New answers tagged teaching
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‘Lies to children’ in mathematics and statistics education
As OP asks for examples "particularly at the undergraduate level or higher", here is a meta-mathematical "lie-to-children" that undergraduates tend to learn (often probably ...
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‘Lies to children’ in mathematics and statistics education
Anyone who was taught about Venn Diagrams was probably told that a set is a collection of objects.
This is, of course false. But, it is a handy way to think about sets, and even when you get around to ...
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‘Lies to children’ in mathematics and statistics education
Students are often taught the chain-rule as a trivial cancellation law. In reality, there are intricacies within the chain-rule.
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‘Lies to children’ in mathematics and statistics education
My biggest pet peeve:
"A vector is a quantity with both magnitude and direction"
One is required to say this to pick up marks on on A-level physics exam, say, despite it being very, very ...
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‘Lies to children’ in mathematics and statistics education
$$\frac{1}{0} = \infty$$
I was told this by my Math teacher in my 8 or 9 grade. I only knew at that time about infinity was that it is a very large number; so large that no can ever write it.
I don't ...
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‘Lies to children’ in mathematics and statistics education
Whether or not the derivative $\frac{dy}{dx}$ is a fraction. Similarly, what, exactly, are $dy$ and $dx$?
This actually goes through several iterations of lies:
We first hammer it into Calc I ...
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‘Lies to children’ in mathematics and statistics education
We can define irrational numbers to be those numbers which are not rational, and then define the real numbers to be the union of the rationals and irrationals.
The problem with this definition is that ...
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‘Lies to children’ in mathematics and statistics education
1-2-3-4-5-6-7-8-9-10... Well, not if you are using binary...
The angles on a triangle add up to 180 degrees... Only if the triangle is on a flat surface.
Multiplication is repeated addition. Have you ...
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‘Lies to children’ in mathematics and statistics education
I was told in high school that Euclidean geometry can be derived from the five postulates written by Euclid, but this is not the case. Several of Euclid's proofs have holes in them and one can create ...
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‘Lies to children’ in mathematics and statistics education
Independence in probability theory is not independence in usual sense because it does not take into account causation.
Addition1: The notion of independence is well-known en.wikipedia.org/wiki/...
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‘Lies to children’ in mathematics and statistics education
$ $
$\LARGE\mathbb R$
Students are introduced to real numbers long before they are ready for the formal definition. At second level they are primed for dealing with fractions and not fractions and ...
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‘Lies to children’ in mathematics and statistics education
Young children 5-8 years old, are taught to subtract the smaller number from the bigger number. They are told that you can't subtract a bigger number from a smaller number. This lie has its ...
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‘Lies to children’ in mathematics and statistics education
We usually teach:
$$\int\frac1xdx=\ln{|x|}+c$$
Whereas it should be:
$$\int\frac1xdx =
\begin{cases}
\ln{x}+c_1 & x>0 \\
\ln{(-x)}+c_2 & x<0
\end{cases}$$
Why don't we teach the correct ...
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‘Lies to children’ in mathematics and statistics education
The idea that “a number” means “this decimal expansion”, rather than the expansion being a way of representing a number that has some more set-theoretic definition. It's the de facto truth for ...
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‘Lies to children’ in mathematics and statistics education
The average
where the lie-to-children is the word "the".
Ask anyone what "the average" of a set of values is, and immediately you'll be told the arithmetic mean. That's how it's ...
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‘Lies to children’ in mathematics and statistics education
A lot of things around the limitation and construction of number spaces come to mind such as:
You cannot divide 5 by 2.
You cannot take the square root of a negative number.
You must not divide by ...
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‘Lies to children’ in mathematics and statistics education
I was introduced to the real numbers as "all the points on a [two-sided infinitely long] line".
At best this is a circular definition. It's certainly very sloppy, and those words could be ...
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‘Lies to children’ in mathematics and statistics education
I think sometimes when introducing $\pi$ to children they are told that it's exactly $3.1415$ or some other arbitrary number of decimals, or even that it equals $22/7$
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‘Lies to children’ in mathematics and statistics education
"Random variable."
...because, as we all know, a random variable is neither random nor a variable. It is a real-valued function. But if we tried to introduce the concept, the feeling, of a ...
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