CMV: I believe division should only be taught as fractions in school. Ignoring the division sign "÷" ":"
An extreme amount of students has issues with correctly understanding fractions like "1/2". I have seen many who don't even know that it is equivalent to 0.5 or that it means 1÷2.
Even more of those students don't understand that something like 10 × 1/5 is the same as 10 ÷ 5.
I believe this comes from students looking back at their early education and not really bothering with new things that appear more complicated but do the same.
Thus I believe that fractions are taught too late and when taught, their complete usage is ignored for too long.
I believe that we shouldn't teach division as early as we do. Instead we should go from multiplication directly to fractions. Completely ignoring the division symbol, only using the upper and lower half of the fraction.
Explaining divisions directly on fractions. No usage of "÷" or ":"
I believe this would make understanding fractions as what they are a lot easier for students in the long run. Nothing is lost by not using the division sign. In actual maths I've only ever seen it used in something designed to trip you up, not something actually useful.
It also makes it a lot clearer for teachers to explain how you can divide by multiplying.