Math seems like an Arts subject, where you must learn all the cultural background, as in English Literature. I'm not sure it's necessary, given it's not logical nor self-contained, but is arbitary and historical. Then again, I'm not absolutely convinced it's not necessary...
To complain about the effort to build a common vocabulary is to complain about the effort of participating in any society.
I think that an interest in maths, is the fuel to help one cross from problems to solutions. With how mathematics is taught nowadays, mechanical rather than analytical, I can imagine how easy it is for kids to develop a negative sentiment towards math especially when they get dozens of rote problems every day.
I suspect curiosity is of paramount importance, and that curiosity is not fostered in school about math.
This is exactly how I felt growing up. It wasn't until actually looking at the practical applications of math that I got it. Doing equations for the sake of it without any actual context constantly frustrated me to no end and made me hate math and physics because it made me feel incompetent and stupid, it's been a struggle getting rid of this feeling even to date.
What makes the difference is that video games aren't compulsory. So they represent true play. Which is what makes them educational, unlike a school curriculum, however much it is tweaked. Well, until something more fun than video games arrives on the scene...
Just like in sports, where you must also do a lot of basic practise to get good.
Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it gets boring.
I'm just making things up tho
Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph theory or even combinatorics perfectly well even if you have no idea what 11*15 is off the top of your head and have to look it up every time.
Its just a ridiculously backwards approach to teaching. We don't teach CS by testing people on memorizing syntax and API calls - they are rightly relegated to "google it when you need it, eventually you'll remember it". Of course algorithms are more interesting and building things is more fun so we focus on that.
Current way of teaching math is just a historical accident IMO. No real reason it couldn't be conceptual and interesting from the start if there wasn't so much inertia around current systems.
Years later when I worked in a shop I used to cost complex print jobs in my head and co-workers though it was magic.
The way maths is taught in the UK is largely how and very rarely why.
Splitting out arithmetic from "Maths" doesn't seem terribly sensible to me. Times tables aren't really problematic, and they do provide opportunities to teach valuable concepts (5x6 = 6x5).
I'm honestly dubious of anyone who claims that the reason people hate maths is because of times tables.
If someone thinks of math that way, I can understand why it would be boring to them. Thats what I mean by blocked on arithmetic. If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes.
A hammer and a chisel are tools. You can use them to shave a bit of wood off the door, or you can use them to carve a beautiful sculpture. You can do neither without knowing how to use them.
I agree that too much of maths teaching is "here are 100 quadratics, go solve them" - which is obnoxious and dull. But "blindly following process" (matrix multiplication, change of variables/base, sum to infinity etc) happened throughout my degree and is a component of higher maths as well. Heck, most of the proofs I remember use "tricks" that any mathematician is expected to just know.
I sure as hell don't think children are taught maths well. I remember being taught how to take the derivative of x^2 without the teacher bothering to show where that came from or what it really meant. Heck - children are given the quadratic formula to memorise and basically told "it's magic, learn it" instead of showing them how you can trivially create it by completing the square.
But mathematics does involves a ton of following some process or other to get the problem into a format you can do something with. Probably by following a different process that you've done before. I'm not sold that you can simply eliminate that aspect.
The times tables are BS math? The thing I've used IRL literally hundreds (thousands?) of times more than I've ever used anything from, say, calculus? The thing that yes I could use a calculator for but damn would it get annoying because I use it so often? That's what we should stop teaching?
Math things I use a lot in actual real life: basic arithmetic (drilled skills/knowledge!), basic algebra, factions/percentages (converting one to the other, and scaling other numbers by them—the basic arithmetic stuff is also vital here), and generally how triangles work. That's... almost all of it, actually. Some high-school-level stats stuff from time to time, I guess.
On the other hand, I can't imagine anywhere that would expect one to know 11x15 off the top of ones head.
Learning how to perform mental arithmetic with the aid of pencil and paper was a way to escape from the grind of farm work. One could get a respectable job as a clerk. However with the advent of electronic cash registers and smartphones a way around this later form of grind has also been found. So no need to make it compulsory. Which isn't to say that people don't choose to practice specific things they personally consider useful. Even gamers do that.
