Welcome back! Today’s post was requested by one of my followers earlier, so if you’re struggling with a particular subject you’d like advice on, please send me a request and I’ll try my best to get a post out in a timely manner. Now without further ado, I’ll teach you how to take notes and efficiently study for the mother of all necessary evils, math class.
TAKE GOOD NOTES
It can be difficult to take notes during fast-paced math classes. However, remember that you shouldn’t (and probably can’t) copy down every single little thing that was said. After all, you’re a student, not a court stenographer. Ignore all of the filler information and focus on getting down two things: formulas/theorems and example problems.
Mark these with something noticeable (stars, boxes, highlighting, etc) so you can easily find and reference them later.
Simplify theorems so you can understand them. For example, this is the binomial theorem written formally:
Looks intimidating, right? Would you still understand what that means two weeks after the lesson, when you’re studying for a test? Instead of attempting to decipher and memorize that confusing chain of hieroglyphics variables, break it down for yourself into straightforward language. You might say to yourself, “Oh, so it looks like the exponent of x starts at 0 and increases by 1 every term until it reaches n. And vice versa, the exponent of y starts at n and decreases by 1 every term until it reaches 0. And the coefficient of each term is just n choose k, where k increases by 1 every term.” Better, right? Put theorems and definitions into your own words to make them much more tangible and graspable.
Similarly, aim for understanding, not memorization. Try to write a proof for every formula/theorem. If you don’t cover the proofs in class, I highly encourage you to try to prove them yourself. There are also tons of great proofs on the Internet you can search for if you get stuck. Also make sure you know when to apply each concept. Memorizing the quadratic formula is peachy and all, but if you don’t know that the formula can only be used for a quadratic in standard form that’s set equal to 0, you’re going to run into some issues. Understanding the reasoning and applications for what you learn will tremendously improve your retention of all those complicated formulas as well as challenge you to think outside of the box.
If you’re really, really rushed, just copy the problem and answer. You can fill in everything in between later.
Ideally though, you’ll want to show your work. It’s helpful to add short comments next to each step to explain what you did and why you did it (“u-substitution”, “multiplied by denominator to cancel terms”, “subtracted 7x on both sides to use Zero Product Property”). Don’t show each itty bitty step if you don’t need it, but write down enough so that you could follow your train of thought if you were to look back at these notes come finals season.
Lastly, make sure to include units with all of your answers, follow any conventions your teacher tells you to (rounding to a certain decimal place, rationalizing denominators, etc), and always use correct notation. Develop these habits now so you won’t be kicking yourself for forgetting to include units on a test, when it actually matters.
At the end of class or as soon as possible afterwards, quickly review your notes and fill in clarifications, corrections, or explanations you missed while everything is still fresh in your memory.
PRACTICE, PRACTICE, PRACTICE!
They say that math isn’t a spectator sport, and they’re right. In other subjects, you might be able to get away with passively sitting back and hoping something the teacher says will work its way into your brain. But in math class, flipping through your textbook will not help you. Highlighting your formulas in different color schemes will not help you. Watching Sal Khan solve problems on YouTube without picking up a pencil yourself will not help you.
The only way to become a successful math student is to be actively involved in solving as many practice problems as you can get your hands on.
So where can you find practice problems?
- your homework problems
- your textbook
- any problem sets or worksheets you recieve in class
- the Internet, especially Khan Academy, IXL, and Kuta Software
- if you ask your teacher nicely, I’m sure he/she will direct you to some helpful resources
- if your school has two or more teachers who teach the same level math and use different problems, see if you can get extra worksheets from the other teacher/a friend in the other class
- you can use problems from smaller quizzes and tests to prepare for midterms and finals
While working through the practice problems, simulate test conditions as much as possible. Close your textbook and notes. Put away your calculator, unless you’re allowed to have one on test day. Show all appropriate work and use correct notation for each problem. Maybe even set a timer for yourself if you’re someone who tends to work too slowly.
If you have an answer key, check all your answers at the end. If you get a problem wrong, attempt to solve it at least one more time before asking for help (see section below).
ASK FOR HELP (THE RIGHT WAY)
You can get math help from your friends, parents, tutors, teachers, online resources, or a combination of any of the above. (Or even me, if I’ve taken your level math before.) However, even if you’re completely bewildered, don’t just slump back in your seat and whine, “I don’t get itttttttt” because that won’t help anyone help you. First, as mentioned above, always attempt a problem at least twice before asking someone else for assistance. Oftentimes an incorrect answer is due to a silly error that you could catch by doing the problem again. When asking for help, instead of vaguely gesturing at a problem and shrugging, tell whoever’s helping you which parts you were able to follow, which step tripped you up, which formulas you understood, and which ones you didn’t– the more specific, the better.
Never be afraid to ask for help! Each concept in math builds off of previous ones, so if you hold in your questions and remain confused, you’re going to have more and more trouble in the future. As long as you start early, practice consistently, and clarify confusion as soon as it arises instead of the night before a test, you should be well on your way to excelling at math!