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Manifesto on the Teaching of Mathematics (2015)

intellectualmathematics.com

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Re: Manifesto on the Teaching of Mathematics (2015)

#11

Post by defrost »

murkt wrote: post #6

Is there something similar to this, but for school-grade mathematics? I agree with this manifesto wholeheartedly, just it’s too damn difficult to think of all the whys on the spot to get my son to be interested in that. He’s doing “remote learning” at home, it’s basically Coursera-like lessons, since his school was hit by artillery during the first month of the war with Russia, and it still doesn’t work.

Depends upon your son but perhaps youtube + forum engagement with others centred about math channels that have lower+upper school and university material.

> It follows that we must not introduce any topic for which we cannot first convince the students that they should want to pursue it.

There are several good math related youtube channels and they have the advantage of allowing viewers to find questions | topics that they find of interest and then pursue .. which can lead to following for the latest releases and discussing with others that comment.

Matt is very engaging and there's a fair bit of back and forth from others on his channel comments which might take your son down a path of greater engagement and exploration.

https://www.youtube.com/user/standupmaths

Re: Manifesto on the Teaching of Mathematics (2015)

#13

Post by murkt »

danielmarkbruce wrote: post #9
murkt wrote: post #6

Is there something similar to this, but for school-grade mathematics? I agree with this manifesto wholeheartedly, just it’s too damn difficult to think of all the whys on the spot to get my son to be interested in that. He’s doing “remote learning” at home, it’s basically Coursera-like lessons, since his school was hit by artillery during the first month of the war with Russia, and it still doesn’t work.

If your kid likes sports, there are endless lessons to teach around it.

True, we’re going ice skating with him regularly, and it’s a great source of lessons. Doesn’t help very much with math, though :)

Re: Manifesto on the Teaching of Mathematics (2015)

#14

Post by alimw »

murkt wrote: post #6

Is there something similar to this, but for school-grade mathematics? I agree with this manifesto wholeheartedly, just it’s too damn difficult to think of all the whys on the spot to get my son to be interested in that. He’s doing “remote learning” at home, it’s basically Coursera-like lessons, since his school was hit by artillery during the first month of the war with Russia, and it still doesn’t work.

"In Intellectual Mathematics a topic is introduced only when the student can be convinced of the value of doing so."

If I understand this correctly, you cannot bend the approach to the teaching of any particular topic (e.g. what's in your son's homework this week). Rather you would have to bite the bullet and teach your own parallel course, abandoning the school curriculum to the teachers.

Re: Manifesto on the Teaching of Mathematics (2015)

#15

Post by throw_pm23 »

oofnik wrote: post #8

One of my most memorable courses in undergraduate was taught by a spritely lecturer who must've been in his 80s. He'd make a statement or proposition, write it on the board, then quickly turn around, point at a student somewhere in the classroom with an open palm, and shout, "do you believe this?" It was partly theatrical, but it seemed genuine. It was very engaging and it really prodded me to consider whether what h…

Interesting perspective. Why someone would downvote it is beyond me.

Re: Manifesto on the Teaching of Mathematics (2015)

#16

Post by Tainnor »

WoahNoun wrote: post #10

I read the manifesto and somewhat disagree with the claim "It follows that we must not introduce any topic for which we cannot first convince the students that they should want to pursue it." But in skimming the book, it's just seems not very good.

I also took a brief look at the calculus "book" (more a set of lecture notes) and far from being the revolutionary novel approach that it claims to be I found it fairly... standard?

Re: Manifesto on the Teaching of Mathematics (2015)

#17

Post by Tainnor »

I do definitely agree that something is lacking in current mathematical education, but calling your own counter-program "intellectual mathematics" is a bit ... on the nose.

Judging from the rest of the website, the author appears to have some rather idiosyncratic opinions. For example, he seems to be unconvinced that rigour is an essential component of mathematics (even going as far as claiming not to understand what it means): https://intellectualmathematics.com/blog/what-is-rigour-anyw...

He also has his own take on the "two cultures" distinction often postulated for mathematicians, but also apparently assigning distinctly less value to so-called "lesser technocrats", seemingly going as far as calling Euler of all people a "technocrat" and calling into question the value of Euler's famous equation e^pi*i = 1 - why? https://intellectualmathematics.com/blog/four-types-of-mathe...

I see no indication that the author doesn't know the mathematics he's talking about, but I also feel like he's incredibly biased towards the particular way he likes doing mathematics without considering that there are legitimately valid different approaches to doing mathematics - probably even among students.

Re: Manifesto on the Teaching of Mathematics (2015)

#19

Post by murkt »

alimw wrote: post #14
murkt wrote: post #6

Is there something similar to this, but for school-grade mathematics? I agree with this manifesto wholeheartedly, just it’s too damn difficult to think of all the whys on the spot to get my son to be interested in that. He’s doing “remote learning” at home, it’s basically Coursera-like lessons, since his school was hit by artillery during the first month of the war with Russia, and it still doesn’t work.

"In Intellectual Mathematics a topic is introduced only when the student can be convinced of the value of doing so." If I understand this correctly, you cannot bend the approach to the teaching of any particular topic (e.g. what's in your son's homework this week). Rather you would have to bite the bullet and teach your own parallel course, abandoning the school curriculum to the teachers.

It’s already practically abandoned, he has only to pass “exams” twice a year, which is quite easy for him and doesn’t take much time. He finished second grade in February.

It doesn’t bring much understanding, though. It’s hard to create parallel curriculum for my kids, while I have my startup running. And the war isn’t helping either, with air alerts and rockets/drones trying to strike Kyiv seemingly every night.

Would be helpful to have concrete examples, directions, etc.

Re: Manifesto on the Teaching of Mathematics (2015)

#20

Post by jstrieb »

It's small, but one of my favorite math professors in college, when he could tell the class was losing focus on the lecture, would begin proofs with a shouted "BEHOLD x!" instead of the more traditional "let x..." It always woke people up.

Even for the most diligent students (which I was not), there will always be some dry material. Often, when I was struggling with writing up a difficult proof, I imagined him saying "BEHOLD," and it would cheer me up. Little things can make learning much more fun.

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