Teaching Mathematics and History of Mathematics

Introduction

1. To collect the information in order to be aware of the existing sources.

2. To organize the information in order to be able to incorporate it in  the teaching activity and to search for new related sources.

The second goal is more subjective, but on the other hand it is of a great importance especially when the number of sources becomes large.

The information is partitioned into sections: books, journals, websides, videos, societies and organizations, conferences.

In each section we differentiate several areas such as:

- teaching of mathematics,
- research in mathematics,
- history of mathematics,
- psychology of understanding in mathematics.

All the four areas have a strong influence on each other but they have different methodologies and therefore are presented separately.

This portfolio does not pretend to cover the subject in full generality.
The primary emphasis is on materials that are used in  teaching of mathematics at the undergraduate and
graduate university levels in North America. However,  some of the listed items maybe usefull for high school educators.

Nowadays, the Internet becomes a dominant data source. There are advantages and disadvantages of using it. Undoubtedly, it contains lot of useful,  comprehensive and readily accessable information. But  sometimes sites are not properly organized, maintained and updated, or the information is not accurate. Therefore it is wise not to relay only on the electronic sources.

That was one of the reasons for this portfolio development.
 
 

I. Books.

Books on teaching mathematics.
Books on history of mathematics.
Psychology of mathematics.

II. North American Journals.

Mathematics education journals.
Research journals for professional mathematicians.
Journals adopted for students of mathematics.
Journals on the history of mathematics.

III. Websides.

General information and links
Teaching of mathematics.
Research in mathematics.
History of mathematics.
Distance education in mathematics.

IV. Videos.

Teaching mathematics.
Topics in mathematics.
History of mathematics.
Related topics.

IV. Societies.

For professional mathematicians.
For educators and teachers of mathematics.

V. Conferences.

For mathematicians
For math teachers and educators
 

Appendix A. AMS List of world wide Journals in mathematics.

Appendix B. AMS List of world wide mathematical societies.
 
 
 

I. Books:
 
 

1 Teaching math

1.0 Teaching techniques

Teaching Tips: strategies, research and theory for college and university teachers, Wilbert McKeachie, Houghton Mifflin Company, Boston New York 1999 (378 pp.) The book answers the questions posed by new teachers to get them started effectively in the classroom.  It  discusses such topics as course preparation, meeting a class for the first time, facilitating student learning, testing and assessing, collaborative learning, problem-based learning, using technology effectively,  large classes,  motivating students, etc.

1.1 Art of teaching mathematics: general topics

Teaching First: a Guide for New Mathematicians, Thomas Rishel, 2000 (150 pp.). This book is written for the mathematics TA or young faculty member who may be wondering just where and how to start. Rishel opens the eyes of the reader to pitfalls they may never have considered, and offers advice for balancing an obligation to the student with an obligation to mathematics. Throughout, he provides answers to seemingly daunting questions shared by most new TAs, such as how to keep a classroom active and lively; how to prepare writing assignments, tests, and quizzes; how exactly to write a letter of recommendation; and how to pace, minute by minute, the "mathematical talks" one will be called upon to give.

How to teach mathematics, Steven Krantz, AMS Providence, Rhode Island , 1999 (307pp). The book can be seen as a discussion between the traditionalist and reform camps which allows the reader to glean ideas from both camps to benefit his or her teaching. This edition is broken up into chapters on "Guiding Principles", "Practical Matters", "Spiritual Matters", "Difficult Matters" and "A New Beginning". The new Appendices, written by twelve distinguished scholars for this edition, help to balance out the book, and to demonstrate that any teaching question has many valid answers.  The book discusses broad issues associated with teaching: preparation, respect, adjusting students expectations, time management, use of technology, clarity, demonstrating the applicability of mathematics. The book also deal with difficult matters in teaching, such as instructors for whom English is a second language, cheating students, late assignments, discipline, mistakes in class.

You're the Professor, What Next? Bettye Anne Case, Editor, MAA Notes, 1994  (362pp). This is a guide for doctoral mathematical sciences departments wishing to prepare their advanced graduate students and postdoctoral instructors for collegiate teaching and related academic responsibilities. The book also will be useful to faculty mentors of new assistant professors and as personal reading for many, especially inexperienced members of mathematics faculties. Users will find discussion of a wide range of pedagogical issues, extensive references to other sources of information, and numerous practical suggestions. Forty essays, published for the first time, and a hundred reprinted articles, provide a variety of views and reflections from the mathematical community. The centerpiece of the book is a collection of reports from eight graduate mathematics programs which piloted special seminars in teaching and professionalism for students about to receive PhD degrees.

Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom, in Faculty and Graduate Student Editions, Solomon Friedberg, AMS, MAA ,  2001  (158pp) This volume uses the following idea in the context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professional mathematician. These teaching situations are the Case Studies of the title. Each case raises a variety of pedagogical and communication issues that may be explored either individually or in a group facilitated by a faculty member. Teaching notes for such a facilitator are included for each Case in the Faculty Edition.

