New Insights and Their Implications

I never thought I would actually learn an easier method in math when I was in college that I was not previously aware of. I thought my ELED teachers did an okay job teaching me math as a child (although I was never very good at it). Now I'm wondering: is the reason I wasn't very good at math because my teachers were taking the wrong approaches to teaching me? I have always struggled with math, but while doing the area exercises a "light bulb" came on in my head - and I suddenly understood the concepts of finding the area for ANY figure. I never knew the trick of boxing out the figure, then finding the area of the boxed figure, then the area of either the figure or the empty space around the figure to come up with a total area. Although it seems like more work than just plugging in a formula, it seems to make a lot more sense. I also realized WHY area formulas are written how they are. After breaking down the figure to find smaller figures that I was familiar with finding the area of, it made creating a formula and figuring out the area of any figure simple. I wish my math teachers would have provided me with those types of examples when I was in school - I think it would have made my experiences with math much more enjoyable.

After realizing how much of a difference learning a new method now, as a senior in college, can make on my math career - I can now see the importance of explaining the why you do a math problem the way you do to students, not just giving them the way to solve a problem. Having an insight of why you're doing the formulas and problems the way you are truly helps create a much deeper understanding of math that sticks with you; it is much more effective than just memorizing formulas and plugging in numbers to get answers.