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As I said on the show, there's a nuance to Dr. Benjamin's point that was of concern to me and that I think should be looked at more closely.  My reaction to Dr. Benjamin was a rejection of the idea that either calculus or statistics can just be claimed to be "better" than each other.  What is key to understanding professional mathematics is that regardless of the field you specialize in, be it Number Theory, Statistics or Matrix Algebra, no one cares what you know in the field if you can't actually prove what you're saying.  And like in other fields of study or hobbies in life, it's being able to prove things that matters more than just being able to say you can do it or you have a trick for that particular problem.  The reason is because the trick is unique, the skill is not.

I suspect there have been many skills you have developed in life since graduating from college.  How did you develop those skills?  When did you actually feel like the skill had "developed" and wasn't just something you were doing?  In going through your career, did you shine when you could just recite some factoid or when you could make a passionate plea with a listener or client about the value of a product or a method of problem solving?

In Mathematics, this art is the Defense of Proof, and it's what separates the good mathematicians from the ones who merely hold degrees in it.  When a mathematician is done talking about a subject, there shouldn't be any questions left to ask.  No extra scenarios, no possibilities that are waiting to be discovered... adding "QED" after a result on a math paper is like putting "The End" when you finish a book:  nothing else happens next, the story is over, move on.

But defending an idea isn't unique to mathematics... it's something everyone does for all of the hobbies and jobs they hold.  If you need to learn this art by studying statistics because you have a natural ability to defend your ideas in there, that's great!  But the same techniques you use to prove yourself right in statistics is the technique you use to derive the correct solutions in all other fields of Mathematics and beyond.

That's why I stressed analysis.  That's the crux of the problem.  That's where I was weak and what I finally had to learn at that 11th hour.  And once I did... everything else was finally able to fall into place.

posted 2 years, 6 months ago
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I might be inclined to agree with your analysis that math is a language, but it's no more or less a language than the jargon involved in banking companies, in cooking, or any of a host of other topics.  Adults are able to get involved even at a late age with sports and learn the language and jargon surrounding it without ever having to actually sit down in a classroom to learn "a freethrow is ____, while a tightend does ____".

Certainly, there is an indication that students find the language of Mathematics to be daunting, but they find the entire field to be daunting in general.  Is it because of the language?  I have taught students without using any mathematical notation.  My first proofs in college were actually more essays than the elegant mathematical symbology that defines proper math papers.  The reason why I started using the notation is because my wrist started to get tired having to write "For all x, there exist gamma such that cheese plus pizza equals a good dinner."  When I got comfortable with what I was writing, I found it was just faster to write "{V x, E y | cheese + pizza = good dinner}"

I think what might feel more natural is to let kids write essays instead of forcing the symbology on them, and then just hand them a reference chart.  Believe me, they'll get tired of writing it long form in no time.

posted 2 years, 6 months ago
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