Opinion
Professional Development Letter to the Editor

Fractions Study Requires Students to Alter Conception of Numbers

December 09, 2014 1 min read
  • Save to favorites
  • Print

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.

Roger Howe

Professor of Mathematics

Yale University

New Haven, Conn.

Related Tags:

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

Events

Student Well-Being K-12 Essentials Forum Boosting Student and Staff Mental Health: What Schools Can Do
Join this free virtual event based on recent reporting on student and staff mental health challenges and how schools have responded.
This content is provided by our sponsor. It is not written by and does not necessarily reflect the views of Education Week's editorial staff.
Sponsor
Curriculum Webinar
Practical Methods for Integrating Computer Science into Core Curriculum
Dive into insights on integrating computer science into core curricula with expert tips and practical strategies to empower students at every grade level.
Content provided by Learning.com

EdWeek Top School Jobs

Teacher Jobs
Search over ten thousand teaching jobs nationwide — elementary, middle, high school and more.
View Jobs
Principal Jobs
Find hundreds of jobs for principals, assistant principals, and other school leadership roles.
View Jobs
Administrator Jobs
Over a thousand district-level jobs: superintendents, directors, more.
View Jobs
Support Staff Jobs
Search thousands of jobs, from paraprofessionals to counselors and more.
View Jobs

Read Next

Professional Development Opinion I Tried AI as a Virtual Coaching Assistant. Here's What Happened
Is using an artificial intelligence note-taking tool appropriate during leadership- coaching sessions? Here's what AI had to say.
4 min read
Screen Shot 2023 11 10 at 6.46.14 AM
Canva
Professional Development Spotlight Spotlight on Instructional Coaching for Personalized PD
This Spotlight will help you investigate strategies for effective teacher PD, evaluate examples of personalized coaching programs, and more.
Professional Development Opinion What Is the Role of Instructional Coaches?
Here’s why structured conversations are the backbone of effective instructional coaching, says Jim Knight.
6 min read
Image shows a multi-tailed arrow hitting the bullseye of a target.
DigitalVision Vectors/Getty
Professional Development Opinion What Do Educators Want From Professional Development?
Traditional PD often overlooks the authenticity and relevancy that teachers need for ongoing professional growth.
7 min read
Images shows colorful speech bubbles that say "Q," "&," and "A."
iStock/Getty