Here are some ways you can become better at mathematics.
1. Realize there’s nothing magic or special about mathematics.
Mathematics has a lot in common with cooking: applying “recipes” (algorithms) to cook up desired results. Math has a lot in common with sports and games: doing as much as you can while still following certain (sometimes arbitrary) “rules” to try and accomplish a goal. Math has a lot in common with exploring: discovering new things, even things you could never have imagined you’d find.
I’m kind of undercutting myself here, since, as a mathematician, I sort of benefit from the common beliefs that there’s something special about math. If people realized how easy math is, I wonder whether I’d still have a job
2. Stop associating mathematics with math teachers.
Many people are “traumatized” by poor math teachers in the early grades of school. Actually, to be honest, it has to be tough for even a great math teacher to breath life into early grade school math. When the curriculum calls for learning how to do arithmetic by hand, that’s pretty lame. People don’t usually do arithmetic by hand in the real world, certainly not long division.
If you’re really interested in getting good with math, I suggest maybe starting with a college level pre-calculus book and teaching yourself. Try to find a book where the author treats you as the intelligent, independent person you are, not as someone who has to take a course for a degree requirement. As a general rule of thumb, any texts sold at an actual university bookstore, at this level, will be trash. Go to the library and try some older pre-calculus textbooks. If the library is doing its job, trash textbooks won’t be kept for so many years. If all else fails, go to some math forums (like Math Overflow) and ask for book recommendations, telling them you want to become good at math and not just pass a required course; give them specific details and they can help find a book perfect for you.
Contrary to public belief, math textbooks aren’t written in some dialect of Ancient Latin which can only be read by the priestly class of mathematicians. At least, not until grad school
A common mistake is to start with “History of Mathematics” books, allegedly aimed for the layman. If you do have some math background, these might be good, but if you’re starting from absolute scratch, you’ll need at least some good pre-calculus to really get much out of a Math History book.
3. Mental shift: From “Problems” to “Exercises”
Unfortunately, most people, including mathematicians, have a bad habit of calling things “problems” when they’re not really problems at all. I wrote about this in my article, “Problems” In Mathematics. Most people have to study math for a long time before they can tackle actual mathematical “problems”. The word “problem” implies that no one actually knows the solution. If the solution is known, as is always the case in the exercises in lower level math texts, then it’s not a “problem”, it’s an “exercise”. Calling it a “problem” is like a weightlifter calling a dumbbell a “problem”. Ridiculous.
The exercises are there for you to get stronger. Anyway, it’s a lot sexier and more motivating to think about doing exercises, than to think about doing problems.
4. Know That Math Is Cool
It may seem surprising, but who do you think is most sensitive to social stigmas against science and mathematics? The answer is, scientists and mathematicians. For many years, I was actually “ashamed” of studying math. When someone asked what I did, I’d try to change the subject as soon as possible.
I realized it’s better to be unapologetic about my interests. (By the way, I’m a big anime fan, I like new agey stuff, and I used to play Dungeons And Dragons behind my parents’ backs) I stopped being ashamed of math and decided to be proud of it, and it turns out, once I made that mental shift, it became pure bling.
I think a lot of people are hindered from ever getting good at math because they think math is uncool. Reject that idea, and become better at math.
5. Believe You’re Good At Math
Whether or not the arbiters of society declare you Good At Math, hold the belief in your heart. Catholics believe that their priest can literally feed them the physical blood and flesh of Jesus Christ, so by comparison, it should be pretty easy to believe in something as mundane as being good at math.
The thing is, belief becomes reality. I experienced this in my own life, because until seventh grade, I did terrible in math classes, hated math (or at least, what I knew of math, which was just mind-numbing arithmetic), and generally believed I was terrible at math. (This, despite learning the BASIC programming language with my brother, which has a lot of overlap with algebra– I just didn’t know it yet) The way I got into math was actually pretty silly. I was going through a phase where I was interested in psychic power development. Of course I never developed psychic powers, but I got seduced by the D&D-ish stereotype of psionicists being extremely smart, and so that led me to start looking at the pictures in Euclid’s Elements. Mostly I didn’t understand them, but I struck out to do geometry on my own, kind of copying the general idea of following axioms and drawing lots of neat pictures with compass and ruler. That made me believe I was a mathematical genius, and by ninth grade everyone was pretty much going along with the “fantasy”
One thing I never mentioned in this article: doing lots of hard studying. Follow the five steps I gave, and the studying should become a joy, something you actually like doing, so it doesn’t seem hard at all. In any case, math is something you should do at your own pace, and this is partly why self-taught math is so much more powerful than school-taught math.
If you ever find yourself fed up with doing math exercises, you’re not studying math right. Like anything else, you’ll learn best when you’re having fun. Take your time, skip around to whatever extent the textbook allows, and have some fun.