His inspiration is that, “Mathematicians are always questioning the axioms. Everybody knows that questioning those often results in the most substantial gains in terms of progress”, and so he has dared to question the axiom of teaching fractions. While it is true that questioning is often the seed of change, it is also true that questions asked just for the sake of questioning are plain idiotic. And when DeTurck adds, “The study of fractions should be delayed until it can be understood, perhaps after a student learns calculus”, this begins to sound like (a) either an April fool’s joke or (b) DeTurck urgently needs to visit his doctor.
I don’t know about Professor DeTurck, but I learnt fractions at the same time I was learning the difference between genders, while I learnt calculus around the time I had my first crush. To my mind, it is pretty clear what should come first. Pennsylvania State professor George Andrews agrees with me, “Arithmetic is the basic skill. If children do not know arithmetic, they can't go on to algebra, which leads to calculus. From there you go on to other things”.
However, I disagree with Dr. Andrews when he adds that, “DeTurck's ideas will unfortunately gain traction because of the misguided belief that math education can somehow be made easy. Math is hard. The idea that somehow we're going to make math just fun is just a dream.” Is Math really that hard? Is it really no fun at all?
Personally, I think that people/kids who find Math hard are the one who come to it as observers. You can't become competent at Math by observing someone else doing it, you have to get your hands dirty and participate in it yourself. When I was a child there was a period when I was doing poorly in the subject and was under the impression that it was because Math is hard, and I just didn't have the chops for it. The real reason I was doing poorly was -- I never opened my Math book at home and even the assigned homework I did at the last minute, sometimes while going to school in the bus. Fortunately I was rescued from this state of affairs by a tutor, who showed me that the people who get Math are the people who sit down and do it.
Languages can be absorbed, history can be memorized, Math, on the other hand, is something that you have to do. You learn Math the same way you learn how to ride a bicycle. From there on, you go on to learn how to drive a car and then a plane. Only, when you are cruising, can you look around and observe and enjoy the view. But, of course, the ride itself is always fun.