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ERIC Number: ED558664
Record Type: Non-Journal
Publication Date: 2013
Pages: 317
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3032-6406-1
Constructing and Modeling Algebraic Statements in the Multiplicative Domain: Investigating Fourth-Grade Student and Teacher Learning
Grandau, Laura
ProQuest LLC, Ph.D. Dissertation, The University of Wisconsin - Madison
This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an investigation of teacher learning that occurred as their teachers implemented and discussed this mathematics work inside and outside of the classroom. The instructional materials that were the context for this work are unlike those typically used in the United States. They comprise an integrated unit, with tasks and discussions that make quantitative relationships salient for young students and offer rich sites for discovery, modeling, and demonstration. These materials were inspired by V. V. Davydov's work in mathematics education - a Russian innovative approach to teaching elementary school mathematics. The study centered on implementation of this mathematics unit in three classrooms. Participants included 67 fourth-grade students and 3 teachers in the same large, urban, public school. Classroom lessons and teacher interviews and meetings were videotaped, coded, and analyzed. Student work and teachers' notes were also coded and analyzed. Student and teacher learning was the focus of the study. In particular, I examined the nature of students' discourse and participation in activities, and how and what in-service teachers attended to, needed, and learned when teaching this unit. Results of this study show that students could access and engage successfully in comparing quantities and describing relationships between them; and constructing and modeling algebraic statements with words, drawings, and mathematical symbols. Some students also demonstrated a rudimentary understanding of mathematical generality. Noteworthy challenges that arose for students are discussed. Analysis of teacher learning identified three shifts in teachers' participation in activities inside and outside the classroom as their work progressed. These changes showed developed use of the language and questions involved in quantitative reasoning; increased ability to use measurement tasks, models, and hands-on tools to support algebraic thinking; and developing roles and ways of participating in learning about early algebra. Results will be useful to curriculum designers, teacher educators, and teachers working in the early algebra domain. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site:
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Education; Intermediate Grades; Grade 4
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A