[acjohnson55]

There are certainly people who can learn that way, but it's not effective for most people. Most people have a limit to the amount of abstraction they can operate under before they need a tangible connection. Once that connection is made, most people can continue on to higher levels of abstraction.

[jshowa1]

The problem is math is entirely abstract. So you must learn the abstraction before applying it. Otherwise, you learn how to add 2 + 3, but you don't learn how to add n + m.

[acjohnson55]

That strikes me as a strange way of looking at it. Most math taught to people who aren't pure mathematicians is taught precisely because of application to concrete situations. We value pure math largely because of the potential for future concrete applications.

In case you aren't aware (and I wasn't until I trained to be a teacher, so this isn't meant to be condescending), there are alternative methods of teaching besides abstraction-first. See https://en.m.wikipedia.org/wiki/Inquiry-based_learning

[jshowa1]

I'm aware. Examples are given to demonstrate abstract concepts. However, that doesn't preclude you from needing to learn the abstract concepts eventually. Otherwise, you go back to knowing times tables for 2's and 3's, but not n's and m's.