Exploring mathematical knowledge for teaching quadratic functions through student work

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Stacey Chanelle Zimmerman (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Peter Holt Wilson

Abstract: The ways teachers understand mathematics that is useful for teaching, known as mathematical knowledge for teaching (MKT), has been a center of attention for the research and policy communities. A teacher’s MKT has been shown to be a significant factor in predicting student outcomes and positively related to the quality of mathematics instructional quality. Yet researchers have almost exclusively focused on elementary teachers’ MKT, leaving very little understanding of MKT for secondary teachers and whether MKT relates to student outcomes and instructional quality in the same ways. Given the gatekeeper functionality of algebra and the seemingly intractable opportunity gap, it is imperative that we build knowledge about MKT at the secondary level. This exploratory, multi-case design study investigated the realms of knowledge used by expert mathematics educators when engaging with student quadratic function work. The experts participated in a series of interviews revealing their use of mathematical knowledge while unpacking student strategies, mathematical understandings, and needs for further instruction. Ball and colleagues’ Mathematical Knowledge for Teaching (MKT) Framework serves as a lens to identify and categorize the realms of knowledge made explicit during the experts’ engagement with the student work. The use of multiple cases provides convergent and complementary evidence of the knowledge used when engaging with student quadratic function work, therefore supporting the evolution of an innovative conception of secondary MKT. While findings from the study specifically address the nature of secondary MKT for teaching quadratics, study approaches also address engagement with student written work and the needed assimilation of MKT research to advance secondary MKT understanding. Three manuscripts collectively convey these results. The first manuscript explores the nature of mathematical knowledge for teaching quadratic functions by using Ball and colleague’s (2008) Mathematical Knowledge for Teaching Framework as a guide and student written work as a source. Through a series of task-based interviews with the six experts, findings indicate that the nature of mathematical knowledge for teaching quadratic functions can be characterized as six interrelated entities: content knowledge, connections, interpretations, anticipations, instructional moves, and resources. The second manuscript details a set of six questions that emerged from my analysis. These questions, which direct a strengths-based engagement with student work and the exploration of one’s own MKT, can provide meaningful learning experiences for individuals, professional learning communities, and large group professional development activities. The third manuscript addresses the advances that have been made in understanding secondary MKT and the barriers that could be hindering progress. Ideas that help to reevaluate differences in the literature are presented to motivate the mathematics education community to continue efforts to develop a unified vision of secondary MKT.

Additional Information

Publication
Dissertation
Language: English
Date: 2020
Keywords
Mathematical Knowledge for Teaching (MKT), Quadratic Functions, Student Work, Teacher Knowledge
Subjects
Algebra $x Study and teaching (Secondary)
Mathematics teachers $x Psychology
Interaction analysis in education
Effective teaching

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