Re your comment that

I don’t know enough about K-12 math education to write a blog article on this, and I don’t read blogs about math education.

, I recently noticed that Frank Quinn has written quite a lot on this topic.

A sample of his conclusions:

]]>Mathematicians tend to focus on teacher education,

with an implicit presumption that the current teacher corps is not sufficiently competent.

The analysis here suggests that

the teachers are competent enough,

butthe methodology they have been taught to use is incompetent.

In other words, significantly better outcomes are unlikely without

profound changes in educational philosophy and teacher-education programs.

Thanks! I tried listening to the names you verbalized after that comment, but couldn’t make them out (Tune?). Seeing them in writing (with a link even!) does the trick.

And thanks very much for your many contributions to communicating math, physics, and environmental issues!

]]>The generalization of algebraic geometry to commutative monoids in a symmetric monoidal category is discussed here:

• Bertrand Toen, Michel Vaquie, Under Spec Z.

This paper will also give you a chance to practice your French!

My slides include a link to Jacob Lurie’s paper where he generalizes this to symmetric monoidal (∞,1)-categories. That may be easier or harder than French.

]]>you mention the study of commutative monoids in an arbitrary SMC (symmetic monoidal category) as a generalization of commutative algebra.

Could you suggest references for that generalization?

Thanks. ]]>

Here’s one idea.

There is an adjoint triple between (the integers Z) and (the reals R): ceiling, inclusion, floor.

Illustrate this in 0-D (i.e. first-order logic), 1-D, and 2-D (2-categorical) diagrams.

Both Z and R have various familiar structures, plus, times, max, min.

Discuss the extent to which the parts of the adjoint triple preserve those structures.

Mention the words and phrases that generalize all this.

The point is to exemplify general “abstract” concepts in a simple, concrete, familiar setting.

]]>I don’t know enough about K-12 math education to write a blog article on this, and I don’t read blogs about math education. Maybe I should start by thinking about this a bit more. (I feel I already have too many projects going–and not enough time to do most of them!)

I feel math teaching is often badly done, and I’ve written up some advice on how to do it better:

I have a feeling professional educators live in a different universe than I do, because they say a lot of complicated stuff, but rarely this stuff.

]]>(“The challenge starts in kindergarten.”)

on improving mathematical education,

I have two questions:

Are there one or several blogs or websites that you feel are useful on this subject?

Your various activities have of course addressed various generally advanced aspects of this.

But I would like to see you write a post here dedicated to K-12 math education.

In particular, an expandable, editable post (starting perhaps merely as a placeholder) to which you could add ideas and thoughts as they come to you, as they surely will.

And, of course, people could add comments.

No joke, just an honest mistake. 7pm here. The confusion arises because next Monday and Tuesday I have a virtual conference, and that is one day AFTER the change to DST here!

See you in a bit more than 10 hours!

]]>I’m pretty sure my talk is at 7 pm tomorrow in Germany and Switzerland. I don’t know why Philip is joking around about this stuff—it’s a serious business!

]]>Wait, it’s 7 pm in Germany and Switzerland, right? https://www.google.com/search?q=18%3A00+UTC+to+Germany

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