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