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Everyone is capable of, and can benefit from, mathematical thinking

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Re: Everyone is capable of, and can benefit from, mathematical thinking

#241

Post by Shosty123 »

sourcepluck wrote: post #204
mbbbackus wrote: post #180

I'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,…

> 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 that were more like "here's how we discovered this, what we used to do before, why it's useful, and here's some scenarios where you'd use it."

Re: Everyone is capable of, and can benefit from, mathematical thinking

#242

Post by diffeomorphism »

notepad0x90 wrote: post #221
itissid wrote: post #207

Earlier 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…

> I don't think UBI is feasible, it is anathema to the human condition to be content with the bare minimum.

Hm? That is exactly why UBI works, no? As the name indicates, the bare minimum is taken care so that you can work towards "the best life possible for our loved ones" without worrying about starving, sickness or homelessness.

In contrast, if you were wrong and people would be content with the bare minimum, then UBI would be a bad idea. Though then they could just commit some felonies and be content with having a cell, bread and water for the rest of their lives, no?

Re: Everyone is capable of, and can benefit from, mathematical thinking

#243

Post by Malidir »

PittleyDunkin wrote: post #109
Malidir wrote: post #75

Earlier quoted context omitted.

>The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s. Nonsense! The brain you are born with materially dictates the ceiling of your talent…

What makes you think that "genius" is nature and not nurture? I'd love to see the evidence for this; i'm deeply skeptical. Edit: I don't mean to argue that there aren't genetics involved in determining aptitude on certain tasks, of course, but the assumption that genius is born and never made feels like a very shallow understanding of the capacity of man.

> I'd love to see the evidence for this; i'm deeply skeptical.

Cool, come and have a coffee with me :) I have older and younger siblings and was the one randomly blessed.

Whereas most recognised talents are associated with hard work and so there is then this visible link, I am a good example as I did the bare minimum throughout education (and beyond...).

The way my brain processes and selectively discards/stores the information it receives is very different to majority of the population. I have no control over it.

I take zero credit for any of my achievments - I regularly meet intelligent people near to retirement who have been to a tier 1 university, may have PHDs, worked 60 hours a week since they were born, been on course and what not and cannot reach the levels I can.

My nurturing was no different to siblings/peers (and was terrible!)

Note: I have my weaknesses too, but as a whole, I am exceptional. Not through effort!! Completely random - neither of my parents are intelligent and nothing up the ancestary tree as far as I know.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#244

Post by manvillej »

nradov wrote: post #206
itissid wrote: post #196

"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.

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.

I would perfect my video gaming art. Teenagers in their basement would fear me after school.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#245

Post by hilbert42 »

stonemetal12 wrote: post #217
jvanderbot wrote: post #135

Earlier 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…

Bobby Fisher won his first US Championships at 14 against people who had been playing chess longer than he had been alive. Suggesting they didn't want it more, or practice more than some kid is silly. "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." Sure we can, the initial orientation of neurons differs b…

"Initial speed usually isn't that important, but speed of learning is important and makes the difference between possible and impossible within a human lifetime."

Likely so, but is suggest that personality, drive and motivation are also very important factors. I know from experience that stuff I had little interest in as a youngster and that I've still little in I still know little about.

Yes, my interests have grown and broadened over the years but simply I regard some stuff so irrelevant to my life that it's not worth a second thought and I am much better off applying my limited number of neurons to matters of greater importance and enjoyment.

Of course, no one has the luxury of just learning about what one finds interesting and or enjoyable, life's knocks and experiences along with utilitarian-like imperatives force one to learn stuff they'd rather not know about.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#246

Post by tzs »

doublerabbit wrote: post #158
sethammons wrote: post #103

Earlier quoted context omitted.

My best friend was like that. Couldn't see the practicality until he got bit by a geology and water science bug. He went from calling me to get help figuring out percentages to doing chemistry equations in his head because he "got" the applicability. My brother's mom tutors math. One of her insights with a former student was that they were in need of forming some number sense. She started by walking them both out to…

> For times tables, have you developed any intuition around it? I've tried different approaches. 4x3 being 3x4 But somehow I end up miscounting and giving the answer for 4x4 or be off a digit every-time. A good example was that I was at a brewery last night. They didn't do pint glasses but glasses of: 1/4, 1/2 and 2/3rd's. I thought 1/2 was more than 2/3rd's so I ordered a 1/2 rather than thinking I was getting more.…

> However I was unable to visual how 2/3 is more than 1/2 when 1/2 is half a pint, or half a glass.

Maybe visualize splitting a pint with a friend. If you split the pint into 2 equal parts and each of you gets 1 of those 2 parts you each get the same amount.

Then visualize splitting it instead into 3 equal parts. You get 1 of those parts and your buddy gets 2. There's no fractions there so it should be easier to visualize that your buddy got twice as much as you did.

Comparing those two visualizations might make it easier to see that someone who gets 2/3 of a pint gets more than someone who gets 1/2 of a pint.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#247

Post by diffeomorphism »

mr_mitm wrote: post #236
diffeomorphism wrote: post #230

Earlier quoted context omitted.

Doesn't follow. Bell curve in, shifted bell curve out. Ideally this also tweaks the variance a bit. In other words: Some students flourish despite their teachers, some flourish because of them.

And how would you call the students in the left tail of the Bell curve if not bad students?

Below average students and as long as the average is high enough they are still very competent.

A bad teacher instead gives you a bimodal distribution and just doesn't bother teaching those students.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#248

Post by TomasBM »

penguin_booze wrote: post #139

To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset. People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike…

I believe you're right, even though I don't have any evidence except for my own experience.

This issue becomes very clear when you see how many ways there are to express a simple concept like linear regression. I've had the chance to see that for myself in university when I pursued a bunch of classes from different domains.

The fact that introductory statistics (y = a + bx), econometrics (Y = beta_0 + beta_1 * X) and machine learning (theta = epsilon * x, incl. matrix notation) talk about the same formula with quite different notation can definitely be confusing. All of them have their historical or logical reasons for formulating it that way, but I believe it's an unnecessary source of friction.

If we go back to basic maths, I believe it's the same issue. Early in my elementary school, the pedagogical approach was this: 0. only work with numbers until some level 1. introduce the first few letters of the alphabet as variables (a, b, c) - despite no one ever explaining why "variable" and "constant" are nouns all of a sudden 2. abruptly switch to the last letters of the alphabet (x, y, z), two of which don't exist in my native language 3. reintroduce (a,b,c) as sometimes free variables, and sometimes very specific things (e.g., discriminant of a quadratic equation) 4. and so on for greek letters, etc.

It's not something that's too difficult to grasp after some time, but I think it's a waste to introduce this friction to kids when they're also dealing with completely unrelated courses, social problems, biological differences, etc. If you're confused by "why" variables are useful, why does the notation change all the time, and why it sometimes doesn't - and who gets to decide - this never gets resolved.

Not to mention how arbitrarily things are presented, no explanation of how things came to be or why we learn them, and every other problem that schools haven't tackled since my grandparents were kids.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#249

Post by Malidir »

fHr wrote: post #143

For example finance is such an important aspect of our lifes and you just need some understanding of math principles to understand how to make good financial choices.

Ironically, the ones who don't do well at school (inc maths) are the ones who then become trades like builders/plumbers etc or run small businesses like a shop. And so are regularly working with numbers via estimates and billing.
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