Jodie Larsen has a BS in applied mathematics from BYU-Idaho with a minor in biology. In addition to teaching at AcerPlacer, she tutors students on several topics in math.
After many years of teaching / tutoring, I have helped and observed an enormous amount of students and have come to recognize the types of mistakes students most often make which has led me to realize what the most common ones are, and it’s not generally as simple as not knowing how to do a problem. Here are the most common mistakes I’ve observed and some suggested remedies.
1. Trying to memorize versus really understanding
I feel this is the most critical problem to correct in order to be accurate in all things math. Math isn’t a subject of memorization. It won’t be mastered simply by knowing verbiage and formulas. Many people have eidetic memories – a trait I always wish I possessed – however, that isn’t enough. Math is beautiful in so many ways, but in large part (in my opinion) because concepts can be combined in new, and endless, ways.
The key to fixing this problem is to ASK QUESTIONS. Students need to be voracious in wanting to know the WHYS in everything they are doing and in understanding the whys, students can then apply them in new situations with much more ease and accuracy. In order for this to be effective, though, the students need good teachers who are willing to teach them the reasons and meanings behind what is being done rather than just talking at them.
2. Not understanding the fundamentals before moving on
For the same reasons you shouldn’t build a house on sand, a person should make sure to learn the fundamental rules (learn and UNDERSTAND them) before trying to use said rules in more complicated applications. If students struggle with exponents, for example, but then try to do intense factoring, the factoring will be much more difficult. This mistake goes along with the mistake listed above because when learning the processes and rules which will continue to be used and applicable, a student must make sure they have a firm hold on the rules and will be able to apply them whenever needed.
The remedy to this problem is to be very vocal with your instructor / tutor and let them know that you’d like more practice and clarification until you feel you’ve mastered each rule or concept.
3. Poor handwriting and disorganization
This one seems perhaps a bit obvious, but it’s actually amazing how often this can throw people off and will cause major frustration when, for example, x’s look like y’s and 5’s look like s’s. Students will often say such things as, ‘I could get it right if I could read my own writing!’ and though they know it and can laugh about it, they don’t often work on it. This may be the hardest mistake to fix, but it just takes care and really slowing down.
Along this same topic, students sometimes aren’t properly taught how to organize their work, or they may just not take heed when they are. I often see cramming in tight spaces, overwriting to avoid rewriting, etc., and thus it becomes a sort of ‘Where’s Waldo?’ situation whenever I need to help students error-check a problem.
One of my biggest recommendations is to get a notebook of graph paper to do work in. There are built-in columns which make it very visually easy to place one number in each box and have everything nicely spaced out. As an added bonus, this can drastically help students who may suffer any form of dyscalculia – I witnessed this with a student years ago and it helped her (and her daughter) tremendously.
4. Using pen
I know, I know, some students are die-hard pen enthusiasts and though I understand the reasons why, it often really hinders them in math. If any mistakes are made, the student often tends to scribble them out or write over them instead of just doing the problem over.
Mistakes are made much more often with these types of actions and so I always recommend working in pencil. If students don’t like the scratching sound of a pencil, then I recommend a pen such as a FriXion pen which ‘erases’ with friction instead of an eraser (we all know how well those don’t work!) which can help avoid the mess.
5. Skipping steps (head math)
Though head math can be impressive, it’s also very error prone. I understand that students want to go as quickly as possible in order to get homework done sooner, but if mistakes are made, then the problem needs to be redone anyway, rendering the step-skipping rather useless.
I firmly believe that writing more steps out yields more correct answers and higher retention overall. A phrase I often use is, “When in doubt… write it out!” If you are working on a problem and you get it wrong, I will recommend you restart the problem and SHOW ME the steps while talking them out. Oftentimes, you will find your own mistake, and that’s empowering!
If I can summarize in one sentence, it would be this: Always ask WHY and practice extra material until concepts are mastered, use a pencil to write out ALL steps neatly, and graph paper is your friend. It’s as simple as that and will greatly increase your chance of success in math (and life) overall!