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And yes, it's a "high horse" topic for me because I hear so many people saying, "Now that computers can do all the math for us, why are we making kids learn math?"
Given Facebook, Twitter, politicians, and the other vast seas of misinformation available at our fingertips, I'd argue that now more than ever we need our kids to have strong critical thinking skills.
(And yes, I also think a class in rhetoric should be a requirement to graduate from high school. The more critical thinking, the better.)
EDIT: Do you like the view from my high horse?
Once we stopped finding out what x was i really fail to see what the point of the math was passed that.One of the most frustrating "lies" in all of mathematics education is, "You will use this in the future."
You won't.
I can list the exceptions on one hand:
(1) Basic addition, subtraction, multiplication, division, and exponents, for balancing your checkbook and understanding the other topics.(2) Compound interest. Because every lender will take advantage of you if you don't know how compound interest works.
(3) Probability. Because every casino, street hustler, sports betting venue, or what-have-you will take advantage of you if you don't understand probability.
(4) The Pythagorean Theorem if you're in construction and for some reason can't use a measuring tape.
Beyond that math isn't for your use. It's for training your brain. There are hundreds of studies that show that an education in mathematics improves your critical thinking, your ability to draw logical conclusions, and your ability to follow sequential steps. The most recent one I found with a quick Google was one on how studying math is visible even in MRIs.
On day 1 of every class, I used to tell my students, "Once you graduate, you are almost certainly never going to use anything I teach you this semester, but..."
...then I'd select the buffest person in class, ask them how often they worked out, how much they could bench press, and finally what the point was: Were they really in a job where they had to bench press 300 pounds every day?And I'd finish off with, "Math is weightlifting for your brain. I'll give you lots of real-world examples of where what we're doing is used, but the chances of you doing that exact thing are pretty minimal, so think of my class as going jogging with your brain."
The party trick approach to math in the name of beating those evil russkies/buying bulk wallpaper or land needs to stop. We need practical math, not living calculator nonsense.
Have not used the quadratic formula, trigonometry or any of that other nonsense. Ever.
I maintain critical thinking and logical thinking can be exercised in other ways beyond math. I have lost track of people who believe complete b#!&+$+@ because they can make a simple mathematical extrapolation that is vaguely related to their arguement.
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Look, I'm just upset that public school didn't teach me how to calculate 20% tips. It was embarrassing to have it explained that moving the decimal makes 10%, then you can just double it.
(Maybe my math classes did and I just wasn't receptive, but damn were they dry and boring.)
...The party trick approach to math in the name of beating those evil russkies/buying bulk wallpaper or land needs to stop. We need practical math, not living calculator nonsense.
Have not used the quadratic formula, trigonometry or any of that other nonsense. Ever.
And that's the problem with how we frame mathematics education.
The most valuable class you ever took (I'll assume you took it) was high school geometry, where you had to prove that two lines were parallel or two triangles were congruent or whatnot.
Absolutely, 100% useless as a life skill. No one EVER does a high school geometry proof once they're out of high school.
Yet fundamentally, in terms of training your brain in logical thought and drawing correct conclusions provided the evidence given, the best class you ever took.
...in other news, the more I deal with DVC's math department, the more I agree with Freehold that math teachers are monsters.But aren't...you a math teacher?
He knows what is talking about then.
(2) Compound interest. Because every lender will take advantage of you if you don't know how compound interest works.
(3) Probability. Because every casino, street hustler, sports betting venue, or what-have-you will take advantage of you if you don't understand probability.
And neither of those two is really taught to a degree that it should be.
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Absolutely, 100% useless as a life skill. No one EVER does a high school geometry proof once they're out of high school.
sometimes when I'm building something knowing that if i have this angle here at this length then i have that angle there at that length. Trig likewise was useful because it can be inconvenient to go 10 or 12 feet up in the air and measure something to the ground.
But I don't buy the idea that math as taught actually teaches or improves anything but math. It might go under the umbrella of critical thinking but besides finding the people that are better with both , an objective provable, math problem seems so vastly different from a subjective ability to absorb and process complex information i don't see how they would translate generally.
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I could certainly do with a better understanding of statistics than I have, and you need a good old knowledge of advance maths to get the best out of that.
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If I had to pick one course I took in my 7+ years of university education that really changed the way I think about the world, it would have to be statistics & probability.
I liked my animal behavior/ evolutionary biology class.
His favorite animal for experiments was human.
After a few incidents he declared whatever the heck i was to be his second favorite.
I always have a measuring tape.
