ERIC Number: EJ1063900
Record Type: Journal
Publication Date: 2015-Mar
Reference Count: 8
Moving beyond Brownies and Pizza
Freeman, Daniel W.; Jorgensen, Theresa A.
Teaching Children Mathematics, v21 n7 p412-420 Mar 2015
A lack of fractional understanding is a well-documented obstacle to student achievement in upper elementary and middle school math (National Center for Educational Statistics [NCES] 1999; Lamon 1999; National Research Council [NRC] 2001). Lamon (1999) notes that one major conceptual hurdle that students must overcome is the idea that fractions are numbers in and of themselves, not a composition of two, distinct, whole numbers. Further, it is likely that students fail to recognize fractions as discrete numbers because much of school mathematics focuses on understanding fractions as parts of wholes or parts of sets. To a great extent, children's earliest experiences with fractions are situated in part-whole contexts where both the part and the whole are whole numbers. Many of these experiences involve partitioning items like brownies or pizzas into equal regions. These are worthwhile endeavors for young children, but at some point, students must transition to thinking about fractions in ways that are more sophisticated. This article describes how Daniel Freeman pursued three concurrent goals while her fourth-grade class began to deeply explore fractions: (1) Build students' understanding of fractions as numbers with a definite magnitude (e.g., 3/4 falls between 3/5 and 1 on the number line); (2) Increase students' understanding of measuring with fractions; and (3) Develop fraction number sense by avoiding early introduction of traditional fraction algorithms. Several vignettes are then described to illustrate a pathway for developing the important concepts that relate to the measure subconstruct of fractions. The article concludes that understanding these concepts moves children along the continuum toward the increasingly abstract uses of fractions, which they will encounter in middle and high school.
Descriptors: Mathematics Instruction, Mathematics Achievement, Mathematical Concepts, Concept Formation, Grade 4, Elementary School Mathematics, Measurement, Teaching Methods, Vignettes
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 4; Intermediate Grades; Elementary Education
Authoring Institution: N/A