Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus

Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus

by Nancy Baxter Hastings
     
 

Each year, over 1,000,000 students take college-level courses below calculus such as precalculus, college algebra and others that fulfill general education requirements. Most college algebra courses, and certainly all precalculus courses, were originally intended to prepare students for calculus. Most are still offered in this spirit, even though only a… See more details below

Overview

Each year, over 1,000,000 students take college-level courses below calculus such as precalculus, college algebra and others that fulfill general education requirements. Most college algebra courses, and certainly all precalculus courses, were originally intended to prepare students for calculus. Most are still offered in this spirit, even though only a small percentage of students have any intention of taking calculus. This volume examines how the courses below calculus might be refocused to provide better mathematical experiences for all students.

This initiative involves a greater emphasis on conceptual understanding with a de-emphasizing on rote manipulation. It encourages the use of realistic applications, math modeling and data analysis that reflect the ways mathematics is used in other disciplines. It promotes the use of active learning approaches, including group work, exploratory activities and projects. It emphasizes communication skills: reading, writing, presenting and listening. It endorses the appropriate use of technology to enhance conceptual understanding, visualization, and to enable students to tackle real-world problems.

The 49 papers in this volume seek to focus attention on the problems and needs of the courses and to provide guidance to the mathematics community. Major themes include: new visions for introductory collegiate mathematics, transition from high school to college, needs of other disciplines, research on student learning, implementation issues, and ideas and projects that work.

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Product Details

ISBN-13:
9780883851791
Publisher:
Mathematical Association of America
Publication date:
02/01/2006
Series:
Maa Notes Ser.
Pages:
396
Product dimensions:
8.40(w) x 11.00(h) x 0.90(d)

Meet the Author

Table of Contents

Contents
Preface vii

Introduction 1
1 The Conference: Rethinking the Preparation for Calculus, Jack Narayan and Darren Narayan 3
2 Twenty Questions about Precalculus, Lynn Arthur Steen 8
Background 13
3 Who are the Students Who Take Precalculus?, Mercedes A. McGowen 15
4 Enrollment Flow to and from Courses Below Calculus, Steven R. Dunbar 28
5 What Have We Learned from Calculus Reform? The Road to Conceptual Understanding, Deborah Hughes Hallett 43
6 Calculus and Introductory College Mathematics: Current Trends and Future Directions, Susan L. Ganter 46

Theme 1. New Visions for Introductory Collegiate Mathematics 55
7 Refocusing Precalculus: Challenges and Questions, Nancy Baxter Hastings 57
8 Preparing Students for Calculus in the Twenty-First Century, Sheldon P. Gordon 64
9 Preparing for Calculus and Preparing for Life, Bernard L. Madison 78
10 College Algebra: A Course in Crisis, Don Small 83
11 Changes in College Algebra, Scott R. Herriott 90
12 One Approach to Quantitative Literacy: Understanding our Quantitative World, Janet Andersen 101

Theme 2. The Transition from High School to College 109
13 High School Overview and the Transition to College, Zalman Usiskin 111
14 Precalculus Reform: A High School Perspective, Daniel J. Teague 121
15 The Influence of Current Efforts to Improve School Mathematics on the Preparation for Calculus, Eric Robinson and John Maceli 129

Theme 3. The Needs of Other Disciplines 151
16 Fundamental Mathematics: Voices of the Partner Disciplines, William Barker and Susan L. Ganter 153
17 Skills versus Concepts at West Point, Rich West 160
18 Integrating Data Analysis into Precalculus Courses, Allan J. Rossman 169

Theme 4. Student Learning and Research 179
19 Assessing What Students Learn: Reform versus Traditional Precalculus and Follow-up Calculus, Florence S. Gordon 181
20 Student Voices and the Transition from Reform High School Mathematics to College Mathematics, Rebecca Walker 193

Theme 5. Implementation 211
21 Some Political and Practical Issues in Implementing Reform, Robert E. Megginson 213
22 Implementing Curricular Change in Precalculus: A Dean's Perspective, Judy E. Ackerman 219
23 The Need to Rethink Placement in Mathematics, Sheldon P. Gordon 224
24 Changing Technology Implies Changing Pedagogy, Lawrence C. Moore and David A. Smith 229
25 Preparing for Calculus and Beyond: Some Curriculum Design Issues, Al Cuoco 235
26 Alternatives to the One-Size-Fits-All Precalculus/College Algebra Course, Bonnie Gold 249

Theme 6. Influencing the Mathematics Community 255
27 Launching a Precalculus Reform Movement: Influencing the Mathematics Community, Bernard L. Madison 257
28 Mathematics Programs for the Rest-of-Us, Naomi D. Fisher and Bonnie Saunders 265
29 Where Do We Go From Here? Creating a National Initiative to Refocus the Courses below Calculus, {\it Sheldon P. Gordon 274
Ideas and Projects that Work: Part 1 283
30 College Precalculus Can Be a Barrier to Calculus: Integration of Precalculus with Calculus Can Achieve Success, Doris Schattschneider 285
31 College Algebra Reform through Interdisciplinary Applications, William P. Fox 295
32 Elementary Math Models: College Algebra Topics and a Liberal Arts Approach, Dan Kalman 304
33 The Case for Labs in Precalculus, Brigitte Lahme, Jerry Morris, and Elias Toubassi 310
34 The Fifth Rule: Direct Experience of Mathematics, Gary Simundza 320

Ideas and Projects that Work: Part 2 329
35 Mathematics in Action: Empowering Students with Introductory and Intermediate College Mathematics, Ernie Danforth, Brian Gray, Arlene Kleinstein, Rick Patrick, and Sylvia Svitak 333
36 Precalculus: Concepts in Context, Marsha Davis 337
37 Rethinking College Algebra, Benny Evans 341
38 From The Bottom Up, Sol Garfunkel 345
39 The Functioning in the Real World Project, Florence S. Gordon and Sheldon P. Gordon 348
40 The Importance of a Story Line: Functions as Models of Change, Deborah Hughes Hallett 352
41 Using a Guided-Inquiry Approach to Enhance Student Learning in Precalculus, Nancy Baxter Hastings 355
42 Maricopa Mathematics, Alan Jacobs} 360
43 College Algebra/Quantitative Reasoning at the University of Massachusetts, Boston, Linda Almgren Kime 364
44 Developmental Algebra: The First Mathematics Course for Many College Students, Mercedes A. McGowen 369
45 Workshop Precalculus: Functions, Data, and Models, Allan J. Rossman 376
46 Contemporary College Algebra, Don Small 380
47 Precalculus: A Study of Functions and Their Applications, Todd Swanson 386
48 Success and Failures of a Precalculus Reform Project, David M. Wells and Lynn Tilson 390
49 The Earth Math Projects, Nancy Zumoff and Christopher Schaufele 393

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