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Shameless promotion: I'm writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. https://jeremykun.com/2016/04/25/book-mailing-list
The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.
What was the other mathematician? Thx for posting this excellent article.
Earlier quoted context omitted.
> In the meantime, rote memorizing your multiplication tables and polynomial expansions might be a necessary evil... I disagree on both ideological and technical terms. Won't students lose the "flow" as soon as they start memorizing? It seems like an anti-intellectual activity to memorize data or particular steps (e.g. (a+b)^2 = a^2 + 2ab + b^2). I think the further we stay from memorization the better the learner's…
I've been doing math for the past 15+ years as well, and the nature of my education (French system) forced me to learn a number of things by rote. I'm very glad I now have these automatisms built in my brain and basic things come instinctively to me. > Won't students lose the "flow" as soon as they start memorizing? The core of my argument is that memorization will help them better find and stay in the flow in the fi…
My view is that pursuing fluency in the basic arithmetic skills as an intermediate goal towards higher understanding might not be a necessary step. Assuming the person learns a lot of math (like five years' worth) then they will be forced to develop fluency in the process of using the basic skills as building blocks for the more advanced topics. You're right that having useful "chunks" of memorized procedures would make learning the advanced stuff easier in the first place, but I think students could also develop arithmetic/algebra fluency "just in time" while learning the more advanced levels.
Shameless promotion: I'm writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. https://jeremykun.com/2016/04/25/book-mailing-list
Shameless promotion: I'm writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. https://jeremykun.com/2016/04/25/book-mailing-list
Have you looked at these two? It might help your writing process to find what readers of those books found confusing or frustrating in the presentation.
Earlier quoted context omitted.
Not the GP, but I'd want to learn both the ideas and the notation. That way, more math would become accessible to me. Just don't let the notation get in the way of reaching clarity on the ideas.
Yes exactly. It seems that no matter what you know math majors don't care. You need to walk the walk and talk the talk. If you read through my comment history you will find me arguing with many mathematicians who think that math is just inherently harder and I must not understand it because I'm not smart enough. I think that the concepts and basic building blocks seem simple when explained outside the context of the…
It’s like if you’re interested in 19th century piano music, but all your experience with reading music is in the form of guitar tablature, then you’re going to have a tough time with your study. You could conceivably find top-down videos of someone playing some of the music you care about, or convince someone to translate some parts of it into guitar tablature. But it would be a better use of your time to just learn to read standard music notation.
Earlier quoted context omitted.
I've been doing math for the past 15+ years as well, and the nature of my education (French system) forced me to learn a number of things by rote. I'm very glad I now have these automatisms built in my brain and basic things come instinctively to me. > Won't students lose the "flow" as soon as they start memorizing? The core of my argument is that memorization will help them better find and stay in the flow in the fi…
I can't argue with the music analogy—it's a very strong point. My view is that pursuing fluency in the basic arithmetic skills as an intermediate goal towards higher understanding might not be a necessary step. Assuming the person learns a lot of math (like five years' worth) then they will be forced to develop fluency in the process of using the basic skills as building blocks for the more advanced topics. You're ri…
Unfortunately, it takes much more teacher skill (e.g. to assess individual gaps in student understanding), doesn’t scale as well to large class sizes (ideally problems should to be catered to the ability level of each individual student), and isn’t as easy to assess with standardized tests.
The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.
The right curriculum is also important. I don't know why so much emphasis is placed on calculus. Why was my calculus class filled with nursing students? Why weren't they off studying statistics, logic, set theory or any other of the more applicable fields of mathematics?
This is a method which was known <50 BCE to the Babylonians, and is taught to every high school calculus student as the “trapezoid rule”.
So here's the dilemma. People who see the beauty and elegance of mathematics are always going to go into something that exercises that, and will never go into teaching. Why would anyone who is seriously good at lots of math go into teaching? Especially in the USA, UK, or other countries where teaching has such a low status. In many cases teachers are genuinely despised. Why would anyone good at math ever go into teac…
Steven Strogratz is a teacher. He's also a popular math writer (he had a NYT column for a while).
So here's the dilemma. People who see the beauty and elegance of mathematics are always going to go into something that exercises that, and will never go into teaching. Why would anyone who is seriously good at lots of math go into teaching? Especially in the USA, UK, or other countries where teaching has such a low status. In many cases teachers are genuinely despised. Why would anyone good at math ever go into teac…
By that logic no student is ever exposed to the real beauty and elegance of any subject.