I’d say that about the first half of Calculus I was useful to me, taught concepts.
However, a lot of the rest of it, as well as most of the next two calculus classes I took, involved memorizing tricks to do symbolic integration by hand. That is, frankly, of limited use to even people who need to do symbolic integration.
I remember going by my calculus professor’s husband’s (another math professor) office once to deal with some project I was doing and some integration came up and he promptly threw it into Mathematica on his computer to do it. I commented on it and he said “yeah, I don’t have time to spend doing these by hand”.
My smartphone and computers have Maxima installed, a free and open-source computer algebra system capable of doing symbolic integration. I have that with me all the time. It’s very rare that I need to do symbolic integration in the first place.
“But what if you don’t have a calculator with you?”
Today, that’s usually a smartphone, but same idea.
In my parent’s generation, they taught people to manually compute square roots. It was some numerical approximation, don’t know what they did exactly, probably something like “pick a number, divide, average result and divisor, repeat with average”. They didn’t bother to teach that by the time I was going to school. It was just expected that you’d use a calculator.
I remember reading Richard Feynman’s book, about how he used to show off some mental math shortcuts (much more useful in an era before calculators).
I agree that memorizing certain mental math processes can be useful, but the time wasted on doing symbolic integration in calculus is still one of my major annoyances, looking back. There is no shortage of material in mathematics that is useful and could be in the curriculum, and instead we did symbolic integration.
Math education is a disaster. It seems to be thought of as symbolic calculation busywork that’s supposed to translate to a good job somehow. I respected the proofwriting classes a lot more than the number crunching ones
At least when I was in school, one thing that kept getting hammered home was that people had difficulty understanding graphs. That I didn’t see as being an issue, not unless you’re talking about something pretty exotic, but if accurate, it seems like it’d be pretty limiting. And I’ve seen a lot of later articles also saying that a lot of people have trouble with graph comprehension.
Last month, Alessandro Romano, Chiara Sotis, Goran Dominioni, and Sebastián Guidi surveyed 2,000 people to demonstrate that “the public do not understand logarithmic graphs used to portray COVID-19.”
They found that only 41% of participants could correctly answer basic questions about log-scaled graphs (v.s. 84% accuracy for linear-scale).
But the problem is harder than log scales. As you’ll see below, much of “the public” struggle with even the most basic charts and graphs, let alone complex visualizations.
I wish they’d had more statistics. In my high school, they had half a semester as an elective. In my university curriculum, it wasn’t a core class (social science majors would study it, I would guess).
I have explained basic sampling to a ton of people on Reddit when polls came up, because they didn’t believe that a sample of 1000 people out of a much larger population could result in a representative outcome. We see poll data all the time. Even if you never perform a poll, understanding the mechanism at least enough to trust it and understand when a poll might not be representative (e.g. self-selecting Internet polls). Confidence levels. I think I covered regressions in high school in an (elective) physics class, not even in a statistics class. That’s a useful skill – get a bunch of numbers, be able to produce a formula to predict more of them and get an idea of how accurate your model is. I assume that if you didn’t take it or it wasn’t offered, then you just wouldn’t ever touch on them.
Have you looked at math education in the US in the last 15 years? Because it is a lot better than the bullshit they did when I was a kid.
Now kids get an actual understanding and hence intuition about all of it instead of the 1970s approach: “this is the rule, you don’t have to understand it; now, shut up and do it!”
Also, they teach kids about useful shit now like media literacy. In elementary and middle school. And they teach them a bit about economics, jobs, salaries, and budgets.
My kid is a freshman in HS now so I can’t speak to whether they teach about personal finance type stuff but I would be surprised if they don’t given the track record so far.
It’s telling how many parents complained because they can’t understand their third grader’s math homework. Math intuition and understanding should be the main focus at the earlier grades and crap like rote memorization of the times tabs should be dropped. Maybe I’d even teach formal logic and basic proofs in middle/high school (besides just geometry class)
I’d say that about the first half of Calculus I was useful to me, taught concepts.
However, a lot of the rest of it, as well as most of the next two calculus classes I took, involved memorizing tricks to do symbolic integration by hand. That is, frankly, of limited use to even people who need to do symbolic integration.
I remember going by my calculus professor’s husband’s (another math professor) office once to deal with some project I was doing and some integration came up and he promptly threw it into Mathematica on his computer to do it. I commented on it and he said “yeah, I don’t have time to spend doing these by hand”.
My smartphone and computers have Maxima installed, a free and open-source computer algebra system capable of doing symbolic integration. I have that with me all the time. It’s very rare that I need to do symbolic integration in the first place.
“But what if you don’t have a calculator with you?”
Today, that’s usually a smartphone, but same idea.
In my parent’s generation, they taught people to manually compute square roots. It was some numerical approximation, don’t know what they did exactly, probably something like “pick a number, divide, average result and divisor, repeat with average”. They didn’t bother to teach that by the time I was going to school. It was just expected that you’d use a calculator.
I remember reading Richard Feynman’s book, about how he used to show off some mental math shortcuts (much more useful in an era before calculators).
I agree that memorizing certain mental math processes can be useful, but the time wasted on doing symbolic integration in calculus is still one of my major annoyances, looking back. There is no shortage of material in mathematics that is useful and could be in the curriculum, and instead we did symbolic integration.
Maybe curriculum has improved since then.
Math education is a disaster. It seems to be thought of as symbolic calculation busywork that’s supposed to translate to a good job somehow. I respected the proofwriting classes a lot more than the number crunching ones
At least when I was in school, one thing that kept getting hammered home was that people had difficulty understanding graphs. That I didn’t see as being an issue, not unless you’re talking about something pretty exotic, but if accurate, it seems like it’d be pretty limiting. And I’ve seen a lot of later articles also saying that a lot of people have trouble with graph comprehension.
googles
https://towardsdatascience.com/numeracy-and-graph-literacy-in-the-united-states-ea2a11251739
I wish they’d had more statistics. In my high school, they had half a semester as an elective. In my university curriculum, it wasn’t a core class (social science majors would study it, I would guess).
I have explained basic sampling to a ton of people on Reddit when polls came up, because they didn’t believe that a sample of 1000 people out of a much larger population could result in a representative outcome. We see poll data all the time. Even if you never perform a poll, understanding the mechanism at least enough to trust it and understand when a poll might not be representative (e.g. self-selecting Internet polls). Confidence levels. I think I covered regressions in high school in an (elective) physics class, not even in a statistics class. That’s a useful skill – get a bunch of numbers, be able to produce a formula to predict more of them and get an idea of how accurate your model is. I assume that if you didn’t take it or it wasn’t offered, then you just wouldn’t ever touch on them.
Have you looked at math education in the US in the last 15 years? Because it is a lot better than the bullshit they did when I was a kid.
Now kids get an actual understanding and hence intuition about all of it instead of the 1970s approach: “this is the rule, you don’t have to understand it; now, shut up and do it!”
Also, they teach kids about useful shit now like media literacy. In elementary and middle school. And they teach them a bit about economics, jobs, salaries, and budgets.
My kid is a freshman in HS now so I can’t speak to whether they teach about personal finance type stuff but I would be surprised if they don’t given the track record so far.
It’s telling how many parents complained because they can’t understand their third grader’s math homework. Math intuition and understanding should be the main focus at the earlier grades and crap like rote memorization of the times tabs should be dropped. Maybe I’d even teach formal logic and basic proofs in middle/high school (besides just geometry class)