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Everyone is capable of, and can benefit from, mathematical thinking
251–260 of 419 posts
Re: Everyone is capable of, and can benefit from, mathematical thinking
#252Earlier quoted context omitted.
The extreme case does not imply a binary scenario ie that there are those that can those that cannot. Rather, learning ability is a continuum. people have varying degrees of ability to learn mathematics. Couple this with environmental factors and society generates a huge variability in mathematical ability that crosses income levels and other demographics. This view is rejected by many because it is against the push…
You get a huge variability if you consider the absolute extreme outliers. Most people should be able to reach a level of competence where they can understand mathematical concepts abstractly and apply that same reasoning to other areas, and not feel a visceral rejection at the mere idea. I think that's a modest enough standard that a good portion of any given population should be able to reach, and yet education is f…
Your statement is not backed up by data and simply wishing it should happen isn’t a strong argument.
You probably have a narrow definition of “most people” (probably some motivated high school or undergraduate student) and too loose with what it means to “understand mathematical concepts abstractly”.
Take an analogy: imagine professional musicians saying that most people should be able to take a piece of music and understand its harmonic structure, then apply it to a new setting to generate a new piece. Most people will reject this idea as absurd.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#253I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…
I really want to try MathAcademy.com. How quickly do you think someone doing light study could move from a Calc 1 -> advanced stuff using that site? In my case I could put in at least 30 minutes to an hour a day.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#254I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…
Sounds really cool.
It reminds me of programming, that moment when new code starts to really sync up and code goes from being a bunch of text to more intuitive structures. When really in the zone it feels like each function has its own shape and vibe. Like a clean little box function or a big ugly angry urchin function or a useless little circle that doesn't do anything and you make a note to get rid of. I can kinda see the whole graph connected by the data that flows through them.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#255Earlier quoted context omitted.
Indeed, speed is often read as "smarts" whereas I would maintain it's much more often "preparation". We can't on one hand believe in the plasticity and retrainability of the mind, while simultaneously believing that speed is something only a few are born with. On the nature/nurture scale, I think it's 20/80 or so - but prodigies and geniuses have an interest that keeps them thinking and learning 10x or 100x more than…
> I'm fond of saying "You can do anything you want, but wanting is the hard part", because to truly be a grandmaster, genius-level mathematician, olympic athlete, etc, requires a dedication and I was having a problem agreeing with this subthread, and I have you to thank for putting it into words that I can finally formulate my disagreement against. Have you never met one of those people for whom they did not need to…
> I think most believe they don't exist for two reasons.
I add third (okay, 2b) - because the pain of coming up with the fact other people are better than you at a deep, fundamental level is too overwhelming.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#256What an incredibly neuro-typical thing to claim
Re: Everyone is capable of, and can benefit from, mathematical thinking
#257Earlier quoted context omitted.
Come on, get real. If people had all of their needs covered a lot more of them would sit around getting high and playing video games than perfecting their art.
Is that not better than the current alternative where they're forced to become grifters?
No one is forced to become a grifter.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#258Earlier quoted context omitted.
> rotated shapes, slot machines, or origami Or gears (like Seymour Papert), or abacus beads, or nomograms, or slide rules, etc etc. Anyone have any more, throw them out! Is mathacademy good? I have been thinking of giving it a month of a try. You say "stressful", which I'm not sure is a mis-type or not. I ordered Mathematica at my local library by the way, and can now forget about it until I get an SMS one day inform…
I've had a MathAcademy subscription for some time and it's quite good. I'd say it's best at generating problems and using spaced repetition to reinforce learning, but I think it falls short in explaining why something is useful or applicable. I don't know, most math education seems to be "here's an equation and this is how you solve it" and MathAcademy is undoubtedly the best at that, but I wish there were resources…
I have so wanted such resources for years. I have found some and should make a list.
The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the same - but some larger area of my brain suddenly connected with all the concepts I had already learned.
While ordering the "Mathematica: A Secret World of Intuition and Curiosity" I came across these books, which looked very promising in the "learning formal math by expanding intuition" theme, so I bought them too:
Field Theory For The Non-Physicist, by Ville Hirvonen [0]
Lagrangian Mechanics For The Non-Physicist, by Ville Hirvonen [1]
The Gravity of Math: How Geometry Rules the Universe, by Steve Nadis, Shing-Tung Yau [2]
Vector: A Surprising Story of Space, Time, and Mathematical Transformation, by Robyn Arianrhod [3]
[0] https://www.amazon.com/dp/B0CN7HMTJN
[1] https://www.amazon.com/dp/B0CN7HMK38
[2] https://www.amazon.com/dp/1541604296
[3] https://www.amazon.com/dp/0226821102
Excited to read each (based on their synopses & ratings), and if I will get compounding fluency across both math and physics between all five books.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#259Earlier quoted context omitted.
Thanks. > art same as entertainment Could you volunteer me how much time you spend on it? And how is your day job? > my pursuit of other things like cryptography, better algorithms, and understanding physics is limited by my primitive understanding of mathematics. Could you volunteer why you would want to learn these subjects? Is it your day job or is it something you would like to pursue in the future. > If I was a…
I don't think UBI is feasible, it is anathema to the human condition to be content with the bare minimum. if not for our own selves, we would want the best life possible for our loved ones (present or future). my "UBI" would be a couple of million dollars. I want to learn those subjects because I enjoy learning and understanding. Life should be lived with knowledge applied through wisdom. > Could you volunteer me how…
> my "UBI" would be a couple of million dollars.
There's a difference between what your human brain would become accustomed to (which you'd be right, it'd scale up and up forever) versus what would allow the base level of health and opportunity. As in, not having to worry about eating the next day.
And because you're right that human brains strive for more wealth, UBI should grant you the opportunity to pursue it without fear of failure.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#260Earlier quoted context omitted.
I've had a MathAcademy subscription for some time and it's quite good. I'd say it's best at generating problems and using spaced repetition to reinforce learning, but I think it falls short in explaining why something is useful or applicable. I don't know, most math education seems to be "here's an equation and this is how you solve it" and MathAcademy is undoubtedly the best at that, but I wish there were resources…
I have so wanted such resources for years. I have found some and should make a list. The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the sam…
Burn Math Class follows that tradition, although it starts pretty basic, so it requires some patience.