I get what the author is frustrated with, although I don't necessarily agree with his conclusion that you aren't doing math - you are doing math, but you are not learning to use math the way it should be used (in his music analogy - you are learning music, but you are not learning to use music the way it should be used, which requires actually playing). It's a common, and valid complaint about American education - we are very good at stripping out all practical applications of a subject and simply teaching a method for solving a problem that is completely unrelated to anything in reality. In one of Richard Feynman's books, he writes about his experience editing textbooks. He notices this, and in his typically fantastic way, rips the textbooks to shreds. One of his examples went something like this:
Some problem, while accurate in that the process to get to the answer worked, was a word problem. Part of this problem read "The Earth has two suns. One is blue, the other is green." He stops this early in the problem, since even here, they have made the problem about something that is completely unrelated to reality. Think back to high school - you have not lived long enough (in most cases) to be able to mentally reapply a process to a problem you have had in your own life, so education should be going far out of its way to present problems in a way that the kids encountering them can understand. The Wire had a great example - using gambling to teach probability (there's a moral argument there that I won't touch - the point is the kids could understand why they were learning math, since it solved a problem or gave them an advantage that they could immediately relate to). Programming could help with this (I haven't taken a math class since my senior year of high school, and always did well in all of them, but I feel like I understand why I would use algebra better now than ever, since I can actually relate to the concept of variables in reality, rather than "make the numbers into letters"). Baseball has taught me more about statistics and data analysis than any class I ever took.
I remember learning about finding the slope of an equation in 7th grade. I had a huge argument with my teacher (I was a bit of a handful back then), because she actually could not give me a single example of why I would ever need to care about the slope of a line beyond future math classes. That's a problem.
TL;DR - The author is likely more frustrated with American education's tendency to remove all relatability from a subject (and then not arming teacher's with good examples of how to reapply the methods they learned to a problem that encourages more investigation) than he is strictly accurate about students not actually doing math. And I agree.
It is interesting that the author had to portray a hypothetical scenario of learning music theory and never practising to get his point (which I more or less agree with) across.
Sometimes, it is necessary to create unrealistic scenarios and problems because real world problems may be too complicated for beginners. So you end up oversimplifying. In this process, sometimes the essence of the material is lost.
A solution is to pay equal attention to the problem sets and examples as the rest of the course content.
His point is that you're not doing "math" in Algebra class because "math" (as practiced by mathematicians) is actually a highly creative process, and there's nothing creative about, e.g., word problems.
Some problem, while accurate in that the process to get to the answer worked, was a word problem. Part of this problem read "The Earth has two suns. One is blue, the other is green." He stops this early in the problem, since even here, they have made the problem about something that is completely unrelated to reality. Think back to high school - you have not lived long enough (in most cases) to be able to mentally reapply a process to a problem you have had in your own life, so education should be going far out of its way to present problems in a way that the kids encountering them can understand. The Wire had a great example - using gambling to teach probability (there's a moral argument there that I won't touch - the point is the kids could understand why they were learning math, since it solved a problem or gave them an advantage that they could immediately relate to). Programming could help with this (I haven't taken a math class since my senior year of high school, and always did well in all of them, but I feel like I understand why I would use algebra better now than ever, since I can actually relate to the concept of variables in reality, rather than "make the numbers into letters"). Baseball has taught me more about statistics and data analysis than any class I ever took.
I remember learning about finding the slope of an equation in 7th grade. I had a huge argument with my teacher (I was a bit of a handful back then), because she actually could not give me a single example of why I would ever need to care about the slope of a line beyond future math classes. That's a problem.
TL;DR - The author is likely more frustrated with American education's tendency to remove all relatability from a subject (and then not arming teacher's with good examples of how to reapply the methods they learned to a problem that encourages more investigation) than he is strictly accurate about students not actually doing math. And I agree.