High-quality mathematics instruction is important for students’ learning, and teachers are a key part of instruction. As they engage in instruction, teachers draw on their beliefs and knowledge. Yet mathematics education still lacks a robust understanding of the specific ways in which beliefs and knowledge contribute to high-quality instruction, particularly at the high school level. The purpose of this dissertation is to explore the mathematical knowledge and beliefs used by high school teachers who facilitate high-quality instruction. Three main research questions guide this dissertation: (a) What is the nature of mathematical knowledge expressed in exemplary high school mathematics teachers’ reflections on teaching? (b) What teacher beliefs and knowledge support high-quality responses to students? (c) How can productive teacher beliefs about mathematics and mathematics teaching lead to instruction that is limited in mathematical richness? To investigate the first research question, I interviewed 11 high school mathematics teachers who were recognized for exemplary instruction. I used grounded analysis to explore the mathematical knowledge for teaching that was expressed through teachers’ reflections on their lessons. In response to the second research question, I observed and interviewed 12 high school teachers, five of whom were recognized for exemplary instruction. I used video-based, stimulated-recall interviews to understand the teacher beliefs and knowledge that supported or hindered high-quality responses to students’ mathematical questions, claims, and solutions. To address the third research question, I explored the case of one recognized teacher who expressed beliefs and goals aligned with mathematical meaning and sense making, yet his instruction did not exemplify these aspects. I used observations and interviews to understand the teacher’s perspectives on his instruction, and I offer explanations for why this instruction was limited in richness. The findings highlight the depth and complexity of mathematical knowledge and beliefs used in high-quality instruction and challenge the assumption that either teacher beliefs or teacher knowledge can be studied in isolation or outside of the instruction in which they are used.
Subject (authority = RUETD)
Topic
Education
Subject (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching (Secondary)
Subject (authority = ETD-LCSH)
Topic
Teachers--Interviews
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5786
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (xi, 266 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Kathryn E. Rhoads
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
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Type
License
Name
Author Agreement License
Detail
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