Twenty Years Before the Blackboard :The Lessons and Humor of a Mathematics Teacher, Michael Stueben with Diane Sandford,  MAA: Spectrum, 1998 (174 pp.) The author shows how he has used humor and wordplay to motivate his students. The book is filled with wonderful problems and proofs, as well as the author's insights about how to approach teaching problem solving to high school students. Sections of the book also treat the use of calculators and computers in the classroom. A section on mnemonics shows how teachers can use memory aids to help their students learn and retain material.

The Dialogue between Theory and Practice in Mathematics Education: Overcoming the Broadcast Metaphor, Proceedings of the Fourth Conference on Systematic Cooperation between Theory and Practice in Mathematics Education (SCTP). Brakel, Germany, September 16-21, 1990 , Edited by F. Seeger and H. Steinbring. Bielefeld, Germany: University of Bielefeld Press, 1992  (363pp.)

Guidelines for the Tutor of Mathematics, Connie Laughlin and Henry Kepner Jr, 2nd Edition, Washington: NCTM: 2001 (48 pp.) Updated, excellent help for the prospective math tutor,who, although successful in math, lacks teaching skills. Presents guidelines from a variety of sources: the authors' experiences, research on tutoring, and direct work with students and others involved in tutoring. Emphasizes that the tutor is most effective as a coach, a supportive listener, a critical - yet compassionate - mathematician, and a cheerleader.

Practice-Based Professional Development for Teachers of Mathematics Margaret Schwan Smith, Washington: NCTM, 2001 (70 pp.) Charts new directions for professional development and provides a new perspective on how to design, conduct, and evaluate professional education experiences for teachers. Explores a specific type of professional development opportunity that connects the ongoing professional development of teachers to the actual work of teaching. Presents snapshots of practice-based professional development, offers ideas for designing high-quality professional development experiences, and explains how to assess the effectiveness of professional development.

Designing Professional Development for Teachers of Science and Mathematics.  Susan Loucks-Horsley, Peter W. Hewson, Nancy Love and Katherine E. Stiles, Washington: NCTM: 1998 (325 pp.).Carefully examines how professional development needs to change to meet the challenges ahead and how to make it an indispensable fixture in educational systems of the future. The book is both a primer on the principles of effective professional development and a conversation among professional developers about ways to create the learning programs. Presents images of what is possible and offers a design framework, many strategies, and resources for professional learning. Also discusses critical issues, such as equity and diversity, in designing programs and the factors influencing professional development.

Effective learning and teachind in mathematics and its applications, Peter Kahn and Joseph Kyle, editors,  Kogan Page, 2002 (208 pp). This book covers all of the key issues the effective teaching of Mathematics, a key subject in its own right, and also one that forms a key part of many other disciplines. The book includes contributions from a wide range of experts in the field, with a broad and international perspective. It has chapters on :Exposing mathematical thought; Developing active learners; Planning learning; Assessment and giving feedback; Using IT; Developing transferable skills; Reflecting on practice; Numeracy in HE; Mathematics in the service of other disciplines; Mathematical modelling; Mathematics for business; Statistics; Pure mathematics; Training mathematics teachers for the future
 
 

1.2 Assessment

Assessing habits of mind: Performance-based assessment in science and mathematics Margaret Jorgensen, ERIC, 1994 (132 pp.) In contrast to achievement tests and other standardized forms of assessment, this book presents performance-based options as a means of determining if students can complete, demonstrate, or perform the actual behaviors of interest. Assessment is presented as a tool for improving classroom instruction.

Student Assessment in Calculus :A Report of the NSF Working Group on Assessment in Calculus, Alan Schoenfeld, Editor, MAA, 1997 (122 pp.) The report provides valuable information on methods for assessing student understanding, illustrating these methods through examples of student work. It also maps out key areas in teaching, learning, and assessment that require further research. It is certainly a worthwhile reference for anyone who is
interested in researching mathematical thinking, or who is concerned about student learning and ways to assess it.

Assessment Practices in Undergraduate Mathematics Bonnie Gold, Sandra Keith, and William Marion, Editors, MAA Notes, 1999, (292 pp.) Assessment techniques offered in this book range from several-minute classroom exercises and examples of alternative assignments and cooperative exercises, to examples of how departments may evaluate their course placement, major, service to other departments, and teaching.

1.3 Specific teaching techniques

Cooperative Learning in Undergraduate Mathematics Issues that Matter and Strategies that Work Elizabeth C. Rogers, Barbara E. Reynolds, Neil A. Davidson, and Anthony D. Thomas, Editors, MAA Notes,  2001,  (150 pp.) The volume discusses many of the practical implementation issues involved in creating a cooperative learning environment: how to develop a positive social climate, form groups and prevent or resolve difficulties within and among the groups,  what are some of the critical and sensitive issues of assessing individual learning in the context of a cooperative learning environment. The authors present powerful applications of learning theory that illustrate how readers might construct cooperative learning activities to harmonize with their own beliefs about the nature of mathematics and how mathematics is learned.

