I grew up hating math. I seriously hated math. It never made sense to me. I couldn't wrap my mind around all those formulas and facts and get them all to stay there in my mind. I was forever forgetting things. Now that I know a little something about learning, I think I know why.
When I was growing up, I learned formulas. I learned that 1+1=2. I didn't learn why; I was never shown that 1 block and 1 block make 2 blocks when put together. I memorized. I remember learning multiplication in 3rd grade. We were each given a paper bowl and a paper banana. For each timed test we passed, we got scoops of ice cream to add to our "banana splits" and then at the end of the year, we actually made those banana splits in class with the scoops of ice cream that we had "earned." I hated those timed tests with a passion. I ended up with a decent banana split, but I can't say I enjoyed the process at all. In fourth grade, we learned long division. We were taught
how to do it. As I got older, I learned more and more formulas, some of which I actually remember, most of which I have forgotten.
This disdain for math followed me to college. It was during our Math Methods class that I had an epiphany. The professor was doing something on the board with repeated addition and made an off-hand comment about that being the basis of a multiplication problem. That off-hand comment changed my life. I never realized that multiplication is just repeated addition. I believe my thought process was, "No way. That's so easy. I can't multiply to save my life, but I can do
that." Keep in mind that I was a junior in college, and that simple fact blew my mind.
From that point forward, I started seeing patterns and relationships. When it's all boiled down to basic concepts, that's all math is. I finally started to understand the concept of borrowing from another column when subtracting - it's all about place value. I finally started to understand the concept of carrying the other number to the next column when adding 2-digit numbers - again, it's all about place value. I began to understand why length times width works to find area. I'm still trying to wrap my mind around division being repeated subtraction. I haven't completely figured out that one yet, but I'm working on it.
Teaching first-grade, I see all these concepts boiled down. I don't teach carrying and borrowing when adding and subtracting 2-digit numbers. But I do teach place value, which is the first step. I don't teach multiplication. But I do teach adding a string of 3 or 4 numbers, which is the first step. I do teach skip-counting, which is second step to multiplication. Being an after-school tutor shows me the fruit of learning the basics. The kids who come to after-school tutoring are mostly 4th grade, with a couple of 3rd graders and 5th graders thrown in to keep me on my toes. The patterns and relationships jump out at me every day. Those who I saw understanding the concepts in first-grade are the ones who understand the concepts better in fourth-grade. It's not just that they're better students. I've come to believe that anyone can do math - it's a matter of being taught the underlying concepts and relationships first.
That's why I never liked math growing up. I was taught formulas, not concepts. I think that, subconsciously, I wanted to know
why a formula worked. Why do we multiply length and width to find area? Why do we invert and multiply when dividing fractions? (I still don't understand that one, if anyone wants to explain it to me.) Why does 6x9=54? Who decided the answer to all those multiplication facts? I wanted to know
why and all I was learning was
how. I wanted to see the process down on paper - draw me a picture and show me 6 groups of nine circles and count them. I couldn't make sense of it, but didn't know how to express it because I didn't understand that that was what I wanted. Don't misunderstand, I had some great teachers when I was growing up, but they missed the mark when it came to me actually understanding math. I've never taken calculus (I never made it past Algebra 2 and the only reason I got that far was because I was told that I would never get accepted into college without it), but if somebody could explain it to me using pictures and objects, I'm truly believe I could gain a basic understanding of it. (By the way, that's a challenge to anyone who chooses to accept it.)
I wrote earlier that my junior year math epiphany changed my life. It's true. It's certainly changed the way I teach math now. The more relationships I see, the better I can teach the basics because I understand where it needs to lead to. I am applying for a master's program with a specialization in elementary reading and mathematics. The reading part is no surprise to anyone who knows me - I've always loved books and reading. The math part is a surprise. I want to know more. I want to understand all those things that I missed growing up. I want to know how I can better teach it so that no kids end up where I was - in junior high/high school/college and hating math because it makes no sense.