The difference between counting and measuring is that counting is in whole units like one two three four five..
Measurement is a continuous thing so your waist can be 24 inches 24 and a bit more a bit more and a bit more and you can measure all that but the numbers you’re getting are not all whole numbers or even fractions like the square root of 2 is an infinite non-recurring decimal
So you have the concept of continuity which is a very difficult concept in some ways.
But with the digital age we have gone back to counting and you only need two numbers to count zero and one.
It’s rather like the digital radio stations as opposed to the FM radio stations which do you prefer?
I prefer FM.
But I think if we taught mathematics in schools starting when the children are old enough to talk about how numbers happened and these two ways that they happen and then it’s much easier for children or students to learn the technical side of it because they will see some kind of context and some kind of meaning to it
I have yet to find any reasonable way of telling people the ought to learn how to do quadratic equations using a formula that they’re going to understand.
We spend too much time in school learning things we are told when we’re useful later on but it’s very hard for some children to believe it’s going to be useful later on.
Yet if people like to gamble on the horses they soon learn what odds mean even when they can’t do arithmetic at school
How my heart sings 