I like this quote because I do things like this all the time when I tutor college level math*. Rewriting division as a subtraction expression will help students learn one of the underlying mechanics behind arithmetic operations. As an adult Marina Ratner takes for granted the fact that she can evaluate 30/5 entirely from memory. Kids need to be taught this and they need to know how to parse and manipulate math expressions. If they do not learn how to do this they’ll have more difficulty handling both basic and more abstract operations. I’ve tutored a lot of students who have serious difficulty understanding that division is the same as multiplying by the reciprocal of the denominator.
And then if you learn something like computer science you actually will have to “relearn” the mechanics behind basic arithmetic since computers can’t store numbers as abstract concepts like our brains can.
If you want to read the whole article put the link in a search engine.
If anyone’s interested here’s a problem that illustrate’s what I’m talking about: 20 people are competing in a race. The race will award a first, second, and third prize (assume no ties). How many ways can the prizes can be awarded? I’ll write three underscores on paper and go through the number of people who could be eligible for each prize. This will yield 2019*18. You may notice that this is P(20, 3), but many people won’t when they’re first learning about arrangements.