<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?>
Yet, learning baseball is broken down into drills and skills practice. There's nothing wrong with a junior version of baseball for learners, but shouldn't they have practiced some of the skills first? Having the defense "scramble" to put out runners doesn't seem like a way to learn the game. Where's the force play? What requires a tag? Where should the outfielder throw the ball? Where should the infielders position themselves to take a throw from the outfield? Who's the cutoff man? It's a complex game with many combinations of variables.
I don't know why there's such an "either / or" mindset when it comes to teaching math.
> shouldn't they have practiced some of the skills first
My first reaction here is "no". Take any pro, semi-pro, or skilled amateur in any sport. My guess is very few of them had "skill practice" as their first experience with the discipline.
> I don't know why there's such an "either / or" mindset when it comes to teaching math.
Personally, I'm proposing "both / and" not "either / or" – a blend of practice and performance. Why that should be possible in sports, music, theater, other school subjects, but somehow ... not in math?
Speaking in my capacity as a T-Ball coach, yeah, we don't start with the game. We start with practicing hitting, running, fielding, in isolation.
But false dichotomies are lurking here too, because guess what? Hitting off a tee is fun. It's also a game. So is running. And the game itself is at first incomprehensible to the kids. I'm talking about 4-5 year olds. In our league we make them play a game at the end of practice, and from their perspective it's just hitting and then running.
Also: for the next age group there is indeed a lot of random scrambling on defense. It's such a mess, lol.
But OK my main point is that "skill practice" is its own game. Kids like hitting off of tees, trying to get grounders, catch and throw, etc. And don't misunderstand me as saying you can "gamify" skill practice; I'm saying it's fun. And I mean to say precisely the same thing for math.
I think the first thing every professional baseball player did in the sport was to "play catch." They learned to throw and catch. That's not even close to being the game, but it's definitely a part of it. And I agree that math should be a blend of practice and performance, but I'm sensing the disagreement in this community is about what comprises "practice." Musicians, athletes, performers will tell you practice is often repetitive, but if that happens in math, it's labelled illegitimate. For example, your reaction to the little stamp that created practice problems implied that type of practice is useless. It would literally be like 5 minutes of headwork. That's not legit practice? A means to an end? It would be a small portion of an overall math classroom.
Perhaps catch is the first thing some experience, but I believe watching a game is more likely the first exposure to the game. Seeing other play makes the main skills very relevant. A kid knows why throwing is important, even if it's just because it happens a lot. Same with hitting. Now if someone has never seen the game before, then I like Michael's take: you make a game out of the skill. "See if you can hit the ball" is a game, and the why behind it is so obvious. I also liked that he had them play a game at the end. The fun fundamentals first (no pun or alliteration intended), and then the whole task shortly thereafter. Personally, I'd ideally like take the kids to a baseball game first so they can see it, but that's an unrealistic expectation.
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.
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 know I'm super late to this board, but I find your comments very insightful and interesting. Here's another response from me.
Music is a bit trickier, but I would go into music theory. A local music school teaches music theory to kids for a year before teaching them how to play the piano and it's interesting to see how they see music. Practice is essential, but understanding why the music moves the way it does is akin to knowing why we throw balls in a given sport.
When it comes to math, I like the Hey Arnold episode (dating myself a bit) where the "dumb" bully realizes that what he called business was actually math (https://youtu.be/WWntLJNx54Q?t=230). It's the real-life application of math that takes the character from a failing math student to one who (barely) passes.
As for an action similar to rehearsing in math, prepping for a test is probably the best example.
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.
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?>
Yet, learning baseball is broken down into drills and skills practice. There's nothing wrong with a junior version of baseball for learners, but shouldn't they have practiced some of the skills first? Having the defense "scramble" to put out runners doesn't seem like a way to learn the game. Where's the force play? What requires a tag? Where should the outfielder throw the ball? Where should the infielders position themselves to take a throw from the outfield? Who's the cutoff man? It's a complex game with many combinations of variables.
I don't know why there's such an "either / or" mindset when it comes to teaching math.
> shouldn't they have practiced some of the skills first
My first reaction here is "no". Take any pro, semi-pro, or skilled amateur in any sport. My guess is very few of them had "skill practice" as their first experience with the discipline.
> I don't know why there's such an "either / or" mindset when it comes to teaching math.
Personally, I'm proposing "both / and" not "either / or" – a blend of practice and performance. Why that should be possible in sports, music, theater, other school subjects, but somehow ... not in math?
Speaking in my capacity as a T-Ball coach, yeah, we don't start with the game. We start with practicing hitting, running, fielding, in isolation.
But false dichotomies are lurking here too, because guess what? Hitting off a tee is fun. It's also a game. So is running. And the game itself is at first incomprehensible to the kids. I'm talking about 4-5 year olds. In our league we make them play a game at the end of practice, and from their perspective it's just hitting and then running.
Also: for the next age group there is indeed a lot of random scrambling on defense. It's such a mess, lol.
But OK my main point is that "skill practice" is its own game. Kids like hitting off of tees, trying to get grounders, catch and throw, etc. And don't misunderstand me as saying you can "gamify" skill practice; I'm saying it's fun. And I mean to say precisely the same thing for math.
I think the first thing every professional baseball player did in the sport was to "play catch." They learned to throw and catch. That's not even close to being the game, but it's definitely a part of it. And I agree that math should be a blend of practice and performance, but I'm sensing the disagreement in this community is about what comprises "practice." Musicians, athletes, performers will tell you practice is often repetitive, but if that happens in math, it's labelled illegitimate. For example, your reaction to the little stamp that created practice problems implied that type of practice is useless. It would literally be like 5 minutes of headwork. That's not legit practice? A means to an end? It would be a small portion of an overall math classroom.
Perhaps catch is the first thing some experience, but I believe watching a game is more likely the first exposure to the game. Seeing other play makes the main skills very relevant. A kid knows why throwing is important, even if it's just because it happens a lot. Same with hitting. Now if someone has never seen the game before, then I like Michael's take: you make a game out of the skill. "See if you can hit the ball" is a game, and the why behind it is so obvious. I also liked that he had them play a game at the end. The fun fundamentals first (no pun or alliteration intended), and then the whole task shortly thereafter. Personally, I'd ideally like take the kids to a baseball game first so they can see it, but that's an unrealistic expectation.
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 know I'm super late to this board, but I find your comments very insightful and interesting. Here's another response from me.
Music is a bit trickier, but I would go into music theory. A local music school teaches music theory to kids for a year before teaching them how to play the piano and it's interesting to see how they see music. Practice is essential, but understanding why the music moves the way it does is akin to knowing why we throw balls in a given sport.
When it comes to math, I like the Hey Arnold episode (dating myself a bit) where the "dumb" bully realizes that what he called business was actually math (https://youtu.be/WWntLJNx54Q?t=230). It's the real-life application of math that takes the character from a failing math student to one who (barely) passes.
As for an action similar to rehearsing in math, prepping for a test is probably the best example.
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.