To the Editor:
The article “Approach to Fractions Seen as Key Shift in Standards” makes many good points.
I have long been interested in math education in the United States and am currently serving on the U.S. National Commission for Mathematics Instruction. I also have been involved through an initiative at Yale University to strengthen teaching in public schools through the kind of high-quality teacher professional development that will be necessary if our country is to meet the Common Core State Standards’ goals for mathematics.
A substantial portion of the national seminar I led this year on “Place Value, Fractions, and Algebra: Improving Content Learning Through the Practice Standards” was devoted to fractions, and especially to the unit fraction approach.
In this seminar, we used two main representations: the number line and area models. Each has its advantages. The number line is especially good for conveying the magnitude of numbers, and the fact that fractions with a fixed denominator fit into a system that is quite analogous to whole numbers. It also provides a uniform model for addition. The area model can be quite useful for studying renaming fractions, and related issues, including adding, multiplying, and comparing. The teachers seemed to like this approach.
Although I agree with most of the article, I disagree with a remark made by Zachary Champagne, of the Florida Center for Research in Science, Technology, Engineering, and Mathematics at Florida State University. He said, “I should not have to change what I know about numbers to learn fractions.”
I believe that one of the reasons that fractions are hard is that students do have to change their conception of what a number is—from a count to a ratio—in order to work successfully with fractions. That the need for this change has not been previously recognized, and is not taught, was a consistent theme in my seminar.
Professor of Mathematics
New Haven, Conn.
A version of this article appeared in the December 10, 2014 edition of Education Week as Fractions Study Requires Students to Alter Conception of Numbers