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At game tonight, my players went to a high-end clothing store, in the middle of the day, while there were employees and customers around, and tried to just walk through all the closed/locked doors and investigate the place. They were annoyed when the employees refused to let them, and actually escorted one of them out of the store with instructions never to return. Because of course PCs should be able to do anything they want with no repercussions. Their solution? Go outside, buff up, and bust through a 10' window to get into an area they were curious about. Gonna be fun to see how the city guards react to that.
Yes, please keep us informed, that sounds like it's going to be hilarious!
Just watched Hell Girl Season 3 Ep 1.
A teacher is sent to hell, where he will recite pi for eternity.
Does he have to start over and over again, or does he get to just keep going?
Because, honestly, I imagine some people might be into that. I knew someone once who memorized π to an unnecessary level of precision, and I'm not sure if she was planning to stop. I think she had the first 100 digits down, or so.
:)
I bailed out of math at uni when, at least as it was taught where I was studying, it stopped being the sort of thing I was wired for. At the time, anyway. I think if I had been told to expect coughing up a bunch of old proofs on demand I might have adjusted.
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Fantasy NPC: Abbot Serenity. An abbot of a contemplative, though not ascetic monastery, with a secret of his own- he might stick his nose into lives of his monks, but he has secret of his own.
At game tonight, my players went to a high-end clothing store, in the middle of the day, while there were employees and customers around, and tried to just walk through all the closed/locked doors and investigate the place. They were annoyed when the employees refused to let them, and actually escorted one of them out of the store with instructions never to return. Because of course PCs should be able to do anything they want with no repercussions. Their solution? Go outside, buff up, and bust through a 10' window to get into an area they were curious about. Gonna be fun to see how the city guards react to that.Yes, please keep us informed, that sounds like it's going to be hilarious!Well, before they have to worry about the city guards, they need to deal with the 5 demons they're currently fighting. Plus the store's guards (a group of 7th or 8th level fighters). Oh, and the vampires who use the store as a base of operations.
I did get a good chuckle from the group when the Swashbuckler smashed open the window and I asked "So, are you wearing OSHA approved eye protection?".
Eye protection is essential!
Does he have to start over and over again, or does he get to just keep going?
Because, honestly, I imagine some people might be into that. I knew someone once who memorized π to an unnecessary level of precision, and I'm not sure if she was planning to stop. I think she had the first 100 digits down, or so.
:)
I bailed out of math at uni when, at least as it was taught where I was studying, it stopped being the sort of thing I was wired for. At the time, anyway. I think if I had been told to expect coughing up a bunch of old proofs on demand I might have adjusted.
No. Pi doesn't end. He will recite the digits for eternity, somehow knowing the next number.
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(3) Probability. Because every casino, street hustler, sports betting venue, or what-have-you will take advantage of you if you don't understand probability.If things like the promise seen with ChatGPT, or an up-scaled Wolfram Alpha, become commonplace and free, the only math skill you'll really need beyond primary school basics is how to frame your question well.
Have you seen ChatGPT play chess?
As people in multiple technical fields have found, ChatGPT asserts nonsense as fact with alarming frequency (a rocket scientist had ChatGPT design a booster system for him, and his analysis was that he was fairly sure it would explode on launch). I'd hate to see people risk real money based on ChatGPT recommendations.
Doing a bit more digging, I learned that she'd spent her entire life in "new math" schools where rote calculation was replaced by using calculators all the time. So she had no concept of what might be a "reasonable" answer versus an "unreasonable" one.
I use her as a canonical example of why we still need to teach basic math skills, even after the invention of calculators.
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In other news, my experience at the vet's on Friday finally prompted me to quit the rapidly-declining Berkeley Dog and Cat Hospital and move both of my cats to the local vet a block and a half from my house.
It was a pretty impressive visit:
(1) The vet ripped into me for ever feeding my cat dry food, told me that the research I'd followed at U.C. Davis in the 1990s was "Stone Age" stuff, and pointed me to catinfo.org as "a nonprofit that only cares about your cat's health". It sounded all too much like a dietary supplement infomercial. Sure enough, catinfo.org is a one-vet crusade against dry food. Organizations such as Cornell University's vet school still say both are fine, and the limited research shows that in some cases wet food is better (cats with obesity or kidney problems), but it's certainly not an established fact that you should never, EVER feed your cats dry food. (Cats with dental issues are likely to fare better on dry food, for example.)
(2) The fluffernutter needs her belly shaved (badly matted fur) and blood work done. The vet sent me home with a sedative and told me to "experiment on her a few times until you find the right dose". Yes, unnecessarily sedating my 16-year-old cat sounds like a fantastic idea.