A Practical Guide to Cooperative Learning in Collegiate Mathematics Nancy L. Hagelgans, Barbara E. Reynolds, SDS, Keith Schwingendorf, Draga Vidakovic, Ed Dubinsky, Mazen Shahin, and G. Joseph Wimbish, Jr, MAA Notes,  1995, (190 pp.) This book will greatly help readers introduce cooperative learning in their own undergraduate mathematics classes. Instructors who have tried some group activities as well as those who have not been involved at all with cooperative learning will find here detailed, useful discussions on every aspect of cooperative learning. The book reflects the extensive experience of the authors as well as that of over forty colleagues who responded to a survey on cooperative learning. Throughout the
book cooperative learning is related to educational research results, which are clearly explained in one chapter.
 

Readings in Cooperative Learning for Undergraduate Mathematics Ed Dubinsky, David Mathews, and Barbara E. Reynolds, Editors, MAA Notes,
1997, (324 pp.) 17 papers were field-tested and selected for inclusion based on their effectiveness in faculty development courses.  The papers are organized into three parts. Part 1 covers constructivism and the teacher's role in the classroom. Part 2 discusses the effectiveness of cooperative learning, supported by educational research. Finally, the focus of Part 3 is on implementation issues. The book concludes with a valuable annotated bibliography of science, mathematics, engineering and technology resources in higher education.

Technology-Enhanced Teaching and Learning: Leading and Supporting the Transformation on Your Campus. Edited by Carole Barone and Paul Hagner. Educause: 2001 (112 pp.) This book makes recommendations for gaining community consensus for new directions, and for engaging and supporting faculty to use technology. It also describes new roles for faculty in an e-learning environment.

Models for Mathematics Technology Teacher Development Programs John Harvey, Editor, MAA, 1998, (138 pp.) This book contains the papers presented at the TMC conference on Models for Mathematics Technology Teacher Education in April 1995.  Anyone involved in the structure, content and pedagogy of professional development programs for elementary, middle and high school teachers will find much of interest here.

Proofs Without Words, Roger B. Nelsen, MAA, 1993 (160 pp.) In this book the emphasis is  on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into six chapters: Geometry and Algebra; Trigonometry, Calculus and Analytic Geometry; Inequalities; Integer Sums; Sequences and Series; and Miscellaneous. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Everyday and Academic Mathematics in the Classroom. Edited by Mary E. Brenner and Judit N. Moschkovich. Washington: NCTM, 2001 (178 pp.) Examines what happens when everyday and academic mathematical practices are considered in designing classroom instruction. Provides a theoretical basis for evaluating the advantages and disadvantages of using everyday mathematical activities as resources to extend students' learning in the classroom.

Putting Students at the Center: A Planning Guide to Distributed Learning Diana Oblinger, Educause: 1999 (36 pp.).This monograph is designed to help individuals and institutions understand the rationale and processes associated with distributed learning.

Scientists and mathematicians become school teachers. Edited by Billie F. Risacher. ERIC, 1998, (136 pp.) This book considers the need to accommodate second-career professionals in teacher preparation programs for secondary science and mathematics. Chapters address issues related to nontraditional pathways to teaching, and a case study of a developed program is included.
 
 

1.4 Teaching of some topics in math

Learning by Discovery: A Lab Manual for Calculus, Anita Solow, MAA, 1993, (184 pp.) This is a book for mathematical faculty who wish to try a new approach to teaching that involves the student in the learning process. It contains 26 laboratory modules, that can be used as lab components in your course, or assigned as independent projects.

Exemplary Programs in Introductory College Mathematics Susan Lenker, MAA Notes 1998, (140 pp.)
This handbook will help you improve your teaching by showing you how you might take advantage of current technology to teach introductory mathematics courses. Browse the winning entries in the Innovative Programs Using Technology Project (INPUT) and learn how others have used technology to teach developmental mathematics, precalculus, business mathematics, quantitative literacy and introductory statistics.

Geometry From Africa: Mathematical and Educational Explorations Paulus Gerdes, MAA:Classroom Resource Materials, 1999 (150 pp.) The author demonstrates the influence of geometrical ideas on African Culture with dozens of stories and beautiful illustrations. He gives examples of geometrical ideas in the work of wood and ivory carvers, potters, painters, weavers, and mat and basket makers. He llustrate how diverse African ornaments and artifacts may be used to lead students to discover the Pythagorean Theorem and to find proofs of it.  He also explores connections to Pappus' Theorem, similar right triangles, Latin and magic squares, and arithmetic modulon.

