The mistakes made sometimes lead to the most significant lessons.

I often make the above phrase after sharing the scored test and exam papers with my learners. Then, I give them some time to analyze their mistakes thoroughly. I instruct them to monitor and track their performance, taking note of the pattern of their mistakes as well. The capacity to identify your mistakes and how you made them will aid in overall learning and better grades. This is a habit only good math learners have advanced in. It is, therefore, predictable for me to use the different mistakes made by my learners to create subsequent exams.

How often do you go over your scored paper and analyze your mistakes? In doing this, how often have you instantly identified the point you had it all wrong and hoped you had detected the error earlier before passing your paper over to your teacher. Or, how often have you carefully examined the places you made errors, and while proffering the right answers, you encounter one of those revealing moments, “A-Ha.” That quick eye-opening moment when you uncover a new skill relating to the mistake you made out of lack of understanding, or the ” A-Ha” moment, normally leads to a major advancement in learning, which means that you are most likely to avoid making such mistakes again.

When teaching new concepts, mathematics educators usually watch out for those moments because those are the moments that lead to success. Mostly, past mistakes are not caused by committing to memory the different formulas, rules, or patterns. On the contrary, these errors originate from an in-depth understanding of “why” a resolution was made for the problem rather than “how.” We usually understand a particular idea more profoundly, when we know the ” whys” that follow a mathematical idea instead of focusing on the “hows”. Here are the three most seen mistakes and some solutions to them.

Basic Causes of Errors and their Signs

 It is essential to know the kind of errors you made and why you made them when you go over the errors in your papers. Here are some things to watch out for:

1. The Order of Operation (usually arises from repetitive practice and not from having real understanding like many have argued)
2. Errors due to mechanical reasons (poor mental math, interchanged number, rushed approach, forgotten step, absence of revision)
3. Knowledge-based errors (lack of necessary info about the idea, unknown terms)
4. Incompletion (an easier-to-use knowledge that comes from continuous practice).
5. Errors from the application (misunderstanding some of the necessary steps)

Success is Reversed Failure

Mathematicians learn from their previous mistakes and for you to improve, you have to think like a mathematician. This will require you to monitor the sequence of your past mistakes and enter them into a book. Look back to your past exams and revise the concepts that made you unhappy, keeping in mind that you only get better in Math with continuous practice. Do not dispose of your scored test papers because this will help you prepare better for subsequent additive exams. Detect issues instantly. Seek help as soon as possible when faced with difficult issues in a particular idea. Don’t wait around for help, it’s like visiting the doctor three days later, after breaking your arm. If your teacher or professor is not reachable, you can take your questions online, search for interactive tutorials for guidance, or post in discussion groups for deliberation.