(3) When I expressed concern that there might be something wrong in her mouth, his attitude was, "Since you're not a professional, your opinion means nothing. I'm the professional here."
(4) He mansplained to me in excruciating detail how microwaves work. I would've interrupted him to tell him I had a B.A. in physics from U.C. Berkeley and probably understood microwaves better than he did (Impus Major and I are in fact right now studying torque induced on a dipole by electric fields), but it wasn't worth it. I just wanted to get the heck out of there.
So the fluffernutter still needs her matted fur removed and her blood work done, but I suspect my trip to the new vet on Saturday will be FAR less atrocious.
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** spoiler omitted **
I don't think there's any amount of education thats going to fix that. Why make the rest of us suffer?
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I don't think there's any amount of education thats going to fix that. Why make the rest of us suffer?
** spoiler omitted **
The fact is, she was incredibly intelligent. She was taking graduate-level classes in biology as a college junior. She simply had no "feeling" for the order of magnitude of numbers, because no one had ever expected it of her.
She's one of my "pride" stories. After talking with her, I knew something was up so I took her straight to student services and had her tested for a learning disability. She was off the chart on mathematical numeracy, so she got the assistance she needed (I suspect lots of addition and multiplication tables were involved) and went from a low F to a solid A in a single quarter.
So yes, she was absolutely "fixable". No one had ever bothered to try.
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(3) Probability. Because every casino, street hustler, sports betting venue, or what-have-you will take advantage of you if you don't understand probability.If things like the promise seen with ChatGPT, or an up-scaled Wolfram Alpha, become commonplace and free, the only math skill you'll really need beyond primary school basics is how to frame your question well.Have you seen ChatGPT play chess?
As people in multiple technical fields have found, ChatGPT asserts nonsense as fact with alarming frequency (a rocket scientist had ChatGPT design a booster system for him, and his analysis was that he was fairly sure it would explode on launch). I'd hate to see people risk real money based on ChatGPT recommendations.
** spoiler omitted **
We need to show people how to use calculators properly, not insist on turning everyone into a savant.
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We need to show people how to use calculators properly, not insist on turning everyone into a savant.(3) Probability. Because every casino, street hustler, sports betting venue, or what-have-you will take advantage of you if you don't understand probability.If things like the promise seen with ChatGPT, or an up-scaled Wolfram Alpha, become commonplace and free, the only math skill you'll really need beyond primary school basics is how to frame your question well.Have you seen ChatGPT play chess?
As people in multiple technical fields have found, ChatGPT asserts nonsense as fact with alarming frequency (a rocket scientist had ChatGPT design a booster system for him, and his analysis was that he was fairly sure it would explode on launch). I'd hate to see people risk real money based on ChatGPT recommendations.
** spoiler omitted **
Typos happen. I don't want someone to be able to multiply 458 x 873 in their heads, but they should know that the answer should be somewhere between 10,000 (100 x 100) and 1,000,000 (1000 x 1000). Without a concept of magnitude, the calculator is a disaster waiting to happen.
(Another of my favorite bits of trivia: Once AutoCad was fully approved and used for building design, the rate of catastrophic collapses in newly-constructed buildings tripled. Why? Because old-school engineers put in a "fudge factor" because they knew they might be wrong. New-school engineers built to the exact specifications provided by the computer, and computers can't predict everything.)
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. I don't want someone to be able to multiply 458 x 873 in their heads, but they should know that the answer should be somewhere between 10,000 (100 x 100) and 1,000,000 (1000 x 1000). Without a concept of magnitude, the calculator is a disaster waiting to happen.
Nope. All of those are numbers so big i need paper to keep track of. Or at least fingers.
[quotebuilt to the exact specifications provided by the computer, and computers can't predict everything.)
Those would be the ones supplied to the computer by the building code. AKA minimum government standards. Which is the problem, not the cad.
Every educator has some story about one exception that means we need to educate more people in their particular field. The result is an education that's so well rounded its difficult to see the point.
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At this point I think we simply agree to disagree.
I consider the idea of implicitly trusting the answer that comes out of a computer or calculator to be intrinsically dangerous; in the tech industry an oft-repeated quote is, "Your code is only as good as the worst programmer on your team."
So I am of the strong opinion that people need basic numeric literacy to be able to recognize whether the answer coming out of the computer/calculator makes sense and is in a reasonable range. Whether they're a rocket scientist or a cashier at Starbuck's, they're working with numbers all day, every day, and again, I am of the opinion that they should be able to immediately tell if a number seems "wrong".
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At this point I think we simply agree to disagree.
