My Favorite Tip for Learning Math

When I was in 8th grade, I had a hardcore geometry teacher that made sure that we knew his class was no joke. He was a fun man and an interesting teacher but his tests were hard. He would ask these complicated questions combining subjects from previous units and culminating them into a word problem that was complex and required an understanding of the subject like no other. When we first started the class, he told us: "Only a certain amount of you will get A's in my class." It was something like the top 10 students. With the right kind of work, I got an A for both semesters of that class.

There was one tip that he told us about that stuck with me. When he was in university and studying for finals, he would have a practice test and its answer key. No step-by-step instructions, just the answer to a potentially complicated problem. On problems you don't know how to do, look at the answer key. This isn't to cheat. Rather, you can look at the answer and if you understand the concepts of the topics that you are learning, you can apply the knowledge you have to see how they got that answer.

Benefits to this technique:

Sometimes, you'll be stuck on a super hard problem that doesn't have an obvious method of getting there. It may cause you to shut down and all of a sudden your brain won't know how to go about solving the problem. By having the answer there, it kickstarts the thinking process which allows you to analyze how to do the problem. If you figure out the method they used to get to the provided answer, you can use that method for similar problems without having to find the answer.

This technique helped me a lot, especially once math got harder. Once you get to harder math levels (Calculus AB and BC specifically), it's hard to know where to start because there are just so many concepts that you've had to keep in your head. By giving myself the hint through looking at the answer without step-by-step instructions, I came up with my own steps to find the answer using the methods that I had at my disposal. It was useful in so many ways and I'm glad I still remember that tip to this day.

Drawbacks to this technique:

You don't always have the answers. Sometimes it's an even-numbered problem in the textbook where there are no answers or there's no answer key for the worksheet or, oh no, it's the *test*. In those cases, there's no answer key. So how do you come up with a solution?

Circumventing the drawbacks:

Find similar problems that do have an answer. You can figure out the method they used in that particular problem and apply it to the problem that doesn't have the answer to it. Generally speaking, theres only a certain amount of variability that a math problem can have under a particular subject. You'll find a way around it.

As for the test, you'll have to have identified your methods beforehand in order to circumvent the drawbacks of being unable to find an answer. Coming up with steps to figuring out a problem is a part of the study process, and by the time your test rolls around, there aren't many on-the-spot tips that can help you figure out the answer. If you have already found methods, though, just try to recall which practice problems were similar to the one on your test and apply the method that you found works best for you.

Recommendations for this study tip:

Make sure that you are using concepts from the particular unit to come up with steps to solve the problem. Don't just arbitrarily choose theorems in hopes that they'll apply to only that particular problem. Use what you know from what you are currently working on before referencing earlier math subjects or classes.

Then, make sure that the method you came up with is correct. Apply it to similar problems and check the answer to make sure that your steps didn't only work for one specific problem. If it didn't work, you may have to try again.

Don't give up! Solving problems yourself is an important study method for retention. Whether you get it right the first time or the tenth time, the process is what helps ingrain information into the brain for long term storage.

As always, please feel free to contact me with any questions! My email is listed in the Contacts tab of the website, or you can DM my Instagram by clicking here.