Geometry Turned On: Dynamic Software in Learning, Teaching and Research, James King and Doris Schattschneider, Editors, MAA,1997, (275 pp.)
Dynamic geometry is active, exploratory geometry carried out with interactive computer software. It has had a profound effect in classroom teaching wherever it has been introduced and has become an indispensable research tool for mathematicians and scientists. The papers in this volume give a good idea of the ways in which the software can be used, and some of the effects it can have. It is clear that the software raises various questions for teaching and research, and its continuing evolution raises questions on the design of the software itself.

Laboratory Approach to Teaching Calculus, Editors: Carl Leinbach, Joan R. Hundhausen, Arnold M. Ostebee, Lester J. Senechal, and Donald B. Small
MAA Notes , 1991 (290 pp.) Twenty-six academic institutions that have used the laboratory approach to teaching calculus evaluate their experiences, and tell us what has worked for them and what has not. A range of experiences is presented. Every reader will find in this volume at least one example of a setting that is adaptable to their institution. All of the ideas presented in this book have been tried, tested and evaluated, and you will learn what worked and what did not.

Laboratory Experiences in Group Theory ,Ellen Maycock Parker , MAA, 1996, (112 pp.) This is a workbook of 15 laboratories designed to be used with the software Exploring Small Groups as a supplement to the regular textbook in an introductory course in group theory or abstract algebra. Written in step-by-step manner, the laboratories encourage students to discover the basic concepts of group theory and to make conjectures from examples that are easily generated by the software. The labs can be assigned as outside work or they can be used in a structured laboratory setting. Since the software is very user-friendly and the laboratories are complete, students and faculty should have no difficulty in using the labs without training.

Resources for Teaching Linear Algebra David Carlson, Charles R. Johnson, David C. Lay, A. Duane Porter, Ann E. Watkins, William Watkins, Editors,
MAA Notes, 1997, 306 pp. This book argues that the teaching of elementary linear algebra can be made more effective by emphasizing applications, exposition and pedagogy. This volume includes the recommendations of the Linear Algebra Curriculum Study Group, with their core syllabus for the first course, and the thoughts of mathematics faculty who have taught linear algebra using these recommendations. It includes elucidation of these ideas, trenchant criticism of them, and a report on putting them into practice.

Revolutions in Differential Equations Exploring ODEs with Modern Technology Michael Kallaher, MAA Notes, 1999, (140 pp.) The central theme of this book is to show how modern technology can be incorporated into the differential equations course. The articles do not constitute a textbook, rather they provide material for study and reflection that will help the teacher pull out ideas relevant to their own classroom situation. Articles touch on a variety of topics: the use of laboratories in ODE courses, modeling using ODEs and computers, dynamical systems, computer exploration of concepts taught in ODE courses, ODE solvers and their use in the classroom, and Internet resources available for the ODE class.

Discrete Mathematics in the Schools. Edited by Joseph G. Rosenstein, Deborah S. Franzblau, and Fred S. Roberts. Copublished with the American Mathematical Society. Washington: NCTM, 1998 (458 pp.) Explains why and how discrete mathematics should be taught in K-12 classrooms and provides assistance and guidance on how this can be accomplished. Covers a variety of topics, such as mathematical modeling, the role of applications, activities, the role of computer science, and many more. Gives information on the many resources available to teachers who are seeking to enrich their classrooms with discrete mathematics. This book developed from a conference on discrete mathematics that took place at Rutgers University in October 1992.
 
 

1.5 Student research projects in math

Inverse Problems: Activities for Undergraduates Charles Groetsch, MAA: Classroom Resource Materials, 1999 (229 pp.) This book introduces mathematics instructors to inverse problems and provides them with resources that are useful for teaching the lessons of inverse problems to students in the first two undergraduate years. Inverse problems are introduced by an historical essay that is meant to provide, without any formal mathematics, a scientific and cultural context for the mathematical lessons that follow. The next four chapters deal with inverse problems in Precalculus, Calculus, Differential Equations and Linear Algebra. Each module opens with advice on mathematical and scientific prerequisites, and the type of appropriate technology .

Calculus Problems for a New Century Robert Fraga, MAA, 1993 ( 448 pp.)
Emphasizes conceptual understanding over rote drill. Graphs and tables, rather than rules, are used to define functions, in the
belief that "real world" data generally come that way. The problems are organized in groups that parallel traditional grouping of
ideas, making it possible to use them as supplements to most texts. Most of the problems can be done without the use of a
calculator or computer.

Calculus Mysteries and Thrillers R. Grant Woods, MAA: Classroom Resource Materials, 1998. This book consists of eleven mathematics projects based on introductory single-variable calculus, together with some guidance on how to make use of them. Each project is presented as an amusing short story.The problem solvers are required to present to their client a detailed written report of their findings. Thus, students must produce and analyze accurate mathematical models of complex, verbally presented "real life" situations, and write a clear technical account of their solution. Instructors who are looking for problems that are novel, interesting, and several levels more complex than the typical text book "word problem" will find them in this book. It will be of particular value to instructors who wish to combine training in applications of calculus with training in technical writing. The complexity of the problems makes them suitable for use as group projects.

