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Dissertation Critique. Gwenanne Salkind George Mason University December 8, 2007 EDCI 858 & EDCI 726 Dr. Patricia Moyer-Packenham Dr. Margret Hjalmarson. Examining the Work of Constructing a Representational Context in Elementary Mathematics Teaching. By Rhonda B. Cohen

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Dissertation Critique

Gwenanne Salkind

George Mason University

December 8, 2007

EDCI 858 & EDCI 726

Dr. Patricia Moyer-Packenham

Dr. Margret Hjalmarson


Examining the work of constructing a representational context in elementary mathematics teaching l.jpg

Examining the Work of Constructing a Representational Context in Elementary Mathematics Teaching

By Rhonda B. Cohen

University of Michigan

Doctoral Committee:

Professor Deborah Loewenberg Ball, Chair

Professor Hyman Bass

Professor Magdalene Lampert

Professor Elizabeth Yakel


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Research Questions Context in Elementary Mathematics Teaching

  • What is the work of constructing a representational context in elementary mathematics teaching?

  • How does studying the work of constructing a representational context make more visible what teachers need to know and be able to do to use these kinds of instructional representations effectively in elementary mathematics teaching?


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Central Questions Context in Elementary Mathematics Teaching

  • What might teachers need to know in order to help students develop meaning for a representation?

  • What might teachers need to be able to do to help students learn to use a representation?

  • What might be some of the challenges or dilemmas in this work?


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Methods Context in Elementary Mathematics Teaching

  • Data Sources: Records of teaching (videotaped lessons, lesson transcripts, copies of student work, and teachers’ notes) of a third grade mathematics class taught by Deborah Ball during the 1989-90 school year.

  • Qualitative Case Study: Analyzed 3 teaching episodes where Ball introduced a representation to help students solve a mathematics problem.


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Theoretical Foundation of Analysis Context in Elementary Mathematics Teaching

  • Mathematical Knowledge for Teaching

    • Common content knowledge

    • Specialized content knowledge

    • Knowledge of content and students

    • Knowledge of content and teaching


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Representations Context in Elementary Mathematics Teaching

  • Square Tiles – How does the teacher establish the language needed to deploy a representation?

  • Elevator Model – How does the teacher make a representation usable to students?

  • Number Line - What does the teacher do to make connections to other representations (especially representations that students introduce)?


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Results Context in Elementary Mathematics Teaching

  • The work of launching and preparing to use a representation involves knowing mathematics in ways that are special to the work of teaching.

    • Demand for mathematical knowledge, skill, and sensibilities

    • Need to be judicious in how language and mathematical symbols get used

    • Importance of attending to the ways in which students’ prior knowledge and experience can both support and hinder the work of constructing a representational context


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Establishing the Language Context in Elementary Mathematics Teaching

  • Helping students record mathematical ideas in ways that emphasize the correspondences among the words, symbols, and materials

  • Attending closely to the meaning of mathematical terms and the use of language

  • Using transitional language

  • Noticing the mathematical ideas for which a representation can be used and relating those ideas to what students need to learn


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Making Representation Usable Context in Elementary Mathematics Teaching

  • Attending closely to the meaning of the mathematical symbols and the use of language

  • Piquing students’ interest

  • Drawing students’ attention to key features and teaches students how to use the representation

  • Comparing the relative merits of different representations


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Making Connections Context in Elementary Mathematics Teaching

  • Attending closely to what students mean by the terms “same” and “different”

  • Drawing students’ attention to a structural elements that need to be the same for different representations

  • Helping students give explanations

  • Attending to task design considerations


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Teaching Challenges Context in Elementary Mathematics Teaching

  • Establishing the language needed to deploy a representation

  • Making a representation usable for students

  • Making connections to other representations


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Ideas for Teacher Education Context in Elementary Mathematics Teaching

  • Help teachers attend closely to how recording work with mathematical tools (e.g., base-ten blocks) can be used to emphasize the mathematics content being studied

  • Have teachers explain the correspondences between a representation and the mathematics content


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Ideas for Teacher Education Context in Elementary Mathematics Teaching

  • Use caution in emphasizing the motivational purposes for using representations in teaching mathematics

  • Help teachers develop criteria for discriminating among representations used in mathematics teacher – compare the relative merits of different representations


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Critique Context in Elementary Mathematics Teaching

  • Redundancy

  • Focus

  • Organization & Structure

  • Omit the section on “Designing Introductory Tasks”


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Questions I have Context in Elementary Mathematics Teaching

  • Does this study generalize to other teachers’ work?

  • If she had studied a different teacher, would she have found the same results?


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Key Components – things I learned Context in Elementary Mathematics Teaching

  • Her acknowledgement page was eloquently written

  • She identified themes in her literature review

  • Her argument for the study was both broad and specific – approached from many angles

  • She defined terms and assumptions (tons of this!)

  • She described her perspectives (lenses)

  • She tells what she is doing and why she is doing it (over and over again!)

  • She used stories and vignettes as examples and illustrations of her analyses


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