So yeah, I think you still need to grind these multiplication tables, even if you have perfect version of Wolphram Alpha on your smartphone. It won't tell you what question to ask.
This is because coercion in education is: (1) painful, (2) prophetic, (3) it doesn't work!
What happens in real life is that if somebody needs to know something because they are keen to do something else then they will learn it efficiently, 'just in time' and precisely to the extent needed. Assuming their creativity is relatively intact...
But I can kinda understand why, you almost never have to multiply 9*7 by hand. If you're doing algebra or any symbolic calculations you rarely use digits other than 0-4.
In real world Benford's law + usual rounding greatly reduces the need to multiply by 7 or 9 (or 8 for that matter).
The way around is to just not do that.
Students get huge amounts of practice with basic multiplication if they are assigned more interesting problems/projects that use multiplication as one step, and will inevitably memorize all of the same basic facts, assuming they actually do the work.
Memorizing multiplication facts for their own sake is a soul-sucking waste of time that turns kids off from math for good.
Similarly, the way to get good at spelling is by reading engrossing books for hours every day and writing about subjects of personal interest. Studying lists of spelling words in school is beyond pointless.
These are not skills like sports or playing musical instruments, where there is a particular physical technique involving fine muscle coordination, where practicing incorrectly will establish wrong movements. Instead we’re talking about simple verbal/linguistic recall of previously seen information.
[1] http://www.pbs.org/video/math-is-amazing-and-we-have-to-star...
Video games are safe e.g you can always try again, you can do incrementally well.
Video games are scary in an exhilarating way, you blood will pump and your pupils will dilate but at the end you can put it down, turn the lights on and watch funny cat videos to recover.
Math (at school) is hard because you get one shot. Finite lives. After enough retries society says "nope, you're done". It's hard because you can't test yourself when ever you want and your study is not directly related to your tests.
Math is scary like anxious scary. Like stay up at night dreading your exam or don't sleep for a weekend to finish your report scary. You can't watch cat videos and hope it goes away because it won't. You can't buy a new math or try it again in a few years.
You get one shot. You get little to no feed back.
That's hard and scary.
I love learning new areas and new techniques. And when Im teaching myself, I can fail and I go back a step or 2. Not the end of the world.
If I do similar in a class, then I set myself further back with a slowly growing chance of doing badly (D or F). And in College, then its another 1-4 credit hours to pay for the privilege. They not only fail me, but demand more money.
Edit: misspelling that looked bad (dong=>doing)
Without the pressure I'm not scared of revisiting hard things, I'm driven to actually.
Edit: to indicate that a "simple" perceptron isn't actually that simple.
How did you know it wasn't right? Did you run into a problem trying to implement requirements which you knew all along and accepted? (As in, you started coding without planning for some of these requirements ahead of time, then got stuck?)
Or did you learn about and adopt new requirements which weren't easy to retrofit into the existing work in progress?
In my early attempts it was things like parsing which tripped me up. I'd implement something that broke the bracketed lists up into a list of tokens and then get stuck nesting those lists into an ast. Abandon an implementation for a while and then try again at the problem, often with a fresh implementation.
Then is was evaluating expressions, when to evaluate the arguments and exploring different approaches (fexprs).
I'd do these iterations across months and with different languages. First python then JavaScript, Ruby, C.
My favourite was the JavaScript implementation. Lisp code is literate and I bootstrapped most of the built in functions by exposing the environment as a cons tree (and working with cons trees internally in the interpreter).
"No matter how good the student is now, they sucked at one time and they can never escape this eventuality".
Imagine a game that's tough, full of oft-used rules, failure potentialities everywhere, limited lives, and punishes failure/learning cycle. That's School.
If you get a mediocre grade on a math test, even a failure, we shove you into the next subject in the curriculum. When you start failing that because new math builds on mastery of old math, we tell you you're not a math person and should probably major in Literature.
Then we go complain to the other math teachers that students are lazy and apathetic, and ask each-other how it is that math PhD students manage to spontaneously generate from such piles of shit.
> Plenty of video games are known to be scary and hard
Those statements seem related because of the ambiguous definition of "scary". In relation to math, "scary" causes anxiety, whereas in relation to video games, "scary" causes excitement.
