it's that there seems to be this strain in elementary education of NOT giving problem sets at all
Ah, yes, if we're talking about elementary school, then I'm on board with a problem-set oriented approach. For the simple reason that you're going to actually use this in real life.
Starting around middle school and definitely by high school, whether you're going to use this math is highly career- and interest-dependent. If you're not, at best you need the concepts. If you are--well, I submit that you need the concepts all the more.
So I would make problem sets a whole lot more optional at this stage, make it clear what skills are needed for what, and teach how to acquire these skills if you decide later in life that you're going to want them. (Much of my pedagogical reform is teaching students what information is out there, why you would need it, and how to go about learning it, over preselecting some random subset of information that may or may not be important for them, then forcing them to learn it when they're just going to forget it.)
The one branch of math I know I would make mandatory at the post-elementary math level is statistical concepts. Because at one point I made excellent grades based on my (promptly-forgotten) memorized ability to calculate sigma and whatnot, but I made it to almost the end of grad school without understanding what a standard deviation was, and most people still don't.
Number of times I've needed to calculate a standard deviation in my life: well, maybe for my dissertation, but other than that, 0.
Number of times I've needed to understand what a standard deviation is? A very, very large number.
People are going to encounter claims about science in the news/on social media, and statistical concepts are just not taught. You get problem sets on calculating Greek and Roman letters, but not taught how to evaluate claims, and then we end up with a very ill-informed population.
Trigonometry, which I had a whole year of in high school? It was fun because I was a math geek, but that's not the class I would make mandatory for all college-bound students.
Re: Grad school
Ah, yes, if we're talking about elementary school, then I'm on board with a problem-set oriented approach. For the simple reason that you're going to actually use this in real life.
Starting around middle school and definitely by high school, whether you're going to use this math is highly career- and interest-dependent. If you're not, at best you need the concepts. If you are--well, I submit that you need the concepts all the more.
So I would make problem sets a whole lot more optional at this stage, make it clear what skills are needed for what, and teach how to acquire these skills if you decide later in life that you're going to want them. (Much of my pedagogical reform is teaching students what information is out there, why you would need it, and how to go about learning it, over preselecting some random subset of information that may or may not be important for them, then forcing them to learn it when they're just going to forget it.)
The one branch of math I know I would make mandatory at the post-elementary math level is statistical concepts. Because at one point I made excellent grades based on my (promptly-forgotten) memorized ability to calculate sigma and whatnot, but I made it to almost the end of grad school without understanding what a standard deviation was, and most people still don't.
Number of times I've needed to calculate a standard deviation in my life: well, maybe for my dissertation, but other than that, 0.
Number of times I've needed to understand what a standard deviation is? A very, very large number.
People are going to encounter claims about science in the news/on social media, and statistical concepts are just not taught. You get problem sets on calculating Greek and Roman letters, but not taught how to evaluate claims, and then we end up with a very ill-informed population.
Trigonometry, which I had a whole year of in high school? It was fun because I was a math geek, but that's not the class I would make mandatory for all college-bound students.