Fractions

Dennis Deturck, a noted mathematician and the Dean of the College of Arts & Sciences at the University of Pennsylvania, has provoked a little firestorm within the math education community by suggesting that schools consider delaying fraction instruction until students are dealing with higher level math. In a 60 Second Lecture a few years ago, Deturck said: “I have a simple suggestion when it comes to teaching fractions in elementary school: Don’t.” Decimals are sufficient. With a new book offering these and other ideas coming out next year, the UPenn dean’s thoughts about reforming math instruction have been making the news.

Critics of Deturck’s suggestion argue that fractions are a fundamental part of our daily lives, unless, of course, you live with the metric system. Some argue that his suggestion of pushing fractions higher up in the curriculum is elitist. Then again, we delay a lot of content until students are better prepared to handle it. Frankly, I welcome the conversations sparked by this controversy. Math instruction in the U.S. is failing a lot of kids. We should be challenging it.

I met Dennis about a year ago when we were both playing advisory roles for the PBS show Cyberchase (a good program), and we talked about fractions then. Dennis does a lot of work in the Philadelphia area schools. He has a good deal of direct experience with struggling kids, and he feels we push them into finding common denominators and computing with fractions long before they have an understanding of what fractions are. I agree.

We’re doing some work ourselves now at Tom Snyder Productions with fractions. We’ve found kids in upper elementary grades who don’t know that 3/3 is 1. They don’t know how to compare 0.6 and 5/10. And they don’t believe that a fraction can ever be greater than 1; after all, we tell them that fractions are parts of a whole. How could it ever be more than that whole? These students, who don’t get fractions, are being asked to add and otherwise manipulate them. The arcane rules they’re learning for these procedures are meaningless, confusing, and readily forgotten.

We’re seeing what we can do to build a better foundation, to help kids make the tough transition from discrete to continuous quantities, from counting how many to measuring how much. A rich, intuitive sense of fraction quantity and equivalence can provide a much stronger base for learning and understanding rational numbers. We’re working on it.