Mathematics feels like a minefield from time to time. Some days, it seems like you can’t make it through a worksheet or quiz without meeting a nearly impossible problem—or three. Math mistakes can feel impossible to prevent, but some of the most common mistakes made writing, reading, or in math class have the simplest fixes. No two students share the same exact struggles in math class, but there is a set of common mistakes students tend to make. Consequently, students reinforce concepts incorrectly, or merely carry out erroneous computations. In any case, if any of these 5 common mistakes sound familiar, you may want to reevaluate your approach to problem solving. Addressing these simple missteps can save you headaches and points.
1. Memorize? No, Practice
If you catch yourself staring at an old homework problem or worksheet, trying to scan the image up into your brain, you’re on the wrong track. Yes, certain formulas or common expressions might be worth memorizing, but in general, you cannot study mathematics by memorization. Instead, take a breath, and approach the problem that’s giving you grief. Ask yourself, what am I looking for? How do I find it? When you hit a roadblock, or you’re uncertain about your next step, recall yet again, where you are, and where you’d like to be. Studying mathematics is about logically evaluating and navigating problems, not memorizing the routes.
Practice, practice, practice. We get better at mathematics by practicing hard problems and applying our skills from class. Come test day, you’ll receive a new, unfamiliar set of problems, so understanding the underlying processes and relationships underpinning the problem will be more useful than “remembering the steps.”
2. Mental Math is Inferior Math
Mental math skills can save the day when you don’t have paper and a pencil, but why do it otherwise? Sure, writing out “easy” calculations may seem cumbersome and unnecessary, but it could save your grade. Without fail, when we try to do math quickly in our heads, we end up jumbling numbers and fudging operations. The risk of messing up “easy” calculations by computing mentally far outweighs the cost of writing out your thoughts. No less, your teacher would love to see your work too, I’m sure. Whether you get the answer right or wrong, having written your thought process will help your teacher determine how to best support you.
Writing out your work not only helps you skirt math mistakes, but it’ll help you learn the math at hand too. When we do math mentally, we tend to jump from step to step holding onto only the tiny nugget of information we need. Upon completion, we’ve lost sight of our steps along the way, and gain no broader perspective on the problem. However, by writing our steps out, we begin to see how all of our number-crunching is related. Better yet, if we forget a value, or feel confused, we can always trace our steps through our written work rather than start from the beginning!
3. Not Underlining/Highlighting/Circling
For all too long, English classes have monopolized highlighters. Why do we annotate readings in English class? To better remember and find key details quickly. So, why not the same excitement for marking up math problems? Whether you encounter a multi-step, word, or multi-step word problem, there’s probably a lot going on in the question. Highlighting or underlining can help cut through some of the noise and keep your eye on the prize.
With great highlighters, comes great responsibility. Now, don’t go painting your paper willy-nilly whenever you see a number; read the question once fully. After your preliminary read through, you’ll have a clearer sense of what information is worth drawing attention to. Whilst working through the problem, having key details showcased in the question can ensure you don’t miswrite values, or forget parts of the question. Click here for more tips on how to effectively highlight math problems.
4. Not Checking Your Work
What if I told you math mistakes are hiding in plain sight? Far too often, math problems are extremely “checkable” but go unchecked. The most “checkable” of the math problems are those where you must solve for a variable value. More often than not, by simply plugging in the value they’ve found, students can verify whether or not their answer is correct. Occasionally, checking your work can be less straightforward, but no less worthwhile. Even simply sitting back and asking, “Does my answer make sense?” can be enough to sniff out many common mistakes. Regardless, taking the time to go back, and check your answers, can make all of the difference.
5. Sloppy Write-Ups
Not only should you write out your work, but take good care to write it neatly. If you’ve ever gone to check your notes, only to find you can’t read them, you probably know how useless sloppy notes can be. Moreover, it’s possible you’re not the only person struggling to read your work. When students hand in classwork that’s illegible, teachers can inadvertently mark correct answers wrong, or deduct points in all of the confusion. Why lose points or math mistakes you didn’t make?
Strong math abilities aren’t developed over the course of a single week, nor year. Maturing as a young mathematician is a process, as is removing obstacles along the way. These five math mistakes are amongst the most common, and should you be experiencing them, ought to be addressed. However, developing healthy math habits is a journey. Expect to make mistakes along the way, but be vigilant. Common mistakes are always sneaking up on you, so keep an eye out!