I consider the idea of implicitly trusting the answer that comes out of a computer or calculator to be intrinsically dangerous; in the tech industry an oft-repeated quote is, "Your code is only as good as the worst programmer on your team."
So I am of the strong opinion that people need basic numeric literacy to be able to recognize whether the answer coming out of the computer/calculator makes sense and is in a reasonable range. Whether they're a rocket scientist or a cashier at Starbuck's, they're working with numbers all day, every day, and again, I am of the opinion that they should be able to immediately tell if a number seems "wrong".
I'm a big fan of doing things twice to ensure you get the same answer.
I'm a big fan of doing things twice to ensure you get the same answer.At this point I think we simply agree to disagree.
I consider the idea of implicitly trusting the answer that comes out of a computer or calculator to be intrinsically dangerous; in the tech industry an oft-repeated quote is, "Your code is only as good as the worst programmer on your team."
So I am of the strong opinion that people need basic numeric literacy to be able to recognize whether the answer coming out of the computer/calculator makes sense and is in a reasonable range. Whether they're a rocket scientist or a cashier at Starbuck's, they're working with numbers all day, every day, and again, I am of the opinion that they should be able to immediately tell if a number seems "wrong".
That's part of determining if a number seems reasonable.
NH is right here. You have to have some basic understanding to havexan idea when the computer is wrong.
Besides, typos in the calculator can happen the same way twice in a row as well. People have a habit of consistently typing certain words incorrectly with the exact same typos each time.
At this point I think we simply agree to disagree.
I consider the idea of implicitly trusting the answer that comes out of a computer or calculator
That's not what I advocated. I simply disagree that the solution is more math training. It really doesn't help.
It's not an issue of mathematics, it's an issue of common sense.
If I have 7 bags of beans, each weight 6 pounds, and you ask me how many pounds of beans I have, if I say, "43,316 pounds of beans", then that should sound wrong to me.
It has nothing to do with arithemetic, higher math, calculators, or anything else except reality. The ability to tell when a number is orders of magnitude different from reality is not a mathematical skill.
It's an issue of common sense to a point. Most people can eyeball how many pounds of potatoes are in a bag, but being able to eyeball whether or not your electrical load calculations are correct is not a skill most people can pull off without training, or at least consulting a reference guide of some sort.
New-school engineers built to the exact specifications provided by the computer, and computers can't predict everything.)
Speaking as someone who's spent much of the last decade working in the building trades, not only does this kind of error happen all the time, but it also leads to other kinds of design laziness (in the vein of "it must be right because the computer didn't give me an error message"). That's how you end up with cracked foundations, blueprints with the water mains coming up through the electrical switchgear, etc.
On the other end, there's also the issue of being able to correctly interpret the specs. On a job site I worked on last year, a concrete company poured and finished a 40-foot-wide pad around an outbuilding instead of a 20-foot-wide one because no one noticed that the updated blueprints were at a different scale than the old ones.
Also, why is this topic, of all things, getting so heated? It's starting to feel like that one scene from Mystery Men...
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Again, it's not the math skills that are the problem. It's the ability to understand the connection between your result and your ballpark estimate of what is a sensible outcome.
Shouldn't you have to understand how you're supposed to get to the result in order to judge whether or not it looks right?
This is getting way too abstract for my tastes...
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More proof of math's evil!
Shouldn't you have to understand how you're supposed to get to the result in order to judge whether or not it looks right?
Depends largely on how abstract the thing is. And at some sense of scale things get abstract. Six potatoes per bag 7 bags is easy enough but how many fill up the back of a dump truck?
More proof of math's evil!
Did you use a math proof that math is evil though?
Depends largely on how abstract the thing is. And at some sense of scale things get abstract. Six potatoes per bag 7 bags is easy enough but how many fill up the back of a dump truck?
Shouldn't you have to understand how you're supposed to get to the result in order to judge whether or not it looks right?
Pretty much what I was getting at. The more abstract the problem, the less you can rely on your "common sense."
I was about halfway toward getting into my standard rant about how engineers and architects need to spend time working in the trades they design for in order to give them a much-needed (and often entirely absent) sense of context, but I already had a headache when this whole mess started...
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I'm not sure which one of these things is worse than the others:
1. I've been spending much of my free time reading long political and philosophical essays
2. One of the essays I just read made an oblique reference to an episode of I Love Lucy
3. I instantly understood the reference
I don't see what's at all wrong with reading long political/philosophical essays.
I don't see what's at all wrong with reading long political/philosophical essays.
In the past, I've been told that it's bad for me. Also, I could be doing literally anything else.