As soon as you grasp the different meanings, you can clearly see that even though both statements are about the same word they are still orthogonal.
The difference between literacy and illiteracy in this case, IMO, is almost an emotional one - its the ability to say to yourself, "ok, I may not know what this keyword means, but I know what is in front of me is not magic, that it can be understood, and I can understand it with some research and patience"
It helps a lot for ones future if someone is able to be taught this skill early on.
I suspect that mathematics being poorly taught is also a major contributor.
It's pretty simple when you realize it's (mostly) all about lines.
It's definitely not an easy problem to solve and I certainly don't envy elementary/middle school teachers.
If I'm not supposed to learn Calculus until I learn Algebra, that must mean I can't learn Calculus until I learn Algebra.
If my Algebra class lasts for a year, that means it must take an entire year to learn Algebra.
If I am supposed to learn Algebra first, then I must not be able to sufficiently wrap my head around anything related to Calculus.
That means that whenever I hear about "limits", "d/dx", I should immediately lose attention; after all, those are Calculus-related things, and my underdeveloped brain will not be able to comprehend such subjects for another year, and I shouldn't even try.
Of course, none of those are true. If I wanted, I could
* learn at my own pace * learn in the wrong order * wrap my head around limits, d/dx, L'Hopital's rule, etc. before understanding factoring, trigonometric functions, etc.
In fact, any of these would have put me far ahead in my education.
"Traditional" education requires a student to be lazy, or hold [him/her]self behind academically. To make matters worse, it requires that student to be a specific, quantified amount of lazy/held back.
For me personally, I struggled to keep up with the obscene amount of expected rote homework, while also feeling miles ahead of lectures, even though the homework and lectures were from the same class.
When I started learning about programming on my own, I suddenly had the freedom to do all of the things I mentioned above. Programming, as a subject, is especially applicable: There are abstractions, paradigms, languages, etc. You can jump into any aspect headfirst, and still get your bearings.
Unfortunately, framing math as hard or scary only serves to reinforce stereotypes and bar people who do not have the keys to defuse that framing from advancing. It's not the rich male kids who are told math is hard and scary.
I can't see him hurting himself with maths, but if he decided he's gonna fix something electrical in a few years time, well that could be very bad indeed.
In UK girls get the better results on average. In part I think this might be because they're taught as they are generally quieter and less desirous of rough-and-tumble (in primary school, by the predominantly female teachers, say) that girls are more studious. Generalising further: boys are thus modelled as either boring swots or good for manual labour (they don't sit still, which for some reason seems to make many female teachers think means they're not intelligent).
[I'm pressing the point probably a bit much I know].
Junk science if there ever was any. The effect sizes for these treatments are tiny, if they even replicate it all. It seems like every day now there's a new rebuttal of stereotype threat, implicit association tests, priming, etc.
Just from today: http://www.tandfonline.com/doi/abs/10.1080/09515089.2017.135... http://internal.psychology.illinois.edu/~acimpian/reprints/j...
From your second link, conclusions section:
>Nonetheless, the evidence overwhelmingly supports the tripartite pattern: (1)Although errors, biases, and self-fulfilling prophecies in person perception, are occasionally powerful, on average, they tend to be weak, fragile and fleeting; (2) Perceptions of individuals and groups tend to be at least moderately, and often highly accurate; and (3) Conclusions based on the research on error, bias, and self-fulfilling prophecies routinely overstate their power and pervasiveness, and consistently ignore evidence of accuracy, agreement, and rationality in social perception.
Namely point 1, which points out it is valid science. Point 3 is the criticism that it is vastly overstated, and personally I would add it is used as a political tool far more than it should be. But the science isn't junk.
Sometimes it is smart to embrace this. Find a grade school student struggling with math, tell them it is easy, and they'll think themselves a failure. Instead, I find it better to tell them that math can be easy or hard, and it depends upon how one is taught. Let the student know the failure to understand math isn't due to something inherent in them, but something that can be changed. (I am assuming a student who tries or has tried in the past, if they don't try at all, that takes a different approach).
Math, as taught in school, is hard.