How to study for a test and how to know if you're just not good at math?

Well it's the end of the exam season and I failed all four courses I took, that is the first semester in uni.

Obviously I'm doing something wrong, so how do you prepare for a test ?

Go over a section of the notes and try to answer questions from homework or from previous tests on that material?

I noticed that the questions on tests are utterly different from homework.

Also, what if I'm struggling with 90% or more of the questions on homework and tests I try since the beginning of the semester until this day?

By struggling I mean that I simply can't solve it on my own, no matter what I try or how much time I try. The generous people here helped me a lot through out the semester, I probably wouldn't finish any homework without them. But even now I don't have any confidence that I'll pass any of the tests if I'll try them again... Is this a good indicator that maybe I'm not cut out for doing math degree?

Some more info on the courses I took:

• Calculus 1 - 67% fail rate.

• Linear algebra 1 - about 45% fail rate.

• Intro to set theory - 40% fail rate.

• Intro to combinatorics - wasn't graded yet but many are sure that they didn't pass.

Solution 1:

There's no such thing (at least at this level) as being "good at math" or "not good at math." There is only "learns math faster" and "learns math slower," "knows more math" and "knows less math." That's it.

If you're someone who learns math slowly, then, well, you'll need to spend more time studying. As to whether there's enough time in the semester to achieve the competency you desire, or whether you want to spend that amount of time, that depends on your goals and your expectations.

I don't know whether or not you're "cut out" for the university math degree -- in part because I don't know how rigorous the math degree program is at your university, and in part because (again) it depends on your standards and your willingness to put in the time/effort.

As to how to study calculus better...

Well, if you're struggling with "90% or more of the questions on homework," then you need to ask yourself whether it's the actual calculus you're struggling with, or whether your algebra / pre-calculus foundation is shaky.

If it's that your algebra / pre-calculus foundation is shaky, then I'm afraid you're in a tough situation. The only thing I can suggest is to get a good tutor who will patiently work through the basics with you, from scratch. Above all, you need to develop not just competence, but fluency with the mechanics of algebra and the techniques of graphing functions.

If your algebra and pre-calculus is solid, but it's the calculus itself that you're having trouble with, then things won't be quite as bad. If it were me in that situation, I would start from the beginning of the semester's notes, from Section 1.1, and for each concept ask myself "do I understand X"? If not, what exactly don't I understand about X? Then I would do lots of problems from that section. If I got stuck, I would get help.

Then I would do the same thing for Section 1.2. And so on and so forth.

Then after all of that -- understanding concepts and doing textbook / homework problems -- I would do many problems from previous exams (if available). If previous exam problems are not available, then you should try to do hard problems from the text.

Ultimately, in my (admittedly limited) experience, students' issues with learning calculus often come down to one (or more) of the following:

• Shaky foundation in algebra / pre-calculus
• Not memorizing the formulas and rules
• Memorizing the rules but not practicing them enough
• Settling for a vague, hazy understanding, rather than developing a clear and precise understanding

The last point applies in particular to theorems like the Intermediate Value Theorem. Many students have a hazy intuitive sense of what the theorem says, yet few can actually state the theorem correctly. As such, it's no surprise that they often misapply it.

In summary: success in calculus (and in most math classes, for that matter) require both (1) technical competence in calculations (or proof techniques), and (2) an intuitive yet clear understanding of the concepts.

Solution 2:

FWIW,

This is my first post on MSE. I stumbled across your question and felt a bit of a connection.

I also struggled with Math throughout High School and even into post secondary school. Luckily I learned a few tricks and came out the other end loving math and with a Computer Engineering diploma. This is what I learned:

• Tutors are amazing. At first you'll feel a fool for needing one but then once you do you'll never look back. It's about confidence, not 'being good' at math.
• Math tests are easy to study for. Once you understand the basics, all you do is practice practice practice practice until you can do it on your own. That's it.

All the best!

Solution 3:

In my experience teaching most students fail because they try to cram for the exams the last week. Much of math is new stuff, it takes time (like a coleage used to say, calendar pages not sitting time) to really grasp new concepts. Do read through your class notes and make sure you understand each class before the next one, if you can read the lecture notes/text before class. Studying in university is harder than at school, the pace is faster and the subject matter is more complex.

If you have trouble with the official material for your course, use the web! There are many, many good lecture notes around, wikipedia has detailed writeups on much material. And then there is this site, where you will find people eager to help if you show earnest interest.

Good luck!