Why is the obelus sign $\div$ exclusively used in elementary school education

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

That $a \div b = \frac{a}{b}$ is not trivial, and can be difficult for some students to grasp. For some students, $a \div b$ doesn't even mean anything unless $b|a$. In most of their experiences, $a \div b$ requires $a \ge b$ and $\frac{a}{b}$ requires $a \le b$.

Most students start out thinking of $x \div y$ as "I have $x$ things that I want to fairly allocate to $y$ people". They think of $\frac{x}{y}$ as "it takes $y$ of them to make $x$". Skipping over the lesson where "the process $x \div y$ results in the thing $\frac{x}{y}$" by conflating notation is not going to result in fewer confused children.

Hmm. But does "/" have advantage over "÷"? (Both are one-dimensional notations) –

Yes! In teaching order of operations to middle schoolers (which I do professionally), everything becomes very natural when we use dots for multiplication and write divisions as fractions. It makes the confusion disappear because the plus and minus signs naturally space out the problem, and the physical closeness of numbers that are multiplying or dividing each other makes it intuitive that you should do those operations first. It's like all of those viral order of operations problems that adults argue about on facebook - there would be no argument if we abolished the obelus.