**Harold Boger** is a mathematics teacher at Crenshaw High School, a comprehensive high school located in Cluster 15 of the Los Angeles Unified School District. In addition to teaching AP Calculus and AP Statistics, he serves as the chairman of the mathematics department and teaches geometry, algebra with transformations, and the second and third levels of an integrated mathematics program. Mr. Boger’s thirteen years of outstanding teaching led to his selection as a visiting lecturer at the University of California at Los Angeles as part of the prestigious Visiting High School Teacher Program. He received his M.A.Ed. from the University of California at Los Angeles in 1996 and is currently completing an M.S. in statistics at San Diego State University.

**Marilyn P. Carlson** is an assistant professor in the Mathematics Department at Arizona State University. Her research area is mathematics education with recent investigations focussed on cognitive aspects of knowing and learning the function concept. In addition, she has developed a broad framework for investigating students' mathematical methods and problem solving behaviors. An NSF CAREER Award is supporting her current development of concept assessment instruments for precalculus and beginning calculus. She teaches preservice secondary methods and content courses, graduate courses in research in undergraduate mathematics education, and recently led the development of two new Ph.D. programs in mathematics education at ASU. She is the Coordinator/President-Elect for the recently formed MAA Special Interest Group, Research in Undergraduate Mathematics Education, and has been active in various professional organizations, including PME, PME-NA, NCTM, MAA and ARUME.

**Roger E. Howe** has been a Professor of Mathematics at Yale University for over twenty-five years. He has been a visiting scholar at numerous universities, both in the United States and abroad. Recently, Dr. Howe was a Phi Beta Kappa Visiting Scholar. Dr. Howe is a member of the AMS, MAA, NCTM, the Connecticut Academy of Science and Engineering, the American Academy of Arts and Sciences, and the NAS. He is a former member of the MSEB. He serves on the board of directors of the Connecticut Academy for Education in Mathematics, Sciences and Technology, and was chairman of the AMS Review Group for revision of the NCTM Standards. He currently serves as chair of the AMS Committee on Education. Dr. Howe received his Ph.D. in mathematics from the University of California at Berkeley.

**Daniel J. Teague** teaches mathematics at The North Carolina School of Science and Mathematics in Durham, North Carolina. His twenty-five years of teaching at both the

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools - Report of the Content Panel for Mathematics
BIOGRAPHICAL PROFILES OF MATHEMATICS PANEL MEMBERS
Harold Boger is a mathematics teacher at Crenshaw High School, a comprehensive high school located in Cluster 15 of the Los Angeles Unified School District. In addition to teaching AP Calculus and AP Statistics, he serves as the chairman of the mathematics department and teaches geometry, algebra with transformations, and the second and third levels of an integrated mathematics program. Mr. Boger’s thirteen years of outstanding teaching led to his selection as a visiting lecturer at the University of California at Los Angeles as part of the prestigious Visiting High School Teacher Program. He received his M.A.Ed. from the University of California at Los Angeles in 1996 and is currently completing an M.S. in statistics at San Diego State University.
Marilyn P. Carlson is an assistant professor in the Mathematics Department at Arizona State University. Her research area is mathematics education with recent investigations focussed on cognitive aspects of knowing and learning the function concept. In addition, she has developed a broad framework for investigating students' mathematical methods and problem solving behaviors. An NSF CAREER Award is supporting her current development of concept assessment instruments for precalculus and beginning calculus. She teaches preservice secondary methods and content courses, graduate courses in research in undergraduate mathematics education, and recently led the development of two new Ph.D. programs in mathematics education at ASU. She is the Coordinator/President-Elect for the recently formed MAA Special Interest Group, Research in Undergraduate Mathematics Education, and has been active in various professional organizations, including PME, PME-NA, NCTM, MAA and ARUME.
Roger E. Howe has been a Professor of Mathematics at Yale University for over twenty-five years. He has been a visiting scholar at numerous universities, both in the United States and abroad. Recently, Dr. Howe was a Phi Beta Kappa Visiting Scholar. Dr. Howe is a member of the AMS, MAA, NCTM, the Connecticut Academy of Science and Engineering, the American Academy of Arts and Sciences, and the NAS. He is a former member of the MSEB. He serves on the board of directors of the Connecticut Academy for Education in Mathematics, Sciences and Technology, and was chairman of the AMS Review Group for revision of the NCTM Standards. He currently serves as chair of the AMS Committee on Education. Dr. Howe received his Ph.D. in mathematics from the University of California at Berkeley.
Daniel J. Teague teaches mathematics at The North Carolina School of Science and Mathematics in Durham, North Carolina. His twenty-five years of teaching at both the

