CLASSROOM CONCEPTS

THE SECRET TO TEACHING FRACTIONS

• Classroom Management of Manipulatives

• The Islands and Geoboard Model

• Modeling and Naming Fractions

• Equivalent Fractions

• Comparison of Fractions

• Complex Fractions

• Mixed Numerals and Improper Fractions

• Finding a Common Unit

• Multiplication of Rational Numbers

• Division of Rational Numbers

• Addition of Rational Numbers

• Subtraction of Rational Numbers

• Decimal Notation and Percent

An excerpt from Teaching with Fraction Islands^®, our product manual and teacher guide   © 1997 and 2001, Pathfinder Services, Inc. All Rights Reserved, by Alice I. Robold, Sandra L. Canter & Nancy A. Kitt

What is there about fractions that make them so difficult to teach and difficult for children to understand?  Prior to their work with fractions students have explored ideas about the set of cardinal numbers and a subset of the cardinal numbers, counting numbers. It is difficult for children to shift from the additive thinking required for cardinal numbers to the relative thinking required for rational numbers.  All their experiences involve the idea of  one-to-one correspondence between the set of counting numbers and the set of objects represented by that number.  To count a set with five objects in it, a child would point to each object while counting “one, two, three, four, five.”   Each number name would be assigned to an object and each object would be assigned a number name.  The difficulty with understanding rational numbers is students must begin to think relatively instead of additively.

Think of two children.  Each child has a sandwich, both sandwiches are the same size.  One sandwich is divided into four parts and the other sandwich is divided into two parts.  Thinking additively, the child with the sandwich cut into two parts would ask why the other child has a “larger” sandwich with four parts.  Rational numbers require the child to make a shift to relative thinking.  The sandwich is now a “unit” or whole and the parts refer to part of the whole.  Many children are unaware of this shift in thinking and they continue to try to apply the rules for cardinal numbers to rational numbers.  They do not understand the need for a change in their thinking and all too often experience difficulty in mathematics beginning with fractions.

Physical models like Fraction Islands^® help children shift their thinking by developing ideas about rational numbers as they are related to the “unit.”  They understand that one-half is an idea and that one-half is relative to the size of the unit.  When children are asked to memorize rules they do not understand they begin to lose interest in mathematics because it does not “make sense.”  Physical models like Fraction Islands^® help children make sense from fractions and allow them to develop “rules” on the basis of their own thinking and explorations; physical models validate the child’s thinking.