291–300 of 356 posts
The author unfortunately has a misunderstanding of equality. Quoting him, "The equal sign is another mathematical concept that’s often misunderstood. It means, of course, that whatever is on either side of the equal sign is equivalent." This is actually wrong. The equals sign (=) is a shorthand for stating not that the two sides are equivalent, but that they are the same (i.e., they are equal). If they were just equi…
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There seems to be a culture of proud ignorance around math more-so than other subjects. While I am sure there is some engineering student out there griping about having to take a psychology course, they don't seem to complain as much as when non-mathy people have to study math. I think it is a mistake for our education system to treat math as something superfluous and abstract from daily life. While neither Laplace t…
> While I am sure there is some engineering student out there griping about having to take a psychology course, they don't seem to complain as much as when non-mathy people have to study math. This is the underpinning of every conversation where engineers say college is a waste of money. If anything, I see engineers complaining more loudly about taking any course that isn't directly related to engineering. This not o…
I suppose I agree with you, but I think math is not given enough credit.
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I don't understand why long division would be a mystery. It's just repeated subtraction - you are finding how many times you can subtract the divisor from the dividend, in a systematic way.
Because the algorithm is so astronomically complicated that people can’t see any pattern or reason in it anymore and it becomes an opaque mystery. I have a PhD in computer science but I cannot understand long division.
My ex taught grade 6 geography. Is a principal now. Thought the seasons were due to earth tilting back and forth. Didn't get that the tilt was the same, but the position around the sun was different
Just a reference frame change right?
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The real world depends on base 10, and so it's way more practical to learn calculations in base 10. I said calculations, not math. I think there is a big confusion between math and calculations. Kids learn calculations, not math. Learning the multiplication table is just a way of how to do quick calculations inside your head. I need to pay 35.15 euros, so how much do I get back? That is calculation not math. In my op…
Wasn't the premise of the article that the reason U.S. students perform so poorly in math in higher grades is because they are only being taught to memorize arithmetical facts and algorithms without properly learning the reasoning behind them? It seems you're prescribing the cause of the problem.
Both have their applicability, but knowing one doesn't imply knowing the other.
Each one also has a proper age group to start teaching it. Little kids have great memory but limited reasoning skills. That changes when they are older, so at that point you should switch from calculations to math. Dropping calculations for math is just as stupid as dropping math because you think calculations are enough.
I struggled with maths as a kid, but gained a much better grasp as an adult, when I had to use it for practical applications. I really think the abstract nature of the way maths is taught (at least in the UK) is a big problem that holds people back - kids don't understand the point of the more complex stuff. I recall asking my secondary school maths teacher what the point of learning about some concept was (logarithm…
I never understood people that questioned the practical applicability of math. Surely they must realize that these things are so elementary that there is no way there was no practical use for them. Logarithms specifically allow you to multiply values quickly by looking up their logarithm in a table, add the values and do a reverse lookup in the same table. This is the foundation of slide rules, which is the way engin…
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Try again? Long division, dividing A by B, is a for loop that maintains the invariant A = QB + R, where Q is the number written on top (initially 0) and R is the number written on the bottom (initially A), by subtracting values of the form B(C)(10^N) from R and adding values (C)(10^N) to Q to compensate. func Longdiv(A, B) { // Assume A > 0, B > 0. N = floor(log10(A)) Q = 0 R = A while (N >= 0) { // Invariant: A = B…
This is just re-stating the algorithm for the umpteenth time. I can read the algorithm. I just can't intuit why it works or why it has been designed this way. I mean your very first line has a logarithmic operation that was not mentioned anywhere in your text or your comment! Just pops in there out of nowhere. I guess it's about the number of decimal digits? But why? Why are we doing things in decimal? A dense ten-li…
The idea of long division is just that to solve A/B, we can find another problem C/B we know the answer to and break it into the smaller problem A/B = (A-C)/B + C/B.
For example, to solve 742/13, the normal way is to observe that 13×5=65 is as close as we can get to 74 without going over, so we can reduce this to
742/13 = (742 - 13×50)/13 + 13×50/13
= (742 - 650)/13 + 50
= 92/13 + 50
But you could also use 13×4=52 and work out
742/13 = (742 - 520)/13 + 40 = 222/13 + 40
222/13 = (222 - 130)/13 + 10 = 92/13 + 10
92/13 = ( 92 - 91)/13 + 7 = 1/13 + 7
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But why not use the abs function or operator rather than squaring and rooting? This is how I always find maths and particularly statistics - I always just want to answer ‘but why’ and then people lose interest in explaining after a while.
> But why not use the abs function or operator rather than squaring and rooting? You can. It's called the mean absolute deviation. Which one you use depends on your application. If you just want to give a summary of how spread out the data is then either would work. Lots of people say that we should use the mean absolute deviation as the default rather than the standard deviation.
I feel like the standard deviation is a black box to basically everyone without statistics degree. It also bothers me that it is so widespread, because almost nobody know how to interpret this value. It seems to me like most scientists treat the standard deviation as a magical number that allows to compare spread between datasets and otherwise doesn't mean anything on it's own. I feel like a lot more insight could be gained from the mean absolute deviation.
I'm also curious how are scientific insights affected by defaulting to something that is extra-sensitive to outliers. The effect can't be big per single research, but in collective?
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What mistake is that? The left hand variable equals the right hand value assigned to it. Foo = bar and 1 = 1 are equivalent in my mind.
The mistake is assuming "=" is a statement of fact (as in mathematics), rather than a request for assignment (as in programming). Depending on which programming language you're using, "foo = bar" can mean either "make foo now equal to what bar is" or "is foo equal to bar now?". Neither one is the same as in mathematics, which is "foo is categorically equal to bar". Consider: foo = 1 bar = 2 foo = bar In mathematics,…
For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels. We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regar…
For those curious, below are some kinds of primary math questions we model after to test teacher applicants. In my experience, many kids are much more enthusiastic about this kind of "challenging" problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well. Note that although they do require a little arithmetic to solve, the ch…
This is a very challenging problem. Without a calculator (or computer), it took me a system of an equation with an inequality in 2 variables, using the fact that the solutions are integers, to solve it.
I would be very surprised (and excited) to meet an 8th grader (let alone a 6th) who could solve this problem without any external help the way I did. I would not expect an elementary school student to have this kind of algebra knowledge. Most elementary school students around here don’t even know what algebra is.