Math, one of the most feared subjects in the classroom. Yet for a lucky few, math class is the most obvious and self-explanatory subject they take in high school. Why this large disparity? Well, obviously a large part of it has to do with natural capabilities: mathematical thinking is something that some people can do more naturally than others. However, this does not at all mean that those people who don’t seem to have the knack for it cannot do well in this class.
Note: This article is written specifically for high school math classes, so it may or may not apply to certain college math courses.
First, however, it will be real helpful to see how those who excel at math view their subject:
1. Math is a game
Many stars approach math as others would approach a crossword puzzle or a sudoku puzzle. Math is something they tinker around with, where they know the basic tools and common strategies and use those with pleasure to solve increasingly complicated problems. For them math is inherently interesting, Obviously, math is useful for those planning to go into certain fields, but unless a person actually enjoys doing sudoku puzzles, fending off Alzheimer’s won’t keep them motivated for long, and they’ll find something else more mentally stimulating. This principle applies to other areas too, unless you find a way to make exercise interesting and inherently rewarding, it is very easy to make excuses and quit, no matter how strong your New Year’s Resolution was.
2. Math is a state of mind
The mind when doing math is a bit different from the normal conscious mind. The math mind is focused on analyzing all facts, looking always to prove what is thinks could be right. It isn’t content to merely know a general formula or a theorem, but it wants to know why the formula is the way it is, and how to prove that theorem. In other words, it is a cold-hearted machine putting all under the grind of logic. When taking a math test, the most important thing to maintain is a calm state of mind. Even the best students skip questions that are too difficult at first, let their subconscious ponder it for a while, and come back to it with (hopefully) fresh insight. Math whizzes are confident in how well they understand the material, so even when a solution to a problem is not immediately clear, they can still trudge along without fear.
3. Math lovers hate memorization
Although most math successes are also gifted at memorizing, they tend to see memorization as the epiphany of all things un-math, something better left to the biologists and pre-meds. Math is all about understanding, understanding how to approach a math problem, go through the steps and solve it. Sure, often there are common types of problems, that eventually become mechanical to solve (as is often the case when solving problems similar to example problems), but you can’t memorize every solution path to every type of problem, you need to problem solve.
As can be seen from the way that math lovers (and hence, most math teachers) see their subject, math is a very different beast from other subjects. Math involves going beyond what the book shows you, the minimum homework problems, and memorizing study guides the night before a test. Here are tips for really succeeding in math.
1. Understand where every formula or theorem came from
Never just memorize a formula or a theorem given to you. Oftentimes, deriving the formula yourself gives insight into the nature of the problems that you are solving. This especially holds true in geometry, where a lot of the proofs have the potential to be related to a deeper understanding of the theorems you know. Furthermore, deriving the formula helps to memorize the formula you need to know (better it gives you an understanding as to why these variables are under the radical, or why that is squared, etc.), and gives you a back up plan in case you forget the formula, because you know how to derive it. However, be warned, deriving or proving a theorem does not mean that you copy the proof out of the book, it is a combination of trying to prove the formula on your own along with looking at the “official” proof (although there are oftentimes many) for guidance. In my opinion, it is a great pity to treat the quadratic formula as simply something that you plug and chug into, even if you may have to use it for that purpose, but everyone should at least realize that it came about from completing the square of a generalized quadratic equation.
2. Do all homework problems
Yes, it can be a bit tedious to have to do five problems of the same type, but nothing reinforces mathematical concepts or reveals your error in understanding than doing problems and checking them against the back of your book. If your teacher is one of those types who never assigns problems with solutions in the back (which I strongly disagree with), then do some of them on your own, since you will get immediate feedback on your progress.
3. Understand the material, then do the homework
Don’t immediately start the homework and then dig up the corresponding example for each problem. Read the section first, even if it was explained in class, in order to reinforce it. Attempt to do the example problems, and understand why you do what you have to do and even do it a different way if you can pull it off (and I also disagree with teachers who do not allow students to do a nonstandard solution). Taking five minutes to understand a step in a solution is leave you better off than always solving a problem in a way that you don’t really understand. Once you understand it sufficiently, then do the homework problems.
4. Correct the teacher in class
This may sound nerdy or whatever you want to call it, but never simply accept what the teacher tells you. If you don’t understand something, ask about it right away, and you see something weird , ask about it, it could be a mistake. Many teachers do make mistakes, which is forgivable, because it offers you a great way to test your understanding. If your teacher is very structured and makes few mistakes, then still, don’t take everything they say for granted, question it. Questioning all is the key to a good mathematical mind.
5. Realize that some math is just plug and chug
Sometimes, like when working with matrices, doing arithmetic or working with weird numbers, you will have to do rather dull plug and chug work. All you can do is to keep checking to make sure you are not making a stupid mistake along the way. All you can do to avoid this is to diligently check yourself.
6. Use the calculator to its full advantage
If you can use a TI-83 or 84 during a test, then there are many great features that you never learn about in class. For examples, there are features on your calculator such as equation solver, which will solve any equation for you, provided that you know how to use it, or programming, where you can either write a program (or pay a friend to write one) that solves messy problems for you.
7. Don’t take calculus
Obviously this doesn’t apply if you’re going to be an engineer, scientist, or go pre-med in college, but I assume that if you are reading this article, then you aren’t opting to continue down the math-filled road. However, most colleges will require you to take a “quantitative reasoning” course as a graduation requirement. Calculus would not be a good way to fulfill this requirement. It tends to be a weed-out class, a lot of theorems encountered are never proven (they are to be left for the math majors to struggle with), and frankly, despite being so important, calculus just isn’t that interesting (actually I do find it interesting, but I don’t count), at least in the way it is often taught. It is taught mainly as a calculating tool, and it’s aesthetic value is often ignored. If you still want to brave math classes in college, then take some that will be more beneficial to the analyzing side of you such as: number theory, discrete math, statistics, programming or even just an overview type course. Many math fearers actually enjoy these courses and find them to be interesting.
So there are seven ways to give yourself the best fighting chance in your math class. Just remember, it is possible to do well in your math class, even if you aren’t considered a genius. The key is hard work
