The Euler Fraction Faction wants to teach fractions as points on the number line that are already meaningful and don’t require some funky abstract definition as a function or equivalence class.
The Euler Fraction Faction says just say fractions must exist because there must be points on a line. Then without any justification they teach the rules for working with fractions. They never admit these rules are not implied by the number line interpretation at all, but are plucked from the air.
The Euler Fraction Faction are covert behavioralists. They pretend to justify fractions in terms of a line, but in fact, they teach a set of algebraic rules that are not derived in any way from any line.
The Euler Fraction Faction are in complete control of math ed. They ignore the fraction as function or fraction as equivalence class approach. But they use the same rules. All that is different is they lie. They claim the rules they teach are based on the number line, when in fact they offer no such justification at all.
They just introduce the rules for pairs of numbers all the time claiming the pair of numbers is a geometric point and the rules come from the line, when in fact they don’t.