...Lol, how have we not talked about this yet? Because I've been saying for years (although apparently not in DW spaces that you've seen or that I can find now -- I know I've said it on DW but possibly in other people's comment spaces) that 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). One could maaaaaybe argue for geometry under "liberal arts education," the same way that reading Shakespeare also isn't something that anyone needs, I suppose, but I'm skeptical about that as well. Obviously, I'd encourage kids to take more math when they had interest/ability, but what the current scheme produces is a lot of adults who hate and despise math, and I don't really see how this is a good thing?? 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 -- some of the kinds of things we do in salon, honestly, where one reads a text/article/whatever, thinks about "did the author have an axe to grind when writing this? Do we know this either from context or from interrogating the text?" [HI VOLTAIRE] and what kind of biases are being brought to it, and how wording can contribute to bias even when factually correct, and how emphasizing/de-emphasizing information can contribute to bias. I think there may be some classes that do this, and I know one probably learns that in history in the college/grad-school level, but I never got anything like this -- and it's relevant ALL THE TIME when reading crap off the internet or news articles or whatever! (And Voltaire! ;) )
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!
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!