The Language of Mathematics
Just the other day, I posted this comment on a thread at andrewducker:
'Mathematics isn't my strongest subject; language is. But I do remember sitting in 2nd semester Calculus, looking for 'u' and 'du' in an integrand, and thinking that it felt very much like a grammatical problem: looking for patterns in a collection of symbols.'
Now - via andrewducker again - here's a fascinating article by a woman named Barbara Oakley who successfully retooled her language aptitude into mathematical ability:
I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now-someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering.
One day, one of my students asked me how I did it-how I changed my brain. I wanted to answer Hell-with lots of difficulty! After all, I’d flunked my way through elementary, middle, and high school math and science. In fact, I didn’t start studying remedial math until I left the Army at age 26. If there were a textbook example of the potential for adult neural plasticity, I’d be Exhibit A.
Learning math and then science as an adult gave me passage into the empowering world of engineering. But these hard-won, adult-age changes in my brain have also given me an insider’s perspective on the neuroplasticity that underlies adult learning. ...
Oakley points out an important connection between mathematics and language learning - a factor that's also often overlooked in the USA: repetition.
In the current educational climate, memorization and repetition in the STEM disciplines (as opposed to in the study of language or music), are often seen as demeaning and a waste of time for students and teachers alike. Many teachers have long been taught that conceptual understanding in STEM trumps everything else. And indeed, it’s easier for teachers to induce students to discuss a mathematical subject (which, if done properly, can do much to help promote understanding) than it is for that teacher to tediously grade math homework. What this all means is that, despite the fact that procedural skills and fluency, along with application, are supposed to be given equal emphasis with conceptual understanding, all too often it doesn’t happen. Imparting a conceptual understanding reigns supreme-especially during precious class time.
And conceptual understanding is a necessary, but not sufficient, condition for mastery. American educators looking toward Japan often forget that 'Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material.'
Read the whole article at the link.
'Mathematics isn't my strongest subject; language is. But I do remember sitting in 2nd semester Calculus, looking for 'u' and 'du' in an integrand, and thinking that it felt very much like a grammatical problem: looking for patterns in a collection of symbols.'
Now - via andrewducker again - here's a fascinating article by a woman named Barbara Oakley who successfully retooled her language aptitude into mathematical ability:
I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now-someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering.
One day, one of my students asked me how I did it-how I changed my brain. I wanted to answer Hell-with lots of difficulty! After all, I’d flunked my way through elementary, middle, and high school math and science. In fact, I didn’t start studying remedial math until I left the Army at age 26. If there were a textbook example of the potential for adult neural plasticity, I’d be Exhibit A.
Learning math and then science as an adult gave me passage into the empowering world of engineering. But these hard-won, adult-age changes in my brain have also given me an insider’s perspective on the neuroplasticity that underlies adult learning. ...
Oakley points out an important connection between mathematics and language learning - a factor that's also often overlooked in the USA: repetition.
In the current educational climate, memorization and repetition in the STEM disciplines (as opposed to in the study of language or music), are often seen as demeaning and a waste of time for students and teachers alike. Many teachers have long been taught that conceptual understanding in STEM trumps everything else. And indeed, it’s easier for teachers to induce students to discuss a mathematical subject (which, if done properly, can do much to help promote understanding) than it is for that teacher to tediously grade math homework. What this all means is that, despite the fact that procedural skills and fluency, along with application, are supposed to be given equal emphasis with conceptual understanding, all too often it doesn’t happen. Imparting a conceptual understanding reigns supreme-especially during precious class time.
And conceptual understanding is a necessary, but not sufficient, condition for mastery. American educators looking toward Japan often forget that 'Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material.'
Read the whole article at the link.