The Euler Fraction Faction says the rules for adding fractions come from the number line when they don’t. This lie creates confusion in everyone. The students, teachers, and math ed profs are all bamboozled by this lie.
The math profs can only sputter teach equivalence classes. The math ed types say that is too abstract. But then math ed types teach the exact same rules but all the time claiming in a BIG LIE that the rules for fractions come from geometric lines. They never try to derive their rules from points on a line.
Try it yourself. Justify the rule for adding 1/2 to 2/3 based on saying 1/2, 2/3 and the sum point are points on a line. You can’t assume any rules for fractions. You have to prove those solely from the assumption that fractions are points on a line.
It is such a stupid lie it is amazing it succeeds. It is a lie you know is a lie. That is the definition of a Big Lie.
Fraud Fraction Faction, Fallacy Fraction Faction, Line Fraction Faction, Confusion Fraction Faction, etc. are alternative names for the Euler Fraction Faction. Euler does this and the rest have copied it. No doubt, Euler was copying from others before him. His books were so influential, however, it is fair to label him with the fallacy.
Fiction Fraction Faction is another good name. This emphasizes it is a total fiction that the rules for factions are derived from just saying fractions are points on a line. No attempt is made to teach the rules of fractions in classes based on this. They just say it and then teach the rules without justification. This only confuses, it doesn’t help.