Sorry that I had only 20 minutes to write this because I had to run out the door at 3:00, but I felt it was necessary to give some response to today’s Bloomberg article . . . .
Saw this Bloomberg View article via a Keith Devlin re-tweet this afternoon:
Frenkel’s Slate piece is a good response to today’s article, but this old blog involving another of Frenkel’s ideas is actually what came to my mind:
In that post you’ll see a simple question that Frenkel asks about math – “So how do we make people realize that mathematics is this incredible archipelago of knowledge?”
Dan Anderson’s project with his students is, I think, one great answer to that question. Dan’s students gave short presentations on math-related topics that they choose because they wanted to learn more about them. The list of topics is absolutely wonderful. I’ve always imagined Frenkel sitting through those presentations with a big smile on his face.
He’d smile because math **IS** this incredible archipelago of knowledge and kids **DO** want to learn more about it. It is hard for me to understand how someone could even suggest that we stop teaching math.
Just a few weeks ago I had the incredible opportunity to sit and watch a 6th grade girl make some amazing shapes out of Zometool sets just playing around as I sat in our kitchen eating dessert with her parents – I see a remarkable young geometer at work here:
Here’s one of her shapes, for example:
Just last week my kids and I were talking about square roots – my older son made this wonderful observation about the graph of
You just never know what kids are going to notice or wonder or think about, or what is going to suddenly capture their imagination. How could you even think that we should stop teaching math?
And, finally, give me just one minute more of your time – if you can watch my kids learning about the Chaos game and think we should stop teaching math, well, I guess there’s nothing I can say or show you that would ever convince you otherwise:
Mike's Math Page 
I think there is a legitimate debate about whether it is optimal for mathematics to be treated as a high stakes subject. One issue is that high-stakes means that (some/many?) students are not actually taught math and instead get test prep or a graduation-requirement patch. I see anecdotes through friends and family who teach remedial math. Their goal is not to teach math, but to get the kids to clear the hurdle that they are currently facing.
Just to be clear, I’m not saying we should stop teaching kids math. I think your examples, and my own blog entries, show what is possible when we are allowed to approach it as a cool thing to investigate, without the high stakes baggage.
The Frenkel piece you linked was really interesting. While this is close to my own professional area, I had still never heard about the role of gauge theory in inflation modeling. However, his argument is a weak justification for required math, partly because the indifferent response of the general population has already occurred in a context of required math classes. This shows that the desired outcome doesn’t result from the proposed treatment. Perhaps what is needed is a more robust civics requirement aimed at creating a more active electorate?