Today we welcome Cory Sweet, veteran math tutor and South Bay calculus department head, to our blog! Cory is sharing his top three math tips for success in any math class, from algebra 1 all the way up through AP calculus and beyond.
Math Tip #1: Show your work! (No mental math!)
My first math tip to help you succeed is something all of your math teachers are already telling you to do on every test, quiz, and homework assignment: show your work! By showing your work on every problem, you’re actually helping the teacher and yourself.
On tests and quizzes, this is your chance to show your teacher what you know. When you only write down the final answer, the teacher has no idea if you know and understand the process of getting to that answer. It might as well be a random guess, or even a result of cheating! When you present your work neatly and efficiently, you demonstrate that you know all of the steps to reach the answer. In case you still have questions, consider Private Tutoring At Home.
There is a second part to this math tip: by showing all of your work, you’re not doing any math in your head. One thing I tell all of my students is that doing math in your head is a great party trick, but it gets you nothing on tests and quizzes. I can’t even begin to count the number of mistakes I’ve seen students make when they could have easily used a calculator or written out the problem.
By doing math in your head, you’re more likely to make a mistake! Instead, write out each step, check your math with a calculator (if allowed), and work methodically and at a decent pace. Writing down your work won’t fix every mistake, but it will reduce your chances of making them. Bonus: if you do make the occasional mistake, your teacher is more likely to give you partial credit if they can see your process.
Math Tip #2: Study a little bit each day
My second math tip has to do with worst and best studying practices. Imagine that you have a test on Friday, and you estimate that two hours of studying should be plenty. Some students will study for two hours the night before the test, thinking that this will be enough time to learn the material.
I’m here to tell you that cramming the night before the test is one of the most inefficient ways to study. It is only slightly better than not studying at all! By having a two-hour study block the night before, you might create more problems for yourself. First, You might stay up late to finish other homework and so are too tired to do well on the test. Also, you might encounter a concept that you don’t understand, with little time to learn it. Lastly, you might not actually learn the material that well!
I want you to think of something you enjoy but need to practice to improve. This could be an instrument, a sport, a game—anything that requires effort. Now, I’m going to offer you two ways to study: you can practice for two hours at 4 p.m. for a week or for ten hours on a Saturday. Which did you choose? Hopefully the first option! Both take the same amount of total time, but you will retain more over a longer period. One word comes to mind when I think about practicing for ten hours straight: fatigue. Instead, the best way to study is to practice persistence and do a little bit each day. With regular practice, you can train yourself to think differently, develop muscle memory, and improve performance and technique. After all, slow and steady wins the race!
Math Tip #3: Spaghetti on the wall
My final math tip concerns what you should do when you come across a problem that you’re not sure how to tackle. I am a huge advocate of throwing spaghetti at a wall and seeing what sticks. No, this doesn’t mean you should start playing baseball with pasta. Rather, it means that trial and error in math is often a valid approach.
Far too often I’ve seen this situation: a student will read a math problem and then will think and think and think but never do anything, frozen with indecision. My advice: pick something and just give it a try.
There’s no way of knowing if that problem-solving method in your head will work until you actually put pencil to paper and try it out. If it doesn’t work, it’s not a big deal—turn your pencil around, erase, and try again! Each time you try a new strategy, you’ll get a little closer to solving the problem. You might notice a piece of information you missed the first time, spot a careless mistake, or realize that you need to draw a diagram. Even if you don’t end up getting the right answer, you may still get some partial credit from your teacher—better to have something written down on the paper to show that you engaged with the problem!