> The vast majority of people think mathematics is about numbers, when it is actually about relations
It is somewhat unfortunate that mathematics is two different things, simultaneously very closely related and very different. One is the abstract study of relationships between axiomatic entities, and the other is arithmetic.
Vast majority of people out there need only arithmetic, and boy they really need it. Calculating tax, taxi fares, shopping bills, splitting bills etc. And to some extent, you need the abstract maths to understand arithmetic.
We have one curriculum for that vast majority of people and for the few who move on to academic maths. Simplifying ideas like integers to number lines doesn't seem like a high price to pay.
It is somewhat unfortunate that mathematics is two different things, simultaneously very closely related and very different. One is the abstract study of relationships between axiomatic entities, and the other is arithmetic.
Vast majority of people out there need only arithmetic, and boy they really need it. Calculating tax, taxi fares, shopping bills, splitting bills etc. And to some extent, you need the abstract maths to understand arithmetic.
We have one curriculum for that vast majority of people and for the few who move on to academic maths. Simplifying ideas like integers to number lines doesn't seem like a high price to pay.