Using manipulatives with fractions, decimals, integers, and algebra : a guide for the intermediate teacher

Smith, Tina M. (2002) Using manipulatives with fractions, decimals, integers, and algebra : a guide for the intermediate teacher. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (6MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

Research in recent years has shown that traditional methods of instruction being employed in many intermediate classrooms today are clearly lacking. The National Council of Teachers of Mathematics (NCTM) states that learning mathematics without understanding has long been a common outcome of school mathematics instruction (NCTM. 2000. p. 19). According to cognitive learning theorists, true learning involves moving from the concrete to the abstract. These concrete representations, or manipulatives, contribute to the development of well- grounded, interconnected understandings of mathematical ideas (Stein and Bovalino. 2001). As such, the NCTM and the Atlantic Provinces Education Foundation (APEF) have incorporated them into recent mathematics reform at the intermediate level. -- The new intermediate mathematics curriculum calls for the regular use of manipulatives by teachers and students (APEF, 1999). This, however, causes problems for the teacher who is unsure of how to use them. Educational methods courses which focus on the use of manipulatives have been restricted to primary and elementary levels. This reinforces the idea that manipulatives are intended only for lower grade instruction. -- This paper will address these issues in light of the new APEF curriculum for intermediate mathematics, culminating with a resource for teachers. This guide is intended to facilitate the efficacious integration of manipulatives into the teaching of fractions, decimals, integers, and algebra at the intermediate level.

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