Six weeks into second semester, I was asked to become the teacher for a group of Algebra II students.
I found myself grading mounds of worksheets, and a couple of quizzes (remediations, really), and I began to wonder if I’d turned into one of those worksheet, algorithmic, obsessed teachers that focus on skill and drill over understanding. And I was beginning to despair, just a little.
I thought about my students, and what allows them to experience success, because it is the successes that motivate each one of them to keep going, to persevere in the “icky, sticky, I don’t get this” parts where they struggle. Part of the reason my students struggle is the lack of fluency. Each concept, each set of steps, each decision they make to solve or simplify, takes a huge cognitive load. They exhaust themselves just remembering what they need to do to factor a number (“Mrs. M., what is a factor again?”)
These children are not fluent. Not in multiplication tables, not in knowing the difference between base and exponent – more than half of them will tell you, “a negative plus a negative is a positive, because two positives make a negative.” I remind them they are adding, not multiplying, and they bravely leap back in, “oh yeah, -11 plus -3 is 8.” And this is after they have laboriously put the computation in the calculator… And I draw another number line on the board, or we play the game where they move their token up and down a number line to the tune of positive and negative numbers.
These babies of mine are not fluent! But they will get there. And therein is my saving grace with the worksheet thing. You see, I learned to play the piano, and I took ballet lessons, and I was on the swim team. And I was good at them in that order. But each of those activities required PRACTICE! I knew what it took to swim 50 meters fast enough to claim the silver, the red, and the blue ( third, second, and first, respectively), but I was better at collecting the silver than the red or blue, because, well, practice was held in the cool early summer mornings – when I’d rather be sleeping, or reading, or doing anything else than getting wet and cold over and over and over…. Well, you get the picture! I never got “fluent” at the swimming thing.
Ballet was a little better – no water! But I wasn’t slender or limber, and I couldn’t lift my leg to the bar without a pulley! I loved the plié, and the costumes and the recitals, but my heart wasn’t in it, (probably because my body wouldn’t cooperate by being tiny and graceful – one can only take so much of that feeling like a cow among graceful swans!)
Then there was the piano. We had an old upright; beautiful and rich sounding tones would pour forth when my mother played. She could play everything! And if she couldn’t play it, she could sight read the music. I soon learned to love the sounds I could produce. I wanted to play the classics – Mozart and Tchaikovsky, and Bach and Beethoven. I wanted to play the rich beautiful pieces mom could play. I had heard them, I could read the notes, but I had to become fluent in the patterns. I would play the pieces haltingly, getting a feel for the notes, but then, to really learn the piece, I would have to practice small sections – bar by beastly bar, until my fingers would traipse the keys of their own accord, and the piano would yield up its beautiful tones for me, the way it did for my mom.
So, back to the piles of worksheets. I look at them: logarithms and exponentials; growth and decay word problems; breaking down the formula, picking out the beginning value, the ending value, calculating the rate factor from the rate; understanding the idea of 100% being expressed as one. My babies are practicing their fluency with the notation, even as we put details to the numbers on the page. While I teach for understanding, I really want to show them the beauty and the majesty of math’s rich and beautiful notes. I want them to want to produce the beauty that comes as they practice; as they practice the changing from exponential to logarithmic so that they can spot what they need to do when they have to calculate for time, instead of finding an ending balance; as they practice because fluency takes a lot of that cognitive, heavy, exhausting work and turns it into a beautiful smile when the light clicks on and the child yells, “Mrs. M, I got it, let me come up to the board and write the answer!” And so I will keep on with the practice, worksheet by beautiful worksheet. Success breeds confidence. Confidence breeds courage – the kind you need when you tackle something new, or when you persevere because you believe you can find a solution.
To cut down on the paper (and the grading) I’ll keep varying the tasks: physical practice, verbal practice, mental math practice, practice through competition, things like Jeopardy or Kahoot, because practice builds fluency, fluency builds success, and success is what keeps us trying.
I did finally learn to play a pretty mean Sonata in C, but there was a price I paid to gain the fluency I needed. And, while I am not as good as I used to be, when my fingers find a piano, they slip into the gracefulness that eluded me in ballet, and the speed my body lacked in swimming competition, and they can “fluently” find the notes that will make the piano, and my heart, sing!