A Network Connecting School Leaders From Around The Globe
By Henry Borenson, Ed.D.
The Common Core elementary math standards place substantial emphasis on fractions. Indeed between grades 3 and 6, more than 40 standards relate to fractions.
These standards present a challenge to many elementary school teachers who have been using traditional teaching methods that focus on procedures and algorithms. These teachers now need to acquire the content knowledge and the instructional strategies to enable their students to make sense of these fractions standards.
That students have difficulty with fractions sense is well known. For example, in a 2009 National Assessment of Educational Progress (NAEP) study only 25% of 4th-graders could select from among 5/8, 1/6, 2/2, and 1/5 the fraction closest to ½. Evidently, these students’ teachers had not been able to explain successfully some basic notions related to fractions.
Yet it is the elementary classroom teacher who is expected to correct this situation. It is through them, according to the Common Core math standards, that students are to develop “expertise” in the “conceptual understanding” of mathematics. The standards define this expertise as “comprehension of mathematical concepts, operations, and relations.” In other words, besides being able to perform calculations with fractions, students must comprehend what they are doing, to have what is known as “fractions sense.” The acquisition of fractions sense cannot happen if teachers themselves do not have this conceptual understanding and the means to communicate it.
To illustrate: At our Developing Fractions Sense workshops, when we ask elementary teachers to explain what is meant by the fraction ½, often we receive this response: “It is one part out of two.” There is no reason to believe that these teachers would tell their students anything different. And so we see how the problem begins: The concept of fraction has not been well defined for students. Without this basic building block, how can students possibly be expected to be successful with fractions?
What is the correct way to define the fraction of ½, or more generally the fraction 1/b? The standards say in 3.NF.1: “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.” Notice the important words that were omitted in the teacher response: “whole,” “partitioned,” “equal.”
Even if a teacher reads this definition, there is no reason to assume that the teacher will immediately understand the necessity for each of these important words. A school math leader or coach may need to provide a fuller explanation. But let’s assume that the teacher does understand the definition. The teacher still needs to develop an instructional strategy to communicate this understanding to students. Simply asking students to write down and repeat the definition will not do. The teacher needs to illustrate the definition in various ways for students to grasp its full meaning and be able to operationalize it in practice.
I would suggest that the most effective way to begin teaching fractions is with fraction blocks (also known as pattern blocks). The teacher can clearly illustrate partitioning a whole—represented by the ...
Dr. Henry Borenson is the inventor of Hands-On Equations, a system he designed to enable young children to learn algebra. He is also the President of Borenson and Associates Inc. His company provides the Making Algebra Child’s Play workshop for teachers of grades 3 to 8. Their newest workshop is the Developing Fractions Sense workshop for teachers of grades 3 and 4. Visit www.borenson.com for additional information.