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Index
STUDIES IN CURRICULUM THEORY
CONTENTS
PREFACE
Footnotes
ACKNOWLEDGMENTS
1 INTRODUCTION TO A PHENOMENON
An Opening Anecdote
“Relationship” to Mathematics
“Knowing” and its Constituent Aspects
A Comparison Across Disciplines
The Design of Things to Follow
Footnotes
A TANGENT PRIOR TO THE RISE (AND RUN)
2 RELATIONSHIP AS RECIPROCITY: GRACE
Gnostic and Pathic
Mathematics as Other: Through the Aperture of Music
Mathematics as Platonic Other
Affect, Feelings, and Emotions
The Cognitive Emotions
Frustration
The Secondary Task: The Nature of Knowing
The Aesthetic Experience
Passion, as an Undergoing
Passion and Aesthetics: Being Seized by a Problem
Aesthetic Responses to Mathematics
The Generative Aesthetic
Understanding as an “Undergoing” Experience
Understanding as “Aha”
One Teacher’s Expression of Understanding as an “Undergoing”-type Experience: a Brief Case Study of Eve29
Subjective Universality
Footnotes
3 A BRINGING FORTH OF SELF: WILL
“Staying with the Problem”
Desirable Difficulties
Repetition, or Repetition?
Understanding as Verstehen: “Standing before” so as to Unlearn Mathematics
Footnotes
4 RELATIONSHIP AS INTEREST
Intertwining with Other and its Relation to Motivation: That which Precedes the Joining of Will and Grace
A Few Examples of “Intertwinings”
Challenge and Arête
Social Connection
Curiosity
Curiosity 1
Curiosity 2
Certainty and Cleanness of Thought
A Case Study of Lewis, and of the Different “Faces” of Mathematics
Self as Reflected in Life Projects and Trajectories
A Case Study of April: On the Life Project of Becoming a More “Effective” Teacher
Inter-esse as the Joining of Will and Grace
Understanding as Inter-esse
Footnotes
5 “DOING” MATHEMATICS AND ITS RELATION TO THE LIFE PATH OF BEING A MATHEMATICS TEACHER/EDUCATOR
Why do Mathematics?—One Rationale
“Doing” Mathematics: A Complementary Rationale Interwoven
Ownership to Inter-esse
Asking Questions and Posing Problems6 as a “Staying With” Mathematics
The Predicament for Teachers: Feasibility and Relevance
Doing Pedagogically Relevant Mathematics: Where the Problems Come From and Where They Remain
Doing Pedagogically Relevant Mathematics: Sense Making and Meaning Making
Footnotes
AN EPILOGUE IN TWO PARTS
Part I: Returning to the Episode of the Straitjacket (from pp. 10–13)
Part II: Relationship as a Returning: Going Past “Understanding”
Footnotes
APPENDIX: A NARRATIVIZED “METHODOLOGY”
Footnotes
REFERENCES
INDEX
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