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MIDDLE SCHOOL CHILDREN’S UNDERSTANDING OF ALGEBRAIC FUNCTIONS AS QUOTIENTS by Cumali Oksuz Adnan Menderes Universitesi Egitim Fakultesi Kepez-AYDIN 09010 TURKEY
James A. Middleton Arizona State University USA
Copyright © 2007 UP NISMED.
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Middle School Children's
Understanding
Cumali Oksuz Adnan Menderes Universitesi Egitim Fakultesi Kepez/ AYDIN 09010 TURKEY
James A. Middleton Arizona State University USA
ABSTRACT
The development of two middle school students’ reasoning about quotients in arithmetic and algebraic contexts was studied through a series of individual teaching experiments. Initially, when children were confronted with algebraic contexts, they viewed algebraic fractions as a new case. As they progressed, it appeared that understanding of quotients of algebraic expressions depended heavily on the students’ understanding of arithmetical quotients. They used analogy to arithmetic fractional reasoning as a tool for initial understanding, followed similar developmental routes when constructing more advanced knowledge, and folded back to arithmetic analogies when new information was presented. In particular, similar to students’ development of understanding in numeric fractions, their thinking began with an understanding of Algebraic Fractions as Part Whole, moved to a notion of Algebraic Fractions as Division, then to seeing Division of Polynomials as Algebraic Fractions. At the end of the teaching experiments, they approached situations involving algebraic fractions or division of polynomials flexibly and used multiple-constructed methods.
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