Embracing Reason: Egalitarian Ideals and the Teaching of High School Mathematics

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This book tells a single story, in many voices, about a serious and sustained set of changes in mathematics teaching practice in a high school and how those efforts influenced and were influenced by a local university. It includes the writings and perspectives of high school students, high school teachers, preservice teacher candidates, doctoral students in mathematics education and other fields, mathematics teacher educators, and other education faculty. As a whole, this case study provides an opportunity to reflect on reform visions of mathematics for all students and the challenges inherent in the implementation of these visions in US schools. It challenges us to rethink boundaries between theory and practice and the relative roles of teachers and university faculty in educational endeavors.

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Product Details

  • ISBN-13: 9780415879040
  • Publisher: Taylor & Francis
  • Publication date: 12/21/2009
  • Pages: 400
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.81 (d)

Table of Contents

List of figures     xi
List of tables     xiii
Acknowledgments     xiv
Preface     xvi
Introduction to our case study     1
Our goals and our own voices     2
The importance of teacher development     4
A school-university PDS two-way relationship     5
Changes in classroom teaching practice     13
Assessment     15
Mathematics performance assessment     15
Alternative formats and a taxonomy of tasks     22
Curriculum and instructional models     26
Starting a functions-based approach to algebra     29
Perspectives on Holt Algebra 1 from the department chair and a newer teacher     41
Another kind of planning     46
Teacher as course-level planner     47
Must teachers create curriculum? For every class?     53
Interlude A: on-campus preservice assignments     60
Preservice teachers as curriculum makers     64
Should preservice teachers be encouraged to create curriculum?     75
Instructional tasks     78
Finding mathematics in the world around us     79
Getting past lame justifications!     85
Classroom roles     88
One teacher's transformation in teaching     89
The vision thing     105
Student experience of the curriculum     109
Lower-track classes     123
From an E to an A with the help of a graphing calculator     125
How important are calculators?     128
Standard-track classes     131
Students' views of mathematical conversation     133
Challenges of managing students' participation in classroom conversation     141
Advanced coursework     144
Developing an interest in mathematics     145
What is "mathematical power"? And related dilemmas of teaching     155
Interlude B: observation in classrooms     160
Field experience really was the best teacher!     162
Our contrasting preservice field experiences     168
Interlude C: student teaching/internship     171
What kind of teacher will I be?     173
How do we talk with other teachers about our "Holt" experiences?     182
Professional growth and development     187
Time and respect     193
Being treated (and treating ourselves) as professionals     195
Thoughts from latecomers     200
Restructuring teacher work      203
Shared teaching assignments     207
What do shared teaching assignments tell us about learning while teaching?     220
Departmental culture     224
One transformed teacher's viewpoint     225
Elementary mathematics + a culture of questioning = complex mathematics     238
Changing the math curriculum     241
Teaching a technologically supported approach to school algebra     244
Talking about what math is for     254
Learning from students and colleagues     257
Questioning ourselves and the authorities     258
Should we ever tell mathematical white lies to our students?     275
Interlude D: learning math from coursework conversation     280
Lines and points: Aristotle vs. modern mathematics     281
A chance to disagree about math     294
Participation in teacher education     298
Becoming a professional teacher; being a mentor teacher     300
The hard work of being a mentor teacher     312
Graduate study     315
Theory is practical!     316
Views of mathematics and teaching mathematics     330
Stepping back: the perspective of a local "outsider"     335
A quiet revolution?      337
Reflecting on mathematics reform at Holt High School     337
Epilogue     352
Cast of characters     355
Notes     359
References     361
Index     369
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