Memorizing Math Facts

the misconceptions of PEMDAS is a great example of mindless memorization without a concept of number sense and process thinking

During off-times, at a long stoplight or in grocery store line, when the kids are restless and ready to argue for the sake of argument, I invite them to play the numbers game.

"Can you tell me how to get to twelve?"

My five year old begins, "You could take two fives and add a two."

"Take sixty and divide it into five parts," my nearly-seven year old says. 

"You could do two tens and then take away a five and a three," my younger son adds. 

Eventually we run out of options and they begin naming numbers. It's a simple game that builds up computational fluency, flexible thinking and number sense. I never say, "Can you tell me the transitive properties of numbers?" However, they are understanding that they can play with numbers.

Sometimes I engage my kids with a real-world context. "I have four dozen donuts and I just have three of them. Will I have enough to feed forty people?" They ask questions like, "Does each person eat one?" or "Is anyone allergic to gluten?" I might say something asking them to organize objects into arrays or I might ask them to double or triple a recipe when we make dinner.

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I didn't learn the rules of baseball by filling out a packet on baseball facts. Nobody held out a flash card where, in isolation, I recited someone else's definition of the Infield Fly Rule. I didn't memorize the rules of balls, strikes, and how to get someone out through a catechism of recitation. 

Instead, I played baseball. I learned the basics through conversation and then I asked questions and observed and remembered the vocabulary, structures, processes and concepts of the game by playing it. In the process, I memorized a ton of facts. However, the facts were in a context, deeply rooted in my own experiences being the Strikeout King. 

 I'm not opposed to memorizing facts. Somewhere along the line, I've memorized the various spells in Harry Potter, the positions on a football field, and the lyrics to my favorite songs. I've memorized lines from conversations, verses from the Bible, and "facts" regarding Social Constructivism, Social Constructionism and Social Connectivism. I never crammed for a test. I never wrote out the facts in isolation under the watchful gaze of a teacher with a timer. 

I learned these things through immersion, critical thinking, context and play.

Note: I use the word "facts" here loosely. I don't think baseball, history, poetry, math or science have "facts," per se. They have processes, experiences, concepts, connections, theories and structures.