The first two are really problems that fall under the last topic but I run across them often enough that I thought I’d go ahead and put them down as well. The reality is that most people simply don’t know how to study mathematics. This is not because people are not capable of studying math, but because they’ve never really learned how to study math.

Mathematics is not like most subjects and accordingly you must also study math differently. This is an unfortunate reality and many students try to study for a math class in the same way that they would study for a history class, for example. This will inevitably lead to problems. In a history class you can, in many cases, simply attend class memorize a few names and/or dates and pass the class. In a math class things are different. Simply memorizing will not always get you through the class, you also need to understand HOW to use the formula that you’ve memorized.

This is such an important topic and there is so much to be said I’ve devoted a whole document to just this topic. My How To Study Mathematics can be accessed at,