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If anyone cares to share, I'd love to hear some opinions about at what point someone switches from "non-mathematician" status to "mathematician" status.
If anyone cares to share, I'd love to hear some opinions about at what point someone switches from "non-mathematician" status to "mathematician" status.
https://terrytao.wordpress.com/career-advice/there%E2%80%99s...
If anyone cares to share, I'd love to hear some opinions about at what point someone switches from "non-mathematician" status to "mathematician" status.
Speaking personally, a lot of people would probably say that I'm "good at math" in the sense that I got through a fairly rigorous engineering program and that I've never had issues with the quantitative side of business or other such pursuits. On the other hand, I've never personally considered myself a "mathematician" in the sense that anything approaching upper-level university math was something that came remotely naturally.
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Unfortunately, probability and stats are not easy to teach, and even many professional scientists / researchers have major confusions about the subjects. Common sense actually provides a decent enough guide for most people (i.e a baseball player with a high batting average is more likely to hit the ball). Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an…
First-order logic is much more abstract. I think a major benefit of geometry is that it introduces visual thinking and is very grounded and real because you can see and draw the proofs. This foundation of visual/spatial intuition seems to be very useful in higher math, as a counterpart to the exclusively symbolic manipulation of algebra or first-order logic.
I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.
Do other disciplines ask similar questions? How should physics be taught to non-physicists? How should writing be taught to non-writers? How should car maintenance be taught to non-mechanics? I guess my point is, why should we teach mathematics any differently to "non-mathematicians" than we do to "mathematicians"? I mean, at the point when you're first teaching someone, how do you even know if they're a "non-mathema…
Sort of: http://paulgraham.com/essay.html
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At the risk of being sarcastic, the suggestion seems to be that mathematics is best taught through stereotypical management consulting interview questions. Or the apocryphal (?) Google interview questions like how many ping pong balls can fit on a bus. ADDED: I also suspect that the average high school student lacks the world knowledge to come up with meaningful guestimates for the inputs to many of those questions.…
Unfortunately, probability and stats are not easy to teach, and even many professional scientists / researchers have major confusions about the subjects. Common sense actually provides a decent enough guide for most people (i.e a baseball player with a high batting average is more likely to hit the ball). Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an…
I'm not sure how much I agree.
Sure, the math and the principles involved in designing scientific studies etc. can get pretty complicated. But there are a number of fairly basic ideas that could be usefully taught. And I'd argue that many people don't have a great common sense view of stats and probability. Sure, they have some idea of what batting average means--though there are lots of interesting sabermetric discussions to be had around baseball measurements--but there are also many well-known and consistent biases that many people have. For example, around ideas like streaks.
I've argued before and continue to believe that a semester long intro-level course on stats and probability that didn't get overly wrapped up in a lot of complex equations would be more useful at the high school level than some of the ways that time is used today.
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A course designed around using a particular "modern" web technology stack will have to change too often (every time it doesn't become "modern" anymore) for it to be sustainable. Imagine that in 2016 you have a course centered around using what was modern in 2006. That would inevitably happen with a course like that. I'd rather teach programming from 0 to making a really basic 2D game (be it in C++ or Python or whatev…
I love games as an introduction to programming. But then you have to teach kids how to do collisions (or physics), you have to teach them how to keep track of multiple sprites that behave the same but are in different places at the same time (I'm talking about classes, yes), and it's harder to point to a "real world" usage of game programming... which makes it harder to get your course approved. I know, teaching toda…
[0] According to the teacher, the class was originally planned as offering a CS credit; but was changed to art when they realized that a CS credit is not a graduation requirement, while art credits were.
[1] This was not out of the norm for my school. The only class that was designed for the AP was calculus.
Do other disciplines ask similar questions? How should physics be taught to non-physicists? How should writing be taught to non-writers? How should car maintenance be taught to non-mechanics? I guess my point is, why should we teach mathematics any differently to "non-mathematicians" than we do to "mathematicians"? I mean, at the point when you're first teaching someone, how do you even know if they're a "non-mathema…
Conversely, a class for "mathematicians" would be one with some background that can be used to begin from, depending on the average grade-level or prior education of the students.
So in a nutshell to teach deep math concepts to 'non-maths', one has to start from the beginning and define each concept in order, ignoring wider scope for the sake of reaching the goal. 'Math' students can start at a middle-depth, depending on their background.
Earlier quoted context omitted.
First-order logic is much more abstract. I think a major benefit of geometry is that it introduces visual thinking and is very grounded and real because you can see and draw the proofs. This foundation of visual/spatial intuition seems to be very useful in higher math, as a counterpart to the exclusively symbolic manipulation of algebra or first-order logic.
As an anecdote, I actually had a fair bit of trouble with geometry in high school even though I did very well throughout high school in math/science generally and went on to major in engineering in college. I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.