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools - Report of the Content Panel for Mathematics
secondary and undergraduate levels have been recognized by awards such as the Tandy Technology Scholar Outstanding Teacher Award and the Presidential Award for Excellence in Mathematics Teaching. Dr. Teague’s previous NRC experience includes appointments to the Mathematical Sciences Education Board and the U.S. Commission on Mathematics Instruction. He received his Ph.D. in Mathematics Education from North Carolina State University where he completed his doctoral work in international comparisons of calculus education.
Alan C. Tucker is a professor with the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook. He has served the Department for over 30 years, previously as the Department Chair and currently as Associate Department Chair and Undergraduate Program Director. Dr. Tucker currently heads the NSF funded Long Island Consortium for Interconnected Learning which explores the teaching and learning of mathematically based subjects through instruction, curricula, technology, and interdepartmental coordination. He has previously served the NRC with appointments to MSEB’s Undergraduate Math Advisory Board and the U.S. Commission on Mathematics Instruction. Dr. Tucker received his Ph.D. in Mathematics from Stanford University.
Deborah Hughes Hallett (liaison) is a professor of mathematics at the University of Arizona; from 1991 to 1998 she was a Professor of Practice in the Teaching of Mathematics at Harvard University. She was a Principal Investigator for the National Science Foundation (NSF)–funded Bridge Calculus Consortium. She has served on committees for the Graduate Record Examination and the Massachusetts state mathematics framework review process, and on the Mathematics and Science Teacher Education Program (MASTEP) Advisory Board, an NSF-funded program to improve teacher training in California. Dr. Hughes Hallett served on the NRC’s Committee on Information Technology in Undergraduate Education. A Fulbright Scholar, she received M.A. degrees from both Harvard University and the University of Cambridge, England.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools - Report of the Content Panel for Mathematics
Box 2-1
INTERNATIONAL BACCALAUREATE MATHEMATICS COMMON AIM AND OBJECTIVES
AIMS
appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives
foster enjoyment from engaging in mathematical pursuits, and to develop and appreciation of the beauty, power and usefulness of mathematic
develop mathematical knowledge, concepts and principles
employ and refine the powers of abstraction and generalization
develop patience and persistence in problem-solving
have an enhanced awareness of, and utilize the potential of, technological developments in a variety of mathematical contexts
communicate mathematically, both clearly and confidently, in a variety of contexts.
OBJECTIVES
Having followed any one of the programmes in group 5 (mathematics), candidates will be expected to:
know and use mathematical concepts and principles
read and interpret a given problem in appropriate mathematical terms
organize and present information/data in tabular, graphical and/or diagrammatic forms
know and use appropriate notation and terminology
formulate a mathematical argument and communicate it clearly
select and use appropriate mathematical techniques
understand the significance and reasonableness of results
recognize patterns and structures in a variety of situations and draw inductive generalizations
demonstrate an understanding of, and competence in, the practical applications of mathematics
use appropriate technological devices as mathematical tools
SOURCE: (IBO, 1997, 1998)

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools - Report of the Content Panel for Mathematics
Box 2-2
SYLLABUS OUTLINE MATHEMATICAL METHODS – SL
The mathematical methods standard level programme consists of the study of six core topics and one option.
PART I: Core
105 hours
All topics in the core are compulsory. Candidates are required to study all the sub-topics in each of the six topics in this part of the syllabus as listed in the Syllabus Details.
1
Number and Algebra
10 hours
2
Functions and Equations
25 hours
3
Circular Functions and Trigonometry
15 hours
4
Vector Geometry
15 hours
5
Statistics and Probability
20 hours
6
Calculus
20 hours
PART II: Options
35 hours
Candidates are required to study all the sub-topics in one of the following options as listed in the Syllabus Details.
7
Statistical Methods
35 hours
8
Further Calculus
35 hours
9
Further Geometry
35 hours
PORTFOLIO
10 hours
Five assignments, based on different areas of the syllabus, representing the following three activities:
Mathematical investigation
Extended closed-problem solving
Mathematical modelling
SOURCE: IB Mathematical Methods SL, September 1997