Dissertation Critique

1
Dissertation Critique

• Gwenanne Salkind
• George Mason University
• December 8, 2007
• EDCI 858 EDCI 726
• Dr. Patricia Moyer-Packenham
• Dr. Margret Hjalmarson

2
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

3
Research Questions

1. What is the work of constructing a
   representational context in elementary
   mathematics teaching?
2. 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?

4
Central Questions

• 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?

5
Methods

• 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.

6
Theoretical Foundation of Analysis

• Mathematical Knowledge for Teaching
• Common content knowledge
• Specialized content knowledge
• Knowledge of content and students
• Knowledge of content and teaching

7
Representations

• 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)?

8
Results

• 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

9
Establishing the Language

• 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

10
Making Representation Usable

• 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

11
Making Connections

• 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

12
Teaching Challenges

• Establishing the language needed to deploy a
  representation
• Making a representation usable for students
• Making connections to other representations

13
Ideas for Teacher Education

• 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

14
Ideas for Teacher Education

• 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

15
Critique

• Redundancy
• Focus
• Organization Structure
• Omit the section on Designing Introductory Tasks

16
Questions I have

• Does this study generalize to other teachers
  work?
• If she had studied a different teacher, would she
  have found the same results?

17
Key Components things I learned

• 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