Problems for Student Investigation Michael B. Jackson & John Ramsay, MAA, 1993,  (224 pp.) Students will learn how to use calculus to solve real problems, how to use the library to find mathematical sources, how to read and write mathematical material, and how to cooperate with their peers in solving difficult problems. Learning that they can solve what at first seems an inscrutable mathematical problem can only increase students' mathematical confidence.

Research Issues in Undergraduate Mathematics James J. Kaput and Ed Dubinsky, Editors, MAA Notes, 1994,  (150 pp.) This book should be on every mathematics educator's shelf not only for personal knowledge but for the ideas that could improve teaching. It is also a great source for mathematics majors who are looking for research  ideas.

Student Research Projects in Calculus Marcus Cohen, Edward D. Gaughan, Arthur Knoebel, Douglas S. Kurtz, & David Pengelly, MAA:Spectrum,
1992, (232 pp.)Over 100 projects are presented, all of them ready to assign to your students in single and multivariable calculus. The projects were designed with one goal in mind: to get students to think for themselves. Each project is a multistep, take home problem, allowing students to work both individually and in groups.  Each project has accompanying notes to the instructor reporting students' experiences. The notes contain information on prerequisites, list the main topics the project explores, and suggest helpful hints. The authors have also provided several introductory chapters to help instructors use projects successfully in their classes and begin to create their own.
 

1.6 Calculus reform

Assessing Calculus Reform Efforts ,James R. C. Leitzel and Alan C. Tucker, Editors,  MAA Notes, 1994 (100 pp.) This special report provides a review of the various aspects of the calculus reform movement. It provides an assessment of the current attitudes and involvement of students, faculty, andadministration in the effort to revise calculus instruction. The study shows that how calculus is taught has changed more than what is taught, and that the changes in instructional practice, more frequent use of technology and increased focus on building students' conceptual understanding are finding their way into both pre-calculus and post-calculus mathematics courses. Calculus reform has also increased interest in how undergraduate students learn mathematics.

Preparing for a New Calculus Anita Solow, Editor , MAA Notes, 1994, (250 pp.) The provides an accurate picture of the current status of the mathematics reform movements. A collection of brief descriptions of a number of developmental projects in calculus and precalculus reform movements provides useful information on a diverse set of projects.

Calculus: The Dynamics of Change A. Wayne Roberts, Editor MAA Notes, 1995 (172 pp.) The four main sections of the book describe the vision of those who have developed materials, offer guidance to departments considering a change, discuss methods of assessment, and describe the effect of calculus reform on other courses in the mathematics curriculum. Taken altogether, this is intended as a handbook for change.

A Call for Change :Recommendations for the Mathematical Preparation of Teachers of Mathematics, James R.C. Leitzel, MAA Notes, 1991 (64 pp.)
How can we improve the teaching and learning of mathematics in our schools to better prepare our students for the future? We can begin by making some changes in the way our teachers learn and teach mathematics. A Call For Change , an MAA Report, offers a set of recommendations that come from a vision of ideal mathematics teachers in classrooms of the 1990s and beyond. The report describes the collegiate mathematical experiences that a teacher needs in order to meet this vision.

Changing Calculus - A Report on Evaluation Efforts and National Impact from 1988-1998 Susan Ganter, MAA Notes, 2001, (94 pp.) Many undergraduate institutions nationwide have implemented programs to improve learning in science, mathematics, engineering, and technology (SMET), including some that are working to eliminate the traditional boundaries between these disciplines to produce a truly integrated teaching approach. These programs represent a change in the fundamental philosophy that has long guided the structure of undergraduate education. It is believed by many that such change is necessary for students who will live and work in an increasingly technical society. Changing Calculus discusses the results from a study conducted as a part of a larger effort by NSF to evaluate the impact of reform in SMET education at the undergraduate level.

Confronting the Core Curriculum John A. Dossey, Editor, MAA Notes, 1998 (82 pp.)
This is the report of a conference that examined the possibility of change in the first two-years of the undergraduate curriculum in mathematics. The participants at the conference, held at the US Military Academy at West Point, NY, focused on what changes might occur in courses in linear algebra, differential equations, discrete mathematics, and probability and statistics due to the changes in the undergraduate calculus program currently being implemented at several colleges and universities nationwide. Leaders in curricular design in each of these core content areas presented papers on their
vision of reform in calculus and the four areas mentioned above. These proposals are accompanied by reactions from others working in the same curricular content areas.

Calculus Catalyzing A National Community For Reform William E. Haver, Editor, MAA, 1998, (120 pp.) The book begins with an overview of the NSF Calculus Program. It describes the characteristics of the program and provides a bibliography of the literature of calculus reform. The book continues with short summaries of all of the awards from 1987 through 1995.

