Description
Teachers must recognize the knowledge they possess as appropriate to employ in the process of achieving their goals and objectives in the context of practice. Such recognition is subject to a host of cognitive and affective processes that have thus far not been a central focus of research on teacher knowledge in mathematics education. To address this need, this dissertation study examined the role of a secondary mathematics teacher’s image of instructional constraints on his enacted subject matter knowledge. I collected data in three phases. First, I conducted a series of task-based clinical interviews that allowed me to construct a model of David’s mathematical knowledge of sine and cosine functions. Second, I conducted pre-lesson interviews, collected journal entries, and examined David’s instruction to characterize the mathematical knowledge he utilized in the context of designing and implementing lessons. Third, I conducted a series of semi-structured clinical interviews to identify the circumstances David appraised as constraints on his practice and to ascertain the role of these constraints on the quality of David’s enacted subject matter knowledge. My analysis revealed that although David possessed many productive ways of understanding that allowed him to engage students in meaningful learning experiences, I observed discrepancies between and within David’s mathematical knowledge and his enacted mathematical knowledge. These discrepancies were not occasioned by David’s active compensation for the circumstances and events he appraised as instructional constraints, but instead resulted from David possessing multiple schemes for particular ideas related to trigonometric functions, as well as from his unawareness of the mental actions and operations that comprised these often powerful but uncoordinated cognitive schemes. This lack of conscious awareness made David ill-equipped to define his instructional goals in terms of the mental activity in which he intended his students to engage, which further conditioned the circumstances and events he appraised as constraints on his practice. David’s image of instructional constraints therefore did not affect his enacted subject matter knowledge. Rather, characteristics of David’s subject matter knowledge, namely his uncoordinated cognitive schemes and his unawareness of the mental actions and operations that comprise them, affected his image of instructional constraints.
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Details
Title
- An examination of the effect of a secondary teacher's image of instructional constraints on his enacted subject matter knowledge
Contributors
- Tallman, Michael Anthony (Author)
- Carlson, Marilyn P (Thesis advisor)
- Thompson, Patrick W (Committee member)
- Saldanha, Luis (Committee member)
- Middleton, James (Committee member)
- Harel, Guershon (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2015
Subjects
- Mathematics Education
- Instructional Constraints
- Mathematical Knowledge for Teaching
- Radical Constructivism
- Reflecting Abstraction
- Secondary Mathematics
- Trigonometry
- Teaching--Psychological aspects.
- Effective teaching--Psychological aspects.
- Effective teaching
- Knowledge, Theory of--Psychological aspects.
- Knowledge, Theory of
Resource Type
Collections this item is in
Note
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thesisPartial requirement for: Ph. D., Arizona State University, 2015
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bibliographyIncludes bibliographical references (pages 608-617)
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Field of study: Mathematics education
Citation and reuse
Statement of Responsibility
by Michael Anthony Tallman