Note: I’m trying out audio narration for at least a few articles to see how much value people get out of it, but it takes a fair amount of time to do. Please don’t be shy with the feedback if it’s something you use - feedback helps. Isaac Asimov’s Dreaming Is a Private Thing
Thanks for the article. Your comment on common core math being developed by absconding with the smart kids' shortcuts and trying to force those shortcuts on everyone--regardless of innate ability or learning style--makes a lot of sense.
The more examples I see of common core math, the more thankful I am that I graduated before that became a thing. I love math, and I've always been good at it (including at a university level; I have a STEMmy degree that required calculus, differential equations, and linear algebra). I can see what common core math is trying to do, but I expect it would have felt confusing and arbitrary if I was taught that method with none of my own experience or intuition to fall back on. I don't know if this is a personal quirk or a general rule, but I've always found that rote memorizing the basics (be it multiplication tables, phonics, or foreign alphabets) is crucial to understanding the more difficult areas of each subject.
I think the problem comes back to the fact that we've never really addressed the question of 'why is studying math valuable'. And while opinions of this will obviously vary, my own is that math is important because of its ability to train your brain to approach problems in a very specific way, and that way is transferable to just about every discipline/pursuit there is.
What does math teach you? I think it boils down to two things.
1) It teaches you how to train the entirety of your attention on a single problem for > 30 seconds.
2) It teaches you that becoming frustrated will destroy your ability to solve a problem.
The ability to avoid getting frustrated, and to focus on a single problem for more than 30 seconds, are just enormously valuable skills that are worth cultivating-- and they apply to everything from analyzing stock values to glazing windows. Moreover, you can cultivate those skills via math regardless of what 'method' your using to solve the problem. If you believe that math is important because of how it trains your mind, and not because of the earning potential of the people who master it, then a lot of these questions about 'how to teach it' start looking irrelevant.
As an academic myself, I feel like that the last quote from the paper is the standard "our data might be incorrect so take the findings with a grain of salt" disclaimer that has to appear in every paper nowadays, (otherwise reviewers are quick to point out that the data might be incorrect!), rather than an attempt to spin results in their own way.
Air Traffic Control is another domain where "not every skill can be taught to every kind of person, and sometimes it’s harmful to try" applies.
Lots of people get 80 to 90% of the way, but can never make it over the last hurdle. All the extra training and studying in the world doesn't help at this point. And continuing training beyond a certain point results in stress, exhaustion, added costs, etc.
I've always wondered though if changing the training structure would yield a higher number of controllers (for example, say 3 in 10 versus 1 in 10). In other words, even though some people just can't be taught the skills needed, some people could probably still make it but don't because the training program falls short.
Common core focused on reading too, though, which kinda undermines your argument about STEM. It wasn't only a math thing, the math thing simply became a culture war rallying cry for the right.
Thanks for the article and podcast. I found it super useful and thought you did an excellent job! Practical feedback would be: the backing music isn't needed for the entire podcast - I listen to podcasts on 1.8x speed and the music can be quite distracting and doesn't add to what you're saying; when describing pictures I feel that if you're better cutting your losses and just saying look at the post to understand as "badly" describing it is probably worse than not describing it at all (not saying you were bad this time, it's just something that could happen); when describing an external link (just saying 'link in post' automatically might help maintain the flow); linking directly to the post in the episode description would be handy. Otherwise I hope you keep it up, definitely would mean I would engage with more of your stuff if you kept this up.
I'm mostly with you, with a few quibbles. First, thank you for the exposition. The weird-ass subtraction example actually seemed really analogous to long division -- call it long subtraction. The mildly racist poster you called "long division" is actually <i>short</i> division, the difference being that in short division you always guess right about what the next digit is, while in long division you can try 6 and subtract out whatever that gives you and then try 2 and then if you have to even 1, and add it all up at the end. So maybe the theory is that "long subtraction" is actually easier for a slow student than learning the shortest-time algorithm with borrowing and all that jazz, not that the manipulation is supposed to make them comfortable with numbers.
Dunno, I've never read any of the educational theory behind common core, or any educational theory for that matter.
One of the other problems with common core is that parents aren't able to tutor their children in math, because they themselves haven't learned the new techniques. This has the effect of cementing teachers as the gatekeepers of educational success. We should be making it easier for parents to take an interest in their child's education, and making parental tutoring more streamlined and normal.
I enjoyed this, but would have been interested for more discussion of the theory behind common core math from the perspective of its proponents. I agree with your critique of the one line of pro-common core thinking you discussed, but am curious how much of the argument for common core is driven by that line of thinking.
(Of course, that's a lot to ask from a blog post - this was already good!)
Of course the narration is useful; I don’t have to be sitting in front of and staring at the text every second in order to be consuming the article.
BUT why are you using “tick” in this sense up there in the text...isn’t it really a Britishism? (The Internet-Age proliferation of Britishisms among Americans is my pet peeve. And why, you ask. It may have something to do with me being a crank.)
Thanks for the article. Your comment on common core math being developed by absconding with the smart kids' shortcuts and trying to force those shortcuts on everyone--regardless of innate ability or learning style--makes a lot of sense.