Heeding the Call For Change Lynn Arthur Steen, MAA Notes, 1992 (260 pp.) In 1991 the MAA Board of Governors issued the publication of an MAA Report, A Call For Change, which heralded sweeping reform in all aspects of collegiate mathematics. Heeding the Call for Change shows how some of the challenges offered in A Call For Change can be accomplished. Each chapter in this volume highlights many options for constructive change; most also offer specific suggestions for improvement in curriculum or instructional practice.
 

1.7 Gender issue in teaching math

Changing the Faces of Mathematics: Perspectives on Gender. Edited by Judith E. Jacobs, Joanne Rossi Becker, and Gloria F. Gilmer. Washington: NCTM, 2001 (170 pp.) This book presents a provocative collection of eclectic chapters that urges teachers to ensure equity in mathematics education for girls and women. It also suggests ways to modify assessment practices to eliminate gender bias, and presents interesting personal stories that illustrate the relationship between an individual and mathematics when performing everyday activities such as sewing or styling hair. Finally, it recounts the struggles of two women of color as they attempt to assume leadership in mathematics education, and discusses how to build a multicultural, gender-equitable mathematics classroom.

Women in Mathematics: Scaling the Heights Deborah Nolan, Editor, MAA Notes, 1997,  (146 pp.) This book presents insight of eight individuals who have taught at the Summer Mathematics Institute at Mills College. They share their course materials and give pedagogical tips on how to teach topics in mathematics that are not usually part of the undergraduate curriculum in ways not usually found in the undergraduate classroom. Although the courses describedhere were designed to encourage talented undergraduate women to pursue advanced degrees in mathematics, the good ideas
found in them are gender free and can be used equally well with male as well as female students.
 

1.8 Mathematical writing

Writing in the Teaching and Learning of Mathematics John Meier and Thomas Rishel
Discusses both how to create effective writing assignments for mathematics classes, and why instructors ought to consider using such assignments. The book is more than just a user's manual for what some have termed "writing to learn mathematics"; it is an argument for engaging students in a dialog about the mathematics they are trying to learn.

Mathematical Writing, Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts
This is an all-out attack on the problem of teaching people the art of mathematical writing. This book will give aid and
encouragement to those wishing to teach a course in technical writing, or to those who wish to write themselves.

Using Writing to Teach Mathematics, Andrew Sterrett, Editor
The mathematics teacher who is trying to understand what can be gained by using writing or is looking for several examples of how teachers have actually used writing in their mathematics classes will find this book to be an excellent source. Need help in getting started as an individual or as a member of a department facing a Writing Across the Curriculum requirement? Learn how others have made use of student assistants, both undergraduate and graduate, in ways that benefit students and faculty members alike. Read how feedback from student journals provides early warning signals for instructors, as well as helps students clarify their own thought processes.
 

1.9 Other topics

The Philosophy of Mathematics Education. P. Ernest, London: Falmer Press, 1991. Influenced by David Bloor and SSK, Ernest proposes a philosophy of mathematics called "social constructivism," which sees mathematics as fallible and objective as meaning socially agreed-upon.

Quantitative Reasoning for College Graduates Linda Sons, Editor, MAA Reports, 1996, (56 pp.) This report provides suggestions on how our colleges and universities can improve the general mathematical knowledge of its graduates. Appendices to the report include references, a list of topics on which one might base a reasonable syllabus, brief descriptions of courses, a list of problems related to minimal competency, project ideas, scoring guides and more.

Great Jobs for Math Majors Stephen Lambert and Ruth J. Decoti, MAA, 1998, (304 pp.) Part I of this useful guidebook covers areas such as preparation of the resume and cover letter, networking, interviewing, and choice of graduate schools. Part II shows the realistic options for candidates with an undergraduate mathematics degree. The authors have designed, investigated, and written each of these chapters with an eye to both the job market for math majors and their own experience in counseling and advising students over the past two decades.
 
 
 
 
 

2. Books on history of mathematics

2.1 History

The History of Mathematics: a reader. Edited by John Fauvel and Jeremy Gray. Basingstoke: Macmillan, 1987. A collection of excerpts from primary sources, spanning ancient and modern mathematics alike.

A History of Mathematics, Carl B. Boyer, 2^nd edition. New York: Wiley, 1989. This is an excellent university-level textbook for the study of history of mathematics, but it lacks coverage of women in the field.

The history of mathematics: an introduction, David M. Burton, Boston: Allyn & Bacon, 1985 (678 pp.) This solid survey of the history of mathematics is written in a lively style and contains "a rather idiosyncratic store of information." "China, the Hindus, and medieval Islam are largely overlooked," as is Napier's work on logarithms. "The interspersed treatment of the development of the calculus is not adequate."

History of Mathematics Florian Cajori, 5thEdition. AMS Chelsea, 1991. Originally issued in 1893, this edition covers the period from antiquity (including Mayan and Japanese mathematics) to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. In one concise volume this unique book presents an interesting and reliable account of mathematics history for those who cannot devote themselves to an intensive study. The book is a must for personal and departmental libraries alike.

