I'm not trying to teach Billy addition anymore. He gets it. I know that he can answer 5 + 1 by methodically working through the problem. He can put up 5 fingers, raise 1 more finger, and then count them all to arrive at 6. He goes from A (the problem) to B (the process) to C (the solution). This is great! Now the next step is to create shortcuts in his brain that cut out that middleman (B) and take him directly from (A) to (C). Memorization is the name of the game!
We always begin and end the day with a run through the deck of flashcards. The rules of the game require that he answer each problem in a very specific way. For example, if I show him a 5 + 1 flashcard, I expect him to say "five plus one is six," and not just "six". This rule requires him to practice holding a solution in memory as he goes back to recite the original problem, connecting A to C, if you will. He hates this rule.
Today, after getting tripped up on a particularly nasty flashcard because of this rule, Billy asked me the question that all teachers, parents, and figures of authority around the world dread: why?
"Why do I have to say the problem every time? Why can't I just tell you the answer?"
I knew he was testing me. Billy wasn't seeking personal edification. Rather, like Socrates before him, his question was intended to poke holes in my rigid methodology, force me to concede my own ignorance, to undermine my authority and humiliate me.
I wasn't falling for it. I kept my cool. I tilted my gaze upwards to focus on a nondescript spot on the ceiling, pausing long enough to reinforce my dominance in this relationship. I then reverted my gaze, looked him straight in the eyes, and proceeded to answer his question with another question of my own design (touche, Billy!).
"Do you know what the five senses are?"
He shakes his head no. I proceed to teach him the five senses: eyes see, nose smells, hands feel, ears hear, tongue tastes. I explain to him that the five senses are what our brains use to remember and learn new things, like math.
"Our brains needs to see math, touch math, hear math, smell math, and taste math (okay maybe not the last two) in order to learn. So when I show you a flashcard, your eyes "see" the problem and your brain remembers it. The more you see the flashcard, the more your brain remembers it. When I make you write, 50 times, each math problem you've answered incorrectly, your hands "feel" the problem, your eyes "see" it, and your brain remembers it. Does that make sense?"
Billy shakes his head yes.
"So the reason I make you say the problem every time, the reason you can't just say the answer, is because I want your ears to "hear" the math. The more times you say the problem and answer together, the more your ears "hear", and the more your brain will remember, until one day, you won't need your fingers anymore! You'll just remember!"
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