Kathleen Clark

Mathematics-Methods and Materials

Dr. Leroy Dupee

November 23, 2007

                                                            Reaction Paper

Title of Article: Using Sharing Situations to Help Children Learn Fractions

Author: Susan B. Empson

Source: Teaching Children Mathematics 2.n2 (Oct., 1995): pp. 110 (5).

Summary:

            Susan B. Empson proposes that equal-sharing problems instead of manipulatives area an intuition-based strategy for teaching fractions to upper grade students. She bases her assumption on a case study project conducted by her and two first grade teachers. This article presents the initial findings of the five-week unit of fraction study, conducted with first grade students, which the author generalizes to third, fourth, and fifth graders.

            The pervading rationale of this approach is that the children need to think of problem- solving ideas based on their own experiences with dividing entities instead of using fraction manipulatives, such as fraction strips or fit-together circles. For example, fraction instruction starts with an equal sharing problem that involves partitioning  left over items in sharing situations with two and four children. Ms Empson describes a typical problem as follows:

Four children want to share fourteen apples so that each child gets the same amount. Show how many apples one child can have.

The children develop individual strategies to divide the leftover two apples, such as cutting them into fourths and giving each person a fourth from each apple. Further encouragement by teachers to engage students in thinking about equivalence involves the discussion of four students, for example, receiving equal amounts of clay from three pots of modeling clay.

Reflection:

            I am intrigued by the notion that first graders have the intuitive cognitive skills to solve problems in the real world that involve the understanding of the concept of fractions. As it so happens, I am observing fourth grade math and science today and I just asked a fourth grader a problem-based question that asked the following:

            If you have four students and two apples, how much will you get of the apples?

The young lad answered, “one half.” He has not studied fractions this year, according to his teachers. I was pleasantly surprised by the answer.

            This article is useful because it questions the use of “hands-on” manipulatives, such as, fraction strips, as the best or only method to teach the concept of fractions. As a novice with an unbiased opinion, I think that it is always helpful and prudent to question the methods and materials used in mathematical pedagogy.  Also, I firmly believe that “passionate educators” from the University of Bridgeport, need to be vigilant about differential learning and multiple modalities for teaching fractions and other strands of mathematics.