81–90 of 343 posts
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Symbols are symbols, are symbols. Instead of trying to compress everything into a very limited set of "daily language" symbols we should be trying to expand our ideas, including our language(s).
Let's add Chinese, Amharic and Arabic characters. Why not, expanding is expanding.
I wonder if a large part of our math problem is our legacy fixation on Greek letters. Would math be more approachable to English speakers if we just used English? I like to think about math as language, rather than thought or logic or formulas or numbers. The Greek letters are part of that language, and part of why learning math is learning a completely foreign language, even though so many people who say they can't…
If the use of greek letters is a major hurdle to learning maths, I'm guessing that the learner has misunderstood something fundamental about symbols in maths. It shouldn't make any significant difference if the symbols are Latin, Greek or even made up by the lecturer (as long as they are sane).
y = f(x)
If you give a problem with x = f(y) it really confuses people. If I label the horizontal axis y and the vertical axis x in the cartesian plane then confusion ensues.
t = b(a) where t is the velocity and a is time
That's confusing. I suppose it's analogous to me saying
"The male, fluffy, white, large sheep."
There is a certain amount of brainwashing that occurs with the symbols that we use. Using symbols other than the ones that have been standardized on is very difficult cognitively. What you say is true in theory but I think not in practice.
As my old boss once said, "never confuse mathematics with mere arithmetic ."
I've always liked that line, but it's clearly being cheeky and there are times it's applicable and times it's not. All arithmetic is math, but not all math is arithmetic. Except that if you dig deep enough, all math is arithmetic under the hood. Algebra is doing the arithmetic on variables before they're numbers. Calculus is just useful shorthand for compound arithmetic; the derivative is a divide and the integral is…
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I find this sentiment somewhat surprising. Limits is incredibly easy to link to real physical things: movement, speed, acceleration. If speed is distance over time, what's the speed of a moving object at a very specific instant?
Are you thinking of derivatives? I agree that those are relatively easy -- it's the rate of change for a function. Or, in geometric terms, it's the slope of the tangent line of the function's curve. Like I said, limits are used when a function "breaks", so they're naturally hard to visualize. I'll use my typical example for when I discuss teaching math by solving problems: Approximating the area under a curve using r…
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Schools (at least around here) do not hold kids back anymore. No matter what. Some of them get behind in one or more subjects (math, say) as early as 1st or 2nd grade and all their later teachers are stuck trying to give them the remedial math help the desperately need, while teaching their other students on-grade-level material, and also trying to teach the remedial kids enough of the new stuff that their scores on…
Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated. Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.
Further, socially-speaking, being with your actual peers is extremely valuable, obviously.
But yes, the ideal would be a tailored-to-each-child education. Personally, having seen the power of a good Montessori education, I think it's frickin' genius and should be the template for all education (specifically the grouping of 3 yrs together -- e.g. 3,4,5-year-olds together), so kids are perpetually working through the cycle of "look up to someone, mimic someone, mentor someone".
... but I digress.
Fact is, grouping by age works socially and it's much, much cheaper than a tailored education, which is all we an afford (get taxpayers to pay for).
At some point, I expect a software company to make headway in this space and you'd see a bunch of kids staring at iPads all day and a bored teacher playing Minecraft at the front of the room, only engaging when someone gets stuck.
Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday stru…
Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi without first explaining how it's calculated? Where does the "four-thirds" part come from in calculating the volume of a sphere?
Not to mention that there's never enough history to go along with the mechanics - who discovered the quadratic formula? What was their life like? Why were they playing with quadratic equations in the first place? This make math seem less like magic incantations and more like something that was sort of cobbled together by flawed weirdos in order to solve real-life problems, and evolved over time.
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If the use of greek letters is a major hurdle to learning maths, I'm guessing that the learner has misunderstood something fundamental about symbols in maths. It shouldn't make any significant difference if the symbols are Latin, Greek or even made up by the lecturer (as long as they are sane).
In theory it shouldn't matter but it does. We brainwash students to think in terms of y being a function of x. y = f(x) If you give a problem with x = f(y) it really confuses people. If I label the horizontal axis y and the vertical axis x in the cartesian plane then confusion ensues. t = b(a) where t is the velocity and a is time That's confusing. I suppose it's analogous to me saying "The male, fluffy, white, large…
in programming, y = f(x) = x^2 is one way; 'y' is a label for a function of one variable.
But in math there is no fixed typing, or distinctions. The symbolic equation represents a relationship.
Hence:
y(x) = x^2 x(y) = (+/-) sqrt(y)
the domain and domain can be switched and the entire equation rearrange so that a 'variable' becomes a 'function'.
Earlier quoted context omitted.
If the use of greek letters is a major hurdle to learning maths, I'm guessing that the learner has misunderstood something fundamental about symbols in maths. It shouldn't make any significant difference if the symbols are Latin, Greek or even made up by the lecturer (as long as they are sane).
In theory it shouldn't matter but it does. We brainwash students to think in terms of y being a function of x. y = f(x) If you give a problem with x = f(y) it really confuses people. If I label the horizontal axis y and the vertical axis x in the cartesian plane then confusion ensues. t = b(a) where t is the velocity and a is time That's confusing. I suppose it's analogous to me saying "The male, fluffy, white, large…
Is this a US thing? Why would people still think that math is about numbers? Math is about patterns, which got drilled into us by our teachers in primary school. I really don't understand how US education system can fuck up so badly on fundamental subject like math.
In middle school in the US you start getting teachers specialized in their teaching subject matter, but often tangentially. Any one with enough college math credits can teach middle school math (with some other certifications, usually). High school you may, finally, get a math teacher who is a mathematician. If you're lucky.
I wonder if a large part of our math problem is our legacy fixation on Greek letters. Would math be more approachable to English speakers if we just used English? I like to think about math as language, rather than thought or logic or formulas or numbers. The Greek letters are part of that language, and part of why learning math is learning a completely foreign language, even though so many people who say they can't…
As I went through school I saw many students who were bilingual either do poorly or exceptionally well in math.
These were students who spoke Spanish, Tagalog, Chinese, Burmese, etc. at home for the most part and then spoke English at school. Some learned well and some didn't.