Practice should look more like performance.
You might be interested in David Perkin's extended riff on this metaphor: https://www.gse.harvard.edu/news/uk/09/01/education-bat-seven-principles-educators
<isthereHTML?><blockquote>Perkins identifies two unfortunate tendencies in education: One is what he calls “elementitis” — learning the components of a subject without ever putting them together. The other is the tendency to foster “learning about” something at the expense of actually learning it. “You don't learn to play baseball by a year of batting practice,” he says, but in learning math, for instance, students are all too often presented with prescribed problems with only one right solution and no clear indication how they connect with the real world.
The way to let young learners play the whole game is to find or construct a junior version of it. A junior version of baseball may involve fewer innings, a diamond that is smaller than standard, or teams consisting of whatever neighborhood kids show up in the park on a given day. Yet the junior version conveys the essence of baseball — swinging at and hitting a ball and then making your way around bases while the opposing team scrambles to put you out.
In teaching math, drilling children in multiplication or long division or even giving them “word problems” is likely to lapse into “elementitis.” But giving a child some money and asking her to calculate whether it's enough to buy the items in her shopping basket is a “junior version” of the way math skills are used in the real world.</blockquote></whatnoHTML?>
This is a really important distinction. When I set up a drill in basketball, the kids know why we are doing it and what aspect of the game we are trying to work on. Plus, it is dynamic and kids react to things that their teammates are doing. Kids don’t necessarily have that same intuition about a fluency topic and don’t often have the bigger picture and narrative about how that skill fits in to bigger questions they are tackling and why they might care about improving it. If someone wanted to take a 100 free throws after practice it was usually the direct result of them missing a bunch of free throws in a game or knowing they get fouled a lot. If I had multiple practices or even one where all I had everyone do was shoot free throws there *might* be some benefit but there would rightfully be a mutiny because it misses the mark of what it means to play basketball. Seems like a pretty big and exciting job to keep thinking about how to get every kid excited about the full and messy performance of math.
You were pretty harsh on them in your tweet. I can see how you got some negative reactions. I laughed though. Sandpaper Kleenex. Like, I'm literally ROFL. If you bring some emotional aggression, expect some pushback.
On the other hand, this is a really fantastic post.
This engages the pre-frontal cortex in a way that your tweet probably poked the amygdala.
...Sandpaper Kleenex... f'n brilliant!
I've often compared getting good at math with getting good at a sport or music. They both require practice. In sports there are drills. In music there are scales. Neither are performance. The idea of practice as a mini-performance doesn't make sense. Practice is breaking things down into parts and learning. In music and theater, rehearsal is a mini-performance. I can't think of an analogy in math to rehearsing. Is there one?
I think practice like this can be effective with small amounts of gamification to reduce the monotony. E.g. computer based drills. Or even spelling bee style competition. Also, speed drills. Just some limited additions. Nothing crazy.
This post is an excellent take on the current teachings of math within our schools. I often felt the same way as a student in my high school math classes with all of the tedious drills we had to do for quadratics. I knew the content, could apply it to the given questions, and slack off the rest of class because I had been able to accomplish the bare minimum that was given to me. If I had a classroom where I had these opportunities to fluctuate and look at problems from different angles, I would have had a lot more of an interest in mathematics earlier on in life as well as preparing me better for the future college math courses to come.
I like the connection you made between math drill worksheet and sports or music, which I agree with your ideas as well. Mathematics in the real world should work like sports and music because practices is one of the best ways to get fluent on the concept, movement, or music structure for studying or performing. Math teachers should not isolate the subject from the real word and the drill worksheet that they give to students should also be connected to other disciplines so that students can see the world from mathematical perspective completely instead of only solving equations, drawing graphs and do not understand the real meaning behind them that they may also not know how to use their knowledge in the real world. From your post, I also agree with the part of saying how Stephen Curry was talking about how to shoot basketball can be reflected in math as well by analyzing ways of solving different types of mathematical problems so that students can learn the methods of learning math instead of just learn how to solve problems. Lastly, I think math should be seen as other disciplines as well because sports, music, dance and all these so-called disciplines can be seen as tools for humans to learn in order to get a better life, which mathematics also has the same functions in our real life.
I wonder if the sports metaphor, and its critics, both miss a key point: interest of the participant.
Math puzzles and games are interesting to participate in, and watch, both. Assuming the audience and participants chose their role. Math classes are overwhelmingly populated by participants who did not choose to participate.
Sports games and athletic contests are interesting to watch and participate in, both. Assuming the audience and participants chose their role. The athletic version of full participation is a PE class, which is often not known for its high level of enthusiasm.