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Historical Characters, Including Frederick the Great, Discussion Post 40
I'm trying to use my other account at least occasionally so I posted about my Yuletide gifts there, including the salon-relevant 12k fic that features Fritz, Heinrich, Voltaire, Fredersdorf, Saint Germain, Caroline Daum (Fredersdorf's wife), and Groundhog Day tropes! (Don't need to know canon.)
Re: Grad school
you feel strongly about problem sets and pedagogy, and I would like to hear your thoughts.
These thoughts are not very profound (although surprisingly controversial), it's that there seems to be this strain in elementary education of NOT giving problem sets at all, even for (especially for, it seems like) skill-building, which is just ludicrous. (I totally am on board, of course, with giving problems that are more interesting than extremely dry drill -- but you can't just not practice the skills.) My kids' school has tried to do it this way, though Good Math Teacher has always tried to push back, and it looks like in the last couple of years there has been more pushback.
ETA: Early elementary math, of course, is another beast entirely, where a lot of the applicable concepts you can practice in ways other than written problem sets.
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.
Curriculum overhaul
The one thing I would differ in may be terminology -- I would absolutely have problem sets! However, they would be problem sets of the "evaluating claims" type. (The following may be more middle-school than high-school kinds of problems, for reasons that should be obvious in a couple of paragraphs, but, you know, modify as needed for high school.) E.g., "Look at this graph, tell me what the author of the graph wants you to see, and whether they are using any tricks to try to get you to see that thing." [I have in mind things like, mucking about with the axes of the graph.] Or: Here's a claim about the average salary of a graduate in this field. Does this sound reasonable? How could an "average salary" number be manipulated? Or: I'm going to show you the studies that a company did. Based on the results of the studies that they reported, do you think that they've shown their product is successful or not? [How probable is it that they could have gotten that result by chance? A more technically-oriented class might directly compute the probability, but a nontechnical class might simply build their intuition about how often things occur by chance, which is not something that people generally have a good intuition about.] Or: A company is making these claims that they can do something spectacular. What kinds of questions/tests would you do to test whether they can actually do the thing? [Theranos! I am thinking of Theranos here!] Or: ~insert your favorite "correlation is not causation" test case here!~
I stand by my assertion that problem sets are really, really useful for building skills! But the skill I want to build here is NOT "can you calculate a standard deviation," it's "can you think critically about this claim/piece of data? Let's practice doing that." This is not a skill that kids are necessarily practicing!
(Honestly, if the majority of students got out of high school understanding that correlation is not causation, and that A implies B does NOT mean that B implies A, I would feel like this was a huge win!)
I actually did a "guest lecture" with E's 6th grade class where we talked about some of this stuff and I gave them (in-class) "problems" of this sort where they talked about them as a class, and they LOVED it. (I did a followup class about bias in articles, more of the "reading critically" thing above, which was mostly OK but didn't land nearly as well -- partially because I had to thread a fine line with not making the material inflammatory or controversial, but still interesting enough that I wanted to spend time thinking about it, which meant it probably wasn't so interesting to the sixth graders; partially because E's class is weighted towards technical types; and also partially because I don't have as much facility with it myself and haven't thought about it nearly as much, lol. I'll probably try this with the sixth graders again next year -- they're on a two-year curriculum cycle -- and see if I can hit the mark better the second time around.)
I also only thought about this this morning, but I'd also put in a LOT more estimation as something that was taught in the middle school/high school level. I don't care a fig whether kids get out of school knowing that you use the quadratic formula to solve a quadratic equation (much less knowing the formula itself) (unless you're a technical person, in which case, sure, you should understand this stuff) but I want everyone to get out of high school with some facility for being able to figure out, so, if X happens to one in 1000 people, and the US has about 300 million people, that means X will happen to about 300,000 people in the US. Or the other way around! Know what numbers mean! Be able to do order of magnitude calculations and Fermi type problems, or at least come out with a sense of what you'd need to know in order to do them!
Re: Curriculum overhaul
if I could redesign the curriculum I would not require non-technically-oriented students to take advanced algebra/trig/etc. Nothing over, probably, Algebra I or so (and I'm not even totally sure about that)
YES PLEASE. I would keep enough algebra to teach at least the concepts of solving for a variable and when you might need to know it, and how to learn it, and then...most of the details can be left to the person to decide when they need to know it.
AND everyone should take statistics and probability (with a focus on "evaluating claims" as you say, more about that in a bit), and I would further make a "reading critically" class mandatory
Yes, these are two of my highest priorities!
The one thing I would differ in may be terminology -- I would absolutely have problem sets! However, they would be problem sets of the "evaluating claims" type.
Yeah, that's just a terminology difference: I've been using "problem set" to mean "working through a calculation" as opposed to other sorts of questions. Your "problem sets" I would just call "homework questions."
NOT "can you calculate a standard deviation," it's "can you think critically about this claim/piece of data? Let's practice doing that." This is not a skill that kids are necessarily practicing!
YES.
(Honestly, if the majority of students got out of high school understanding that correlation is not causation, and that A implies B does NOT mean that B implies A, I would feel like this was a huge win!)
THANK YOU.
I don't care a fig whether kids get out of school knowing that you use the quadratic formula to solve a quadratic equation (much less knowing the formula itself)
YES.
(unless you're a technical person, in which case, sure, you should understand this stuff)
Exactly!
Okay, we are on the same page more than I thought, I thought I was the only one with these opinions! Or, you know, not literally, but the only person I knew. I've encountered them online/in books, but only rarely.
Re: Grad school
Out of curiosity, is this part of the trend to not give elementary school kids homework at all, in your observation, or separate?
Re: Grad school
But also there's been a definite shift towards "teaching concepts" rather than "teaching skills," which works for early elementary and can sometimes work for older students, as well, but there's a middle ground where it's actually important to build the skills!
Re: Grad school
Huh. So in this model, are you having students practice their early elementary math skills at school and not at home? Because early elementary math is the only math where I think building up mental muscle memory/memorization for repetitive math skills is actually valuable across the general, non-technical population!
But also there's been a definite shift towards "teaching concepts" rather than "teaching skills," which works for early elementary and can sometimes work for older students, as well, but there's a middle ground where it's actually important to build the skills!
Yeah, I mean, my stance is that skills need to be taught:
1) Only when important, otherwise just teach students what skills are important for what, and how to learn more when they need it,
2) Not at the expense of concepts.
But I'm with you that some skills do need to be taught and taught well!