In my first tutoring session with an online tutoring organization, I took one look at my student’s worksheet and thought, “Okay, I’ve gone through Calc BC, and this is just fractions. How hard could it be?”
By the end of the session, I was questioning my own understanding of fractions. I tried many different methods: pizza slices, step-by-step instructions, written definitions. Nothing seemed to stick, and I couldn’t figure out why.
Eventually, I realized that while I learned math by memorizing formulas and recognizing common patterns in the numbers, my student learned better through diagrams, proofs, and real-life connections. After I physically cut out paper pies and drew out different-sized blocks, it was easier for him to translate those concepts into symbols.
Often when we learn concepts, we learn HOW to do something but don’t really question WHY things work the way they do.
When creating equivalent fractions, why do we have to multiply instead of adding or subtracting? Why do we use such a strange combination of factors, multiples, and subtraction in long division? Why does long addition go left to right instead of right to left?
Some students may be able to accept a math concept easily, and think, “Well, those are just the rules of math.” If they just memorize the steps, they do well. Others may struggle to remember new concepts without an in-depth explanation of the “why.” It can help a lot to plug in numbers to show the difference between right and wrong methods or even draw picture proofs.
I’ve learned that one-sided lecturing is not enough for effective tutoring. It’s important to first pinpoint exactly why a student is struggling with a concept—whether it’s missing another math concept from the past, difficulties memorizing an equation, or understanding why something happens the way it does.
People learn in very different ways, and that’s okay. It’s important to let them know they’re not “stupid” or “just bad at math.”—they just haven’t found the right explanation that clicks with them yet.
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