The more examples I see of common core math, the more thankful I am that I graduated before that became a thing. I love math, and I've always been good at it (including at a university level; I have a STEMmy degree that required calculus, differential equations, and linear algebra). I can see what common core math is trying to do, but I expect it would have felt confusing and arbitrary if I was taught that method with none of my own experience or intuition to fall back on. I don't know if this is a personal quirk or a general rule, but I've always found that rote memorizing the basics (be it multiplication tables, phonics, or foreign alphabets) is crucial to understanding the more difficult areas of each subject.
I think the problem comes back to the fact that we've never really addressed the question of 'why is studying math valuable'. And while opinions of this will obviously vary, my own is that math is important because of its ability to train your brain to approach problems in a very specific way, and that way is transferable to just about every discipline/pursuit there is.
What does math teach you? I think it boils down to two things.
1) It teaches you how to train the entirety of your attention on a single problem for > 30 seconds.
2) It teaches you that becoming frustrated will destroy your ability to solve a problem.
The ability to avoid getting frustrated, and to focus on a single problem for more than 30 seconds, are just enormously valuable skills that are worth cultivating-- and they apply to everything from analyzing stock values to glazing windows. Moreover, you can cultivate those skills via math regardless of what 'method' your using to solve the problem. If you believe that math is important because of how it trains your mind, and not because of the earning potential of the people who master it, then a lot of these questions about 'how to teach it' start looking irrelevant.
As an academic myself, I feel like that the last quote from the paper is the standard "our data might be incorrect so take the findings with a grain of salt" disclaimer that has to appear in every paper nowadays, (otherwise reviewers are quick to point out that the data might be incorrect!), rather than an attempt to spin results in their own way.
Great article!
I have a few comments about the audio narration, since you asked for feedback:
1. You have a nicely crisp and distinct voice.
2. I gave up on listening once you got to the memes and I realized I could just go take a look at them for myself.
3. A more relaxed approach to reading the article might be better: you sounded pretty stressed out and I don't think that's what you were going for.
Air Traffic Control is another domain where "not every skill can be taught to every kind of person, and sometimes it’s harmful to try" applies.
Lots of people get 80 to 90% of the way, but can never make it over the last hurdle. All the extra training and studying in the world doesn't help at this point. And continuing training beyond a certain point results in stress, exhaustion, added costs, etc.
I've always wondered though if changing the training structure would yield a higher number of controllers (for example, say 3 in 10 versus 1 in 10). In other words, even though some people just can't be taught the skills needed, some people could probably still make it but don't because the training program falls short.
The narration was well done and I appreciate the speed being adjustable. I think the narration is a great addition.
Common core focused on reading too, though, which kinda undermines your argument about STEM. It wasn't only a math thing, the math thing simply became a culture war rallying cry for the right.
Thanks for the article and podcast. I found it super useful and thought you did an excellent job! Practical feedback would be: the backing music isn't needed for the entire podcast - I listen to podcasts on 1.8x speed and the music can be quite distracting and doesn't add to what you're saying; when describing pictures I feel that if you're better cutting your losses and just saying look at the post to understand as "badly" describing it is probably worse than not describing it at all (not saying you were bad this time, it's just something that could happen); when describing an external link (just saying 'link in post' automatically might help maintain the flow); linking directly to the post in the episode description would be handy. Otherwise I hope you keep it up, definitely would mean I would engage with more of your stuff if you kept this up.
I'm mostly with you, with a few quibbles. First, thank you for the exposition. The weird-ass subtraction example actually seemed really analogous to long division -- call it long subtraction. The mildly racist poster you called "long division" is actually <i>short</i> division, the difference being that in short division you always guess right about what the next digit is, while in long division you can try 6 and subtract out whatever that gives you and then try 2 and then if you have to even 1, and add it all up at the end. So maybe the theory is that "long subtraction" is actually easier for a slow student than learning the shortest-time algorithm with borrowing and all that jazz, not that the manipulation is supposed to make them comfortable with numbers.
Dunno, I've never read any of the educational theory behind common core, or any educational theory for that matter.
One of the other problems with common core is that parents aren't able to tutor their children in math, because they themselves haven't learned the new techniques. This has the effect of cementing teachers as the gatekeepers of educational success. We should be making it easier for parents to take an interest in their child's education, and making parental tutoring more streamlined and normal.
I enjoyed this, but would have been interested for more discussion of the theory behind common core math from the perspective of its proponents. I agree with your critique of the one line of pro-common core thinking you discussed, but am curious how much of the argument for common core is driven by that line of thinking.
(Of course, that's a lot to ask from a blog post - this was already good!)
Thanks for the audio! I would read if it didn't exist, but I'll probably subscribe via podcast rss if you keep doing it.
Of course the narration is useful; I don’t have to be sitting in front of and staring at the text every second in order to be consuming the article.
BUT why are you using “tick” in this sense up there in the text...isn’t it really a Britishism? (The Internet-Age proliferation of Britishisms among Americans is my pet peeve. And why, you ask. It may have something to do with me being a crank.)