Any good mathematics educator will know that you can only learn and understand new concepts when you can associate these to existing well-formed concepts.
Today you have graduates who can use advanced calculus theorems, but those same graduates have a very superficial understanding of what they are using. It's no surprise because they can't even tell you what is a number. Well, their professors don't know, so how could they...
Mathematics according to webster:
"...the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations"
There are two words in that description which say everything: number and measurement. The rest is unnecessary because it follows from further investigation.
Most students find math difficult because they never have any real foundation. Since set theory was introduced in the USA, math performance has gone south at an alarming rate. Today the USA is number 37 in the world when it comes to math. Reason: the kind of shit you are peddling here on sci.math.
The reification of number involves measurement, not sets. Certainly NONE of Peano's juvenile ideas. :-)