I am from Taiwan (ROC). When I was in elementary school, as I remember, instructors and textbooks notated division (of real numbers, for sure) as "÷", which (as I just read Wikipedia) I know is called the obelus.
But at that time I read many advanced math book myself, and learned that people use "/", the slash, to notate division (and fraction, if you see this way).
Strangely, when I was in the first year of middle school (equivalent to the 7th grade in the US), the math textbook announced that, from now on, the obelus is to be discouraged and deprecated, and we shall always use fraction, and when the space does not allow, use a slash.
Except elementary school textbooks (and exercise books), I have never seen the obelus.
I don't claim I read widely about math, but I have basic familiarity with like analysis, algebra, geometry. Still, I have nowhere seen the obelus.
Neither does any scientific publication use it, as far as I recall.
I may have had a calculator that has an obelus on it, but I can't find it now.
Why is the obelus taught in the elementary school, though it virtually never occurs elsewhere? I see no advantage in teaching kids one very rare (if ever used) notation — obelus — in the beginning, and abandon it, and then enforce the use of another notation — slash. It is also very mysterious why obelus stands for division, which Wikipedia doesn't say. On the contrary, a slash reminds me it is a fraction "lying down" due to limited space, and is completely intuitive.
From Wikipedia: (lest it be edited away)
Although previously used for subtraction, the obelus was first used as a symbol for division in 1659 in the algebra book Teutsche Algebra by Johann Rahn. Some think that John Pell, who edited the book, may have been responsible for this use of the symbol.
My guess is that the obelus was first used to stand for division.
No wonder 17th century people still used strange notation borrowed from Greek text criticism (see above). The convention of algebra equations was still being formed, and the Principia Mathematica's equations were mainly written verbally!
Afterwards, the slash was probably gradually widely used, but elementary school textbooks, somehow, did not follow the trend.
The appearance of the obelus in elementary school textbooks, then, is probably a relic of old notation.
Do you agree my guess? Is there any source that confirm this, or claim otherwise?
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Best Answer
In elementary school, it's hard for kids to "switch between notation", as we have done later on in our lives.
We start with $\div$, then we go to $/$, and now we do something like $\frac{a}{b}$.
In elementary, students are not familiar with "fractions", or just know the very basics about them. Hence the $\frac{a}{b}$ ratio doesn't make sense ... not until you actually use fractions in middle school and so on.
It's important to realise that $'/'$ the slash, refers to fraction. When we write $(a/b)$, it's because we are lazy and do not want to write $\frac{a}{b}$. So technically it's the same thing as fraction.
This is why students in elementary just use the regular $\div$ symbol. It's just a symbol. No fractions or anything complicated just yet. It's the same reason why kids in elementary use $\times$ to indicate multiplication and not the dot, $\cdot$, as we use when we are older. They do not deal with complex numbers, and so these symbols that we use as adults are really after we see the use of math. In elementary, it's very basic, hence basic symbols.
In the end it's because of the type of math we do. Imagine writing something like this:
$$\int^{\dfrac{x}{5}}_{0}(x^3+\frac{x^2}{5}+\ln(\sin(\frac{x}{4})))dx$$
$$\int^{x\div 5}_{0}(x^3+(x^2 \div 5)+\ln(\sin(x\div 4)))dx$$
We even had to add extra parentheses to make it clear that $x^2\div 5$ is one thing. Heavier math = more compact symbols