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ERIC Number: ED557042
Record Type: Non-Journal
Publication Date: 2014
Pages: 307
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3211-1891-9
A Case Study of How Ninth Grade Mathematics Students Construct Knowledge during a Productive Failure Model
Westbrook, Amy Franks
ProQuest LLC, Ph.D. Dissertation, Mercer University
This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students at a rural high school in Georgia constructed knowledge through student talk when problem solving using Kapur's (2012) productive failure design. An embedded case study design was used to understand how a group of students constructed knowledge through their use of talk, persistence during the task, and use of prior knowledge while working on a productive failure modeled task. The case for this research was a representative group of four ninth-grade students enrolled in a coordinate algebra course. Triangulation resulted from the collected data from multiple sources, which included videotaping, interviewing, and analyzing student artifacts. Utilization of the constructivist perspectives of Vygotsky (1934/1962), Piaget (1971), and Freire (1970/2012) served as a framework for analyzing the data. Analysis of the findings resulted in an in-depth understanding of how students persisted during a productive failure-modeled task and revealed three main themes: (a) the group's processes of interaction, (b) the roles the group members played during the task, and (c) the problem solving approaches the group utilized during the task. An interactive model of persistent problem solving was created to explain how the group utilized the three main themes in order to initiate their prior knowledge, chose different methods for solving, and persevered during the task. Suggestions for future research include study of a non-representative population, focus on the role of gender, writing, group size, and academic conversations; implementation of Kapur's (2012) productive failure design in a different content area; the role of group processes and student roles forwarded their conceptual knowledge; and the determination of the zone of proximal development during the model supports learning. [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: Grade 9; Junior High Schools; Middle Schools; Secondary Education; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Georgia