Table of Contents

 

Abstract

 

Acknowledgments

 

Chapter 1: Introduction

Problem Statement

Overview of the Study

 

Chapter 2: Related Literature:Beliefs, Subject Conceptions, and Teaching Practice

Conceptions of the Nature of Mathematics
Beliefs, Personal Knowledge, and Teacher Thinking

Images of Mathematics

Conceptions of Subject and Teaching Practice: Mathematics

Conceptions of Subject and Teaching Practice: Other Disciplines

Mathematics Teaching Practice

New Visions of Practice

Studying Teaching Practice: Research Paradigms

Capturing a Fuller Picture: A Sociological and Epistemological Perspective

Summary: Subject Conceptions and Teaching Practice

 

Chapter 3: Method

Orientation and Conceptual Framework

Participants

Data Collection

Conceptions of the Nature of Mathematics
Personal Statements: Images of Mathematics

Repertory Grids

Concept Maps

Mathematics Teaching Practice

Data Analysis and Reporting

Analysis

Reporting

Corroboration

Reporting Visions and Practice

Composing a Picture of Subject Vision

Telling the Story of Teaching Practice

 

Chapter 4: Case 1: Jonathan Ode:Forging Ahead on the Reform Path

Guiding from the Back of the Room

Mathematics as Reasoning and Communicating

Challenging Students to Think

Mathematics as Problem Solving

Whimbey-Pairs

Mathematics as the Study of Patterns

Organizing Data for Patterns and Problem Solving

Conflict: Just Give Us the Rules

Mathematical Growth: Experiments and Induction

Working from the Specific to the General

Applications: Mathematics as Modelling

Algebra as Modelling: A Meaning for N

Mathematics as Ill-defined Truth

Exploring Multiple Correct Answers

The Multiple Personalities of Mathematics

Being Visually Creative

Case Summary: Subject Conceptions and Teaching Practice

 

Chapter 5: Case 2: Randy Walker: Tentative Steps along the Reform Path

Three Coins

Mathematics an Experimental Science

Iteration of Functions and Pixel Rainbows

Conflict and Retreat

Mathematics as a Technical Language

Mixed Practices

A Personal Philosophy Under Construction

Mathematics as Problem Solving

Connecting Science and Mathematics

Proofs and Mathematical Truth

Visual Proofs: Helping Students See Mathematics

Mathematics as Art

Mandelbrot Art

Mathematics as a Creative Activity

Supporting Students' Mathematical Explorations

Case Summary: Subject Conceptions and Teaching Practice

 

Chapter 6: Discussion and Reflections on the Study

Visions Into Practice
Visions into Practice: The Struggle

Visions into Practice: The Commitment

Looking Above and Beyond the Curriculum

Reflections on the Study: Internal and External Validity

Implications and Questions for Future Study

Conclusion

 

References

 

Appendix A: Data Coding Scheme [and Data Logs]

Appendix B: Information Given to Participants re

Writing of Personal Statement on the Nature of Mathematics

Appendix C: Information Given to Participants re

the Construction of a Repertory Grid

Appendix D: Information Given to Participants re

the Construction of a Concept Map for Mathematics

Appendix E: Concept Map for Mathematics: Jonathan Ode (JO-INT-D-12a)

Appendix F: School Subjects Repertory Grid:

Jonathan Ode (JO-INT-D-04)

[Appendix G: Pages from Get It Together Used by

Jonathan Ode (JO-LES-D-17b)]

[Appendix H: Instruction Pages Used by Jonathan Ode for

Algebraic Modelling Lesson (JO-LES-D-20b)]

Appendix I: Student Products from Periodic Decimal Art

Project(JO-LES-D-07e,j,m,n)

Appendix J: First School Subjects Repertory Grid:

Randy Walker (RW-INT-D-01a)

Appendix K: Second School Subjects Repertory Grid:

Randy Walker (RW-INT-D-07)

Appendix L: Concept Map for Mathematics:

Randy Walker (RW-INT-D-09a)

 

[not included in this Web version]