IES Practice Guide - Developing Effective Fractions Instruction for Kindergarten through 8th Grade, U.S. Department of Education, National Center for Educational Evaluation and Regional Assistance, Institute of Education Sciences, 2010 (download entire document)

Key recommendations

Base early understanding on fair shares

Use representations of different kinds

Develop estimation skills for comparing fractions by basing comparisons on benchmark fractions such as 1/2.

Develop the meaning of a fraction as a number (a place on the number line); connect a point on the number line to a fraction of a whole through the meaning of denominator and numerator

Use real-world examples including measurement

Develop the reasons behind procedures and expect students to explain their thinking

The Role of Representations in Fraction Addition and Subtraction, by Kathleen Cramer, Terry Wyberg, and Seth Leavitt, published in Mathematics Teaching in the Middle School, 13(8) April 2008, 490-496.

Key recommendations

Before operating with fractions, students need to understand what a fraction means. This involves understanding the part-whole model for fractions and the ability to judge the relative size of a fraction.

Estimation and visualization are important. These abilities will help students monitor their work when finding exact answers.

Students need to experience acting out addition and subtraction concretely with an appropriate model before operating with symbols.

Making connections between concrete actions and symbols is an important part of understanding. Students should be encouraged to find their own way of recording with symbols.

Students need easy recall of their multiplication and division facts.

Connecting the procedure to a new representation may be an effective strategy to reinforce the procedure.

10 Practical Tips for Making Fractions Come Alive and Make Sense, by Doug M. Clarke, Anne Roche, and Annie Mitchell, published in Mathematics Teaching in the Middle School, 13(7) March 2008, 372-379.

Key recommendations

Give a greater emphasis to the meaning of fractions than on procedures for manipulating them.

Develop a generalizable rule for explaining the numerator and denominator of a fraction.

Emphasize that fractions are numbers, making extensive use of number lines in representing fractions and decimals.

Take opportunities early to focus on improper fractions and equivalences.

Provide a variety of models to represent fractions.

Link fractions to key benchmarks, and encourage estimation.

Give emphasis to fractions as division.

Link fractions, decimals, and percents wherever possible.

Take the opportunity to interview several students one on one on the kinds of tasks discussed in this article to gain awareness of their thinking and strategies.

Look for examples and activities that can engage students in thinking about fractions in particular and rational number ideas in general.

IES Practice Guide - Developing Effective Fractions Instruction for Kindergarten through 8th Grade, U.S. Department of Education, National Center for Educational Evaluation and Regional Assistance, Institute of Education Sciences, 2010 (download entire document)Key recommendationsThe Role of Representations in Fraction Addition and Subtraction, by Kathleen Cramer, Terry Wyberg, and Seth Leavitt, published in Mathematics Teaching in the Middle School, 13(8) April 2008, 490-496.Key recommendations10 Practical Tips for Making Fractions Come Alive and Make Sense, by Doug M. Clarke, Anne Roche, and Annie Mitchell, published in Mathematics Teaching in the Middle School, 13(7) March 2008, 372-379.Key recommendations