Mathematics is a language.
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So, when you point out innumeracy I think you should explain it with patience. Explain it understanding that some people who may be well informed and intelligent in other matters might not understand why, for example, decreasing by more than 100 percent is nonsense.
(100 percent is all of something. A 50 percent decrease is half. '100 percent decrease means' it's zero. Decrease by more than 200 percent? means it's less than zero, negative. Negative prices make no sense. )
@futurebird What do you reckon the percentage of people is who understand that the reverse of going up 30% is not going down 30%
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@futurebird What do you reckon the percentage of people is who understand that the reverse of going up 30% is not going down 30%
Among adults? At least like 70 percent. It's not obvious, and in many cases the numerical difference isn't that great...
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@futurebird What do you reckon the percentage of people is who understand that the reverse of going up 30% is not going down 30%
This is one of the neat wrinkles of how percentages work, but I think the most important thing to understand about percents is that they allow us to compare changes in quantities of different sizes.
1,000 people moving to NYC isn't the same as 1,000 people moving to a town with a population of 300.
How do you compare those population increases in a way that makes sense?
A fraction could work, but using a fraction out of 100 is very practical and easy to understand.
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Mathematics is a language. But innumeracy is also a language and our president is fluent.
It's not just that he exaggerates, lies, and says things that make no sense when talking about numbers "often" no this is something deeper.
He is deeply committed to *never* speaking about any statistic or numerical fact in a way that would suggest that it's important to understand how basic math works, or even that it exists at all.
This isn't just ignorance or laziness, it's one of his core values.
@futurebird He's literally done this billions of times.
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@futurebird He's literally done this billions of times.
It just keeps increasing very strongly. He never uses numbers correctly they are 1000 percent more wrong every day. We are seeing this happening worse and worse it's going down to levels of incorrect that have never been seen.
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Mathematics is a language. But innumeracy is also a language and our president is fluent.
It's not just that he exaggerates, lies, and says things that make no sense when talking about numbers "often" no this is something deeper.
He is deeply committed to *never* speaking about any statistic or numerical fact in a way that would suggest that it's important to understand how basic math works, or even that it exists at all.
This isn't just ignorance or laziness, it's one of his core values.
@futurebird In high school, I loved geometry. Doing proofs was fun! But I noped out of math when I was the only female in an algebra class taught by the football coach (who obviously did NOT love math). It was years later that I took math classes again and discovered that math was again fun. Trig identities, whee!
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@futurebird In high school, I loved geometry. Doing proofs was fun! But I noped out of math when I was the only female in an algebra class taught by the football coach (who obviously did NOT love math). It was years later that I took math classes again and discovered that math was again fun. Trig identities, whee!
I was the only girl (and black person) in a calculus course taught by the wrestling coach. LMAO.
I only made it past that one because mom knew calculus and told me she would kill me if I didn't learn it and I think she would have. To this day.
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I was the only girl (and black person) in a calculus course taught by the wrestling coach. LMAO.
I only made it past that one because mom knew calculus and told me she would kill me if I didn't learn it and I think she would have. To this day.
To be fair to "Mr. P" he tried. But you could tell the other math teachers cornered him into teaching that course.
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@futurebird When I was still teaching maths, there were a few things I liked to do specifically to reel in the students who had ended up internalizing a story that they were bad at maths and that maths was incomprehensible arcane magic only used by people with very special brains.
The first was to try to emphasize how *human* a lot of our conception of maths is. (It helps here that I'm not a mathematical platonist.) Why do we use base 10? Why did the practice of writing mathematical proofs first pop up in ancient India and Greece, even though eg. Babylonians had been using pretty advanced maths for millennia without bothering to prove anything? Why has so much of mathematical history been preoccupied with finding the "essence" of various constructs; is it just a coincidence that that came out of a culture that had a strong essentialist inclination?
The second was closely related to the first: Putting human faces on all these things. Did you know Pythagoras was deathly afraid of beans, and also that he was the leader of a weird cult? Or that Georg Cantor spent his later years trying to convince everyone that William Shakespeare was actually Francis Bacon writing under a cover name? That we have no reliable biographical information about Euclid at all, and that he may not have been a single individual at all? That Emmy Noether kept teaching out of her own apartment after the Nazis excluded her from the university? I've had many students - *especially* the ones less comfortable with numbers and pure maths - tell me that they could use some of all these little things as "handles" to jog their memories.
The third was to pose absurd questions that had non-obvious answers that maths clearly illuminated. Are there two people in Denmark who have exactly the same number of hair follicles on their heads? (There's about 150.000 hair follicles on an average Scandinavian head and about six million people in Denmark, so...). The story of Abraham Wald and the airplane armouring, the Linda Paradox, a Zombie Apocalypse version of the river crossing problem, etc.
Mostly, I tried to show students that maths is not an exclusive club at all. I won't say I succeeded evenly, but I know many of them appreciated it.
I'd be interested in getting the answer to your question "Why did the practice of writing mathematical proofs first pop up in ancient India and Greece, even though eg. Babylonians had been using pretty advanced maths for millennia without bothering to prove anything?"
I never thought about it...
(I don't think that I thought much about Babylonian mathematics, actually) -
I'd be interested in getting the answer to your question "Why did the practice of writing mathematical proofs first pop up in ancient India and Greece, even though eg. Babylonians had been using pretty advanced maths for millennia without bothering to prove anything?"
I never thought about it...
(I don't think that I thought much about Babylonian mathematics, actually)Mathematical proofs are as much about philosophy "what (and how) can we know?" as they are about math. In fact, math is simply a subject that is very well suited to deductive reasoning systems. You can accomplish a lot in math with such systems because it's possible (and efficient) to agree on definitions and axioms. This isn't true with ethics, for example.
We apply them in math with hidden hubris that they may solve everything eventually.
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I'm curious what level math you teach. Higher math to older kids or basic arithmetic to the young 'uns?
If it's arithmetic, would you fail your smartest student for answering everything right by doing it in his head without showing his work? That happened to me. I got zeroes on all the tests with every answer right while the kid next to me got a B+ with every answer wrong, she just filled in a bunch of random digits in the proper format.
I teach grades 5 through 12, and I also teach college level courses. The breadth of what I teach is a little unusual but it gives me an interesting perspective and some very strong opinions on math education because I see where problems start and how they develop.
"If it's arithmetic, would you fail your smartest student for answering everything right by doing it in his head without showing his work?"
Absolutely not. Unless the question was "explain your reasoning."
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I teach grades 5 through 12, and I also teach college level courses. The breadth of what I teach is a little unusual but it gives me an interesting perspective and some very strong opinions on math education because I see where problems start and how they develop.
"If it's arithmetic, would you fail your smartest student for answering everything right by doing it in his head without showing his work?"
Absolutely not. Unless the question was "explain your reasoning."
It's worth thinking about when you start asking students to "explain your reasoning?" too early and it get in the way of doing the reasoning in the first place.
I tend to think that around age 13, 14 these kinds of questions become appropriate. And eventually mandatory.
But if I want a student to tell me WHY the question should make that very clear. Most of the time I just want the answer and I want it to be correct.