The history of mathematics: a brief course, Roger Cooke, New York: Wiley, 1997. An excellent reference book with discussion of Japanese and Korean mathematics, as well as problems after each chapter.

An introduction to the history of mathematics, Howard Whitley Eves, 5th ed. Philadelphia: Saunders, 1983 (593 pp.) This classic best-seller by a well-known author introduces mathematics history to mathematics students. Suggested essay topics and problem studies challenge students. 'Cultural Connections' sections explain the time and culture in which mathematics developed and evolved. Portraits of mathematicians and material on women in mathematics are of special interest.

The crest of the peacock: non-European roots of mathematics, G.G.Joseph,Harmondsworth: Penguin, 1991. This text has some errors, but it is particularly valuable for the introductory chapter, which looks at transmission of mathematics from the Middle East to Europe.

History of Mathematics, David Eugene Smith,Boston: Ginn, 1923. A classic in the field of the history of mathematics.

Agnesi to Zeno. Sanderson Smith, Key Curriculum, 1995. A good review of people and concepts throughout the history of mathematics, and includes extensive coverage of women and non-western cultures. Lacks depth of content.

The Beginnings and Evolution of Algebra Isabella Bashmakova and Galina Smirnova, MAA, 1999 (160 pp.) The special merit of the book is that it corrects the widespread view that up to the 1830s the mainspring of the development of algebra was the investigation and solution of determinate algebraic equations, and especially their solution by radicals. The authors show that this viewpoint is one-sided and gives a distorted view of of its evolution. Specifically, they show that the role of indeterminate equation in the evolution of algebra was no less important than that of determinate equations.

A Century of Mathematics :Through the Eyes of the Monthly ,John Ewing,
This is the story of American mathematics during the past century. It contains articles and excerpts from a century of the American Mathematical Monthly, giving the reader an opportunit to skim all one hundred volumes of this popular mathematics magazine without actually opening them:
the controversy about Einstein and relativity, the debates about formalism in logic, the immigration of mathematicians from Europe, and the frantic effort to organize as the war began. More recent articles deal with the advent of computers and the changes they brought, and with some of the triumphs of modern research.

Episodes from the Early History of Mathematics A. Aaboe, New York: Random House, 1964 (133 pp.) Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle. Some of the topics may be familiar to the reader, while others will seem surprising or be new

Episodes in Nineteenth and Twentieth Century Euclidean Geometry Ross Honsberger, MAA, 1995 (174 pp.) Dealing with various aspects of Euclidean geometry, this work begins with the broken-chord theorem, attributed to Archimedes by Islamic mathematicians, an goes on to discuss various properties of circles, triangles, and quadrilaterals.

Essays in Humanistic Mathematics Alvin White, Editor, MAA Notes, A collection of papers published by the Mathematical Association of America (MAA) that give an account of the social and historical nature of mathematics and mathematical knowledge, serving as a manifesto for the humanization of both the philosophy of mathematics and the college teaching of mathematics.

From Pythagoras to Einstein K.O. Friedrichs, MAA:New Mathematical Library, 1965 (88 pp.)

From Zero to Infinity Constance  Reid,  MAA:Spectrum,  1992, (200 pp.) The book has dazzled readers with its freshness and clarity since being published in 1955. This book shows how interesting the everyday natural numbers 0, 1, 2, 3, . . . have been for over two thousand years, and still are today. It combines the mathematics and the history of number theory with descriptions of the mystique that has on occasion surrounded numbers
even among great mathematicians.

Great Moments in Mathematics Before 1650 Howard Eves, MAA:Dolciani Mathematical Expositions , 1982 (270 pp.) The author has the knack of bringing ancient mathematics alive. His exposition is clear and he is not content with generalities, but gives actual examples of early methods.

Great Moments in Mathematics After 1650 Howard Eves,  MAA, 1982 (270 pp) This is a companion to volume Great Moments in Mathematics Before 1650.

The History of Mathematics - A Reader John Fauvel and Jeremy Gray, Editors, MAA, 1996 (640 pp) This book contains a wide selection of readings in the history of mathematics from earliest times to the twentieth century. The variety of sources chosen illuminates several different approaches to the subject. They go from discussions of the origins of counting to the application of electronic computers, and from Euclid's Elements to Cantor's continuum hypothesis.

In Eves' Circles Joby Milo Anthony, MAA Notes, 1994 (220 pp.) A very special volume for all of Eves' thousands of admirers. If your interest is history of mathematics, geometry, or pedagogy, then this book is for you. A valuable sampler or a mathematics educator, particularly one with a strong interest in the history of mathematics.

Indiscrete Thoughts Gian-Carlo Rota, Birkhauser, 1997,  The book gives a rare glimpse into a world that has seldom been described, that of science and technology as seen through the eyes of a mathemat ician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as for the American university.

