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U.S. Department of Education Releases Teaching Guide for Fractions
Developed by CMU Cognitive Psychologist Robert Siegler
PITTSBURGH—The U.S. Department of Education
has released a new guide, "Developing Effective Fractions Instruction,"
created by Carnegie Mellon University Professor Robert Siegler
(right) and a panel of experts. The guide presents five recommendations for educators to improve the understanding of fractions for students in kindergarten through eighth grade.
"Understanding fractions and how to use them is difficult for many children to learn," said Siegler, the Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon. "Teachers, principals and math coaches can use this guide to help students learn basic and more complex concepts and procedures involving fractions."
Siegler led a panel of math educators, psychologists, teachers and a mathematician to review previous research studies focused on children and learning fractions. The guide summarizes the results of the research and suggests guidelines to effectively teach fractions.
"Understanding fractions is crucial not only to success in all more advanced mathematics but also to success in everyday situations, such as adjusting recipes to the number of family members and comparing alternative financing offers," Siegler said.
The guide's recommendations include strategies to develop young children's understanding of early fraction concepts, and ideas for helping older children understand the meaning of fractions and the computations involved. The guide also highlights ways to build on students' existing strategies to solve problems involving ratios, rates and proportions. The five recommendations are:
- Build on students' informal understanding of sharing and proportionality to develop initial fraction concepts.
- Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central tool in teaching this and other fraction concepts from the early grades onward.
- Help students understand why procedures for computations with fractions make sense.
- Develop students' conceptual understanding of strategies for solving ratio, rate and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.
- Professional development programs should place a high priority on improving teachers' understanding of fractions and how to teach them.
For the past 35 years, Siegler has pioneered research studies on the development of mathematical and scientific thinking in children between the ages of 4 and 14. The general overlapping waves theory of cognitive development, described by Siegler in his 1996 book "Emerging Minds,"
has proven invaluable for understanding the acquisition of a variety of math skills and concepts, including arithmetic, proportionality, mathematical equality, decimal fractions, number conservation and estimation. Recently, his research suggested that certain types of numerical board games, like Chutes and Ladders, are especially helpful for improving young children's mathematical understanding. In June, Siegler and two colleagues were awarded a $10 million grant
from the Institute of Education Sciences to fund a research and development center aimed at understanding difficulties students have in math.