“Any fool can know. The point is to understand.”
As a kid, math seemed like a foreign language to me. I remember being mystified … and NOT in a GOOD way … about the concept of fractions. And, quite frankly, my mastery of basic facts was shoddy. Although that was YEARS ago, those helpless feelings remain vivid in my memory. It’s funny. Who would have EVER thought that I would grow to LOVE something SO much when it all seemed so ELUSIVE to me as a child?
I’ve had the blessing of being a teacher for almost thirty years now. WHERE did THAT time go?!? Over the span of nearly three decades, I’ve worked with children who are just as stymied and fearful of math as I was … and … OTHERS who just have a SENSE, an AMAZING understanding, of how to make numbers work for THEM. That ability to see patterns and RIP numbers apart. And, what’s MORE, the confidence in themselves to persevere UNTIL they have found their way around a problem to arrive at a suitable solution.
While I don’t profess to understand HOW that happens, I DO know that the “new”, but really NOT so new, discovery-based method of exploring mathematical concepts IS a BLESSING. The beauty of math is the ability to seek and discover patterns. It is a magical way of making sense. And … if you DON’T understand the “formula” or “algorithm” in the FIRST place … it is NEVER going to be a logical way of thinking for you, for me … for our children.
I don’t remember being exposed to the freedom to play with numbers … or problems, for that matter, as a child. The beauty of the “new, not so new” way of learning math, through discovery and multiple perspectives in arriving at solutions, is the flexibility in thinking. There is often more than one way to find your answer. Sometimes the path is long and winding … sometimes it is efficient. If you don’t understand the “reasoning” behind short and efficient … then you are NOT in control of your thinking. The ability to make PERSONAL sense … the idea that a little struggle, making mistakes, understanding and explaining your thought process … IS a good thing because it EMPOWERS our learners as thinkers who UNDERSTAND the process with OR without the “formula”.
This “new” way of looking at math doesn’t mean that the foundational skills are thrown out, like the baby with the bath water. Those foundational skills are CRITICAL and provide the confidence we ALL need in order to be able to effectively approach “mental math” by ripping numbers apart in our heads. I will be forever grateful to my Grandparents, who spent an entire summer working with me to master my “basic facts”. That, in itself, helped to “open the mathematical door” just a crack. Teaching helped to throw the door WIDE open! While it sounds like SUCH a trivial thing, I am TERRIBLY proud of the fact that I no longer rely on my CALCULATOR to tally the monthly book orders! What I know AND understand about numbers, patterns, rounding and calculating has made me COMPLETELY self-sufficient in this area!
I’m not deluded enough to think that ALL my students will become mathematicians. But, I am hopeful that they learn to love the “process”. Sharing their thinking with others, being exposed to a variety of methods for arriving at a solution … from using concrete manipulatives, to drawing pictures, to making tables or T-charts or solving it in the “traditional” style with an equation … these experiences ALL help us to “make meaning”.
“You don’t understand anything until you learn it more than one way.”
My BIGGEST dream? That my seven and eight year old wonders no longer SEE themselves, at SUCH a young age, as “no good in math”.
“We learn more by looking for the answer to a question and not finding it
than we do from learning the answer itself.”