Learn from the Masters Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, & Victor Katz, MAA: Classroom Resource Materials, 1995, (312 pp.) This book is for college and secondary school teachers who want to know how they can use the history of mathematics as apedagogical tool to help their students construct their own knowledge of mathematics. It covering fields such as trigonometry, mathematical modeling, calculus, linear algebra, vector analysis, and celestial mechanics. Also included are articles of a somewhat philosophical nature, which give general ideas on why
history should be used in teaching and how it can be used in various special kinds of courses. Each article contains a bibliography to guide the reader to further reading on the subject.

Mathematics from the Birth of Numbers Jan Gullberg, W.W.Norton & Company, 1997 (1120 pp.) This wide-ranging survey looks at the history of mathematics from the invention of numbers and language, through the realms of arithmetic, algebra, geometry, trigonometry and calculus, to mathematical logic, set theory, topology, fractals and probability, and onwards to differential equations.

Mathematical Encounters of the Second Kind Philip J. Davis,  Birkhauser, 1997 (304 pp.) It is  pleasant  reading, an appealing tale of the life and friends of a mathematician. The book closes a number of circles, from Euclid as a geometer to Euclid as a number theorist, from Napoleon to Rothschild as amateur mathematicians, from Davis New England friend Alexander Sedgwick Carpenter to his English friend Lord Victor Rothschild.
 

Mathematical Methods in Science George Pólya & Leon Bowden, MAA:New Mathematical Library, 1977 (234 pp.) If you have ever wondered how the laws of nature were worked out mathematically, this is the book for you. Above all, it captures some of Polya's excitement and vision.

Memorabilia Mathematica :The Philomath's Quotation Book, Robert Edouard Moritz, MAA:Spectrum, 1993 (440 pp.) The more than eleven-hundred fully annotated selections in this book, gathered from the works of three hundred authors, cover a vast range of subjects pertaining to mathematics. Grouped in twenty-one chapters, they deal with such topics as the definitions and objects of mathematics; the teaching of mathematics; mathematics as a language or as a fine art; the relationship of mathematics to philosophy, to logic, or to science; the nature of mathematics, and the value of mathematics. To mathematicians the book will be a great source of pleasure, inspiration, and encouragement. To teachers of mathematics and writers about mathematics, it will remain of inestimable value as a source of quotations and ideas.

Numerology or What Pythagoras Wrought, Underwood Dudley, MAA:Spectrum, 1997 (329 pp.) Number mystics, Dudley explains, originated with Pythagoras 2500 years ago and continue to this day. Numerology is applied number mysticism and is a more recent invention. You will find a history of number mysticism and numerology in the book, with a wealth of examples from the past as well as the present. Meet the Elliott Wave Theorists (who explain the movement of the stock market with Fibonacci numbers); the Bible-numberists, who find 7s. 11s. 13s, or perfect square in the Bible; the
researcher who finds 57s throughout the American Revolution; the pyramidologists who see all of human history in numbers derived from measurements of the great pyramid of Egypt, and much more.

Out of the Mouths of Mathematicians : A Quotation Book for Philomaths, Rosemary Schmalz, MAA:Spectrum,  1993 (304 pp.) This book will give pleasure to any philomath. It can be used to facilitate a literature search or to give quick access to an appropriate quote for writers and speakers. It will be particularly  useful to teachers of mathematics at all levels, to encourage, motivate, and amuse their students. Along with R. E. Moritz's
earlier book of this type, Memorabilia Mathematica: The Philomath's Quotation Book, it offers the story of mathematics from its primary source, the mathematicians themselves.

Readings for Calculus Underwood Dudley, MAA 1993 (224 pp.) Presents readings on the history of calculus and of mathematics, on the nature of mathematics and its applications, on the learning of calculus, and on the place of calculus and mathematics in society. Can be used as a supplement to any calculus text, showing students that there is more to calculus than getting the right answer. Exercises and problems included.

Using History to Teach Mathematics Victor Katz, Editor, MAA  Notes 2000 (300 pp.)
This book is a collection of articles by international specialists in the history of mathematics and its use in teaching, based on presentations given at an international conference in 1996.  It hows how  and why an understanding of the history of mathematics is necessary for informed teaching of various subjects in the mathematics curriculum, both at secondary and at university levels.

Vita Mathematica :Historical Research and Integration with Teaching , Ronald Calinger, Editor , MAA Notes 1996, (371 pp.) The book shows us: how two important eighteenth century mathematicians, Colin Maclaurin and Joseph-Louis Lagrange, understood the calculus from these different standpoints and how their legacy is still important in teaching calculus today; why Lagrange's algebraic approach dominated teaching in Germany in the nineteenth century;the ancient history of one of the possible foundations, the concept of indivisibles. This volume demonstrates that the history of mathematics is no longer tangential to the mathematics curriculum, but in fact deserves a central role.

The search for certainty: a philosophical account of foundations of mathematics, M.Giaquinto, Clarendon Pr. Oxford, 2002 (298 pp.)
The author tells the story of one of the great intellectual adventures of the modern era -- the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.Readership: Scholars and graduate students of philosophy, logic