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Calculus they won't teach you [video]

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Re: Calculus they won't teach you [video]

#21

Post by tchaffee »

alexb_ wrote: post #13
tommiegannert wrote: post #5

I.e. mathematical history. I think one power of calculus (and everything else) is that you don't need the history. The same way I don't need the history of the hammer to use a nail. What drives my interest is the examples. At the end, the book author talks about students not paying attention until the teacher starts talking about examples. To me, that suggests you should first contextualize and create a need for the…

I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.

That's not the biggest thing that can help you learn something complex. Practice is the biggest thing. And there are many variations of what motivates people to practice.

Re: Calculus they won't teach you [video]

#22

Post by flashfaffe2 »

earlgray wrote: post #12
tommiegannert wrote: post #5

I.e. mathematical history. I think one power of calculus (and everything else) is that you don't need the history. The same way I don't need the history of the hammer to use a nail. What drives my interest is the examples. At the end, the book author talks about students not paying attention until the teacher starts talking about examples. To me, that suggests you should first contextualize and create a need for the…

Learning names for the sake of learning names is never helpful. However the history of mathematics can help to contextualise the material and its motivation. For example, group theory has myriad modern applications. It can be (and usually is) presented in the standard mathematically-polished form, beginning with the axioms and perhaps using matrix groups or simple geometric symmetries as examples. For many learners t…

I totally second this. For someone who has a tortuous relationship with mathematics, I always lovedthe beauty of som concepts but to a certain point, got lost mainly due to knowledge base not really understood. Getting to know some historical facts would have help to be more critical to myself ( rather than just copy and paste formula).

Years later I surprised myself spending time on new maths problems thanks to YouTube maths contents(3brown1blue, Michael Penn, mindyourdecisions,etc...) Which make me reboot my knowledge. The challenge here is how is it inseminated during your scholarship.

From the what I remember, complex number theory were introduced to me as a rule that need to be acknowledged ( with no incentive to look further).

Welsh lab vid below made me reconsider my own shortcomings.

https://youtube.com/playlist?list=PLiaHhY2iBX9g6KIvZ_703G3KJ...

Re: Calculus they won't teach you [video]

#23

Post by ultra_nick »

pryelluw wrote: post #11
User23 wrote: post #8

Earlier quoted context omitted.

Another possibility is that mathematics education has gotten worse since you were in high school.

Yea, it has gotten worse in the US thanks to the common core bullshit. My daughter’s math education has been eroded with shitty ed tech apps like the ones from MHM[0]. I’ve been able to support her but there’s many kids that are not so fortunate. [0] https://www.hmhco.com/

What's wrong with common core?

Re: Calculus they won't teach you [video]

#25

Post by comte7092 »

pryelluw wrote: post #11
User23 wrote: post #8

Earlier quoted context omitted.

Another possibility is that mathematics education has gotten worse since you were in high school.

Yea, it has gotten worse in the US thanks to the common core bullshit. My daughter’s math education has been eroded with shitty ed tech apps like the ones from MHM[0]. I’ve been able to support her but there’s many kids that are not so fortunate. [0] https://www.hmhco.com/

Common core seems fine tbh. I can’t speak to the “shitty Ed tech apps” but that seems like an orthogonal issue in comparison to the standards.

Re: Calculus they won't teach you [video]

#26

Post by amluto »

alexb_ wrote: post #13
tommiegannert wrote: post #5

I.e. mathematical history. I think one power of calculus (and everything else) is that you don't need the history. The same way I don't need the history of the hammer to use a nail. What drives my interest is the examples. At the end, the book author talks about students not paying attention until the teacher starts talking about examples. To me, that suggests you should first contextualize and create a need for the…

I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.

I don’t see why the history of discovery of something should be a particularly good way to rediscover it.

As a concrete example, if someone asks “how do we know the Earth is round” or “how do we know the planets orbit the sun”, one could go through ways to figure this out with math and minimal technology. But one could also point out that we have spaceships and probes and have actual pictures! You can see the Earth from a satellite or the ISS or the moon, and you can see the planets from space!

I agree that a process of rediscovery can be a useful teaching technique, but that doesn’t mean that rediscovering something the way it was first known to have been discovered is the right approach.

Re: Calculus they won't teach you [video]

#27

Post by [deleted] »

tchaffee wrote: post #21
alexb_ wrote: post #13

Earlier quoted context omitted.

I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.

That's not the biggest thing that can help you learn something complex. Practice is the biggest thing. And there are many variations of what motivates people to practice.

[deleted]

Re: Calculus they won't teach you [video]

#28

Post by friedman23 »

alexb_ wrote: post #13
tommiegannert wrote: post #5

I.e. mathematical history. I think one power of calculus (and everything else) is that you don't need the history. The same way I don't need the history of the hammer to use a nail. What drives my interest is the examples. At the end, the book author talks about students not paying attention until the teacher starts talking about examples. To me, that suggests you should first contextualize and create a need for the…

I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.

I agree, one book I recommend that does this for computing is "Code: The Hidden Language of Computer Hardware and Software"

Re: Calculus they won't teach you [video]

#30

Post by VLM »

amluto wrote: post #26
alexb_ wrote: post #13

Earlier quoted context omitted.

I disagree. The biggest thing that can help you learn something complex is by introducing it as it was discovered, and making someone feel like they could have come up with it on their own.

I don’t see why the history of discovery of something should be a particularly good way to rediscover it. As a concrete example, if someone asks “how do we know the Earth is round” or “how do we know the planets orbit the sun”, one could go through ways to figure this out with math and minimal technology. But one could also point out that we have spaceships and probes and have actual pictures! You can see the Earth f…

Another concrete example of the conflict is classical vs quantum physics which is nearly exclusively taught as the historical story of the quantum revolution or whatever you call it around 1900.

It would be trivial to skip the historical story and just "yo here's a FET transistor, a solar cell, and a vacuum tube, and the math just works, so get used to it" but nobody is ever taught that way.

Would be interesting for someone to attempt to write a non-historical physics textbook.

On the other hand, in IT, this style of learning is considered normal. "This is how the kool kids do things today. The past does not matter and probably didn't exist anyway. The end."

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