Learning to Represent Mathematics: The Negotiation of Meanings of Mathematical Symbols in First Grade

Abstract

95 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.Instructional moments are not all created equal. This project documented the characteristics of a class of events ("teachable moments") that may have particular power in affecting student learning. To investigate students' acquisition of mathematical representation, I examined teacher-student discourse in 45 first-grade lessons, focusing on episodes of teachable moments: errors, confusion, disagreements, and spontaneous contributions. In the lessons errors and confusion occurred most often. Teachers responded to errors and confusion by increasing their use of multiple representations, more often than prior to them. Teachers especially responded to errors with reference to written symbols, and they responded to confusion with concrete manipulatives. Students referenced visual forms at a low rate overall but did so more during errors than confusion and received explicit encouragement to reference visual forms more prior to errors than confusion. Few mathematical disagreements occurred. The rate of spontaneous contributions varied greatly by classroom, but representational processes did not vary significantly during those episodes. These results provide evidence for the role of multiple representations of mathematical ideas during key instructional moments.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD