I’m no math whiz, but maybe I could have been. I prefer the language side of learning opting for a book or listening to the flow of other languages. During my life as a student, I often secretly read, wrote notes in code, and almost every day I counted ceiling tiles. Why? To pass the time.
I loved mathematics in school until teachers started passing out formulas to everyone in line. I wasn’t interested in buying any. I had never been a typical thinker and mindlessly following formulas to solve math problems just turned me off. I was more interested with my own pattern investigations.
I often asked others, why would you follow someone else’s solution? Wasn’t that cheating? It sounded like it to me. After all, this was supposed to be a place of learning. Wasn’t I learning more by investigating how solutions were formed independently or even with a partner rather than being handed the secret code to a mysterious language?
When I was in first grade, we worked on large number subtraction. I worked dutifully and it came easily until the blasted zeroes came in to wreck my day, my week, my very long time. Over and over and over I remember my teacher demonstrating how to cross out zeroes, borrow something from the zero next door, only to keep going. It became a jumble of numbers that made no sense. Rote never worked for me. I couldn’t follow the traditional method if you made me try it a million times-though it seems like they tried.
Finally, I developed my own little trick. Though it lacked the depth of understanding I craved, it worked and seemed to make more sense to me. I pushed on through math realizing by that age that working things out my way would be my path through math. Traditional instruction never worked for me. My brain just didn’t work that way. I had to continue to find detours if I was going to be successful. Most were hard to explain to my teachers, but they worked and I understood them. Then, came division.
Large number division blew my mind. I could divide in my head, but writing down all of the numbers underneath that I was supposed to be subtracting and lining up perfectly wrecked me. Finally, an understanding teacher saved my boggled mind. She taught me short division. Though not conceptual (which I’ve actually learned and taught since), it was a short cut I could accept. Note: It worked much easier for my sons too. Unfortunately, the oldest was not “allowed” to use it in school. ugh.
As I discover more about myself through my child and homeschooling, I’m rediscovering what I’ve always known. I do things the “hard way”. The comforting thing is that by following my own train of thought and sometimes getting help from someone who understands it a bit, I can solve my own problems with different approaches that work for me. They aren’t the “hard way” for me; just for most others. The really interesting thing is that my son does the same.
Call it inquiry, exploration, or discovery learning. It’s all about handing over the tools to a child and encouraging him to fix things. When he begins to struggle, asking to clarify thinking, getting an explanation, and even showing the answer can help an untraditional learner discover his own key to unlock his thinking.
Often, children find that traditional methods DO NOT WORK for them. When that happens, it’s time to do some research. There are many more options and flexible approaches out there than when I was a kid. Many of the Common Core approaches and standards encourage discovery learning. Many current day mathematicians are lending support to conceptual approaches in mathematics. STEM and inquiry learning is prevalent in most schools today even though it may not always be implemented due to time constraints and standardized testing objectives. Additionally, often these methods are being taught by someone who does not understand or blatantly refuses to recognize the value of a learner’s own ideas instead of solely the ideas of the instructor or textbook. Most learners gain a better sense of understanding when given time to play with ideas, discover connections, and share different approaches to understanding material. In doing so, you won’t have so many ceiling tile counters.
Discovery is what comes naturally to lots of learners. We yearn for it. Most gifted children thrive with discovery learning. Sometimes it may take a learner longer with this approach and may not initially be the most efficient, but it has huge analysis, application, and synthesis value for any student.
Learning’s purpose is to extend your thinking; to get to the heart of math and other subjects. True meaning comes through discovering your own solutions.
Learning’s intention is to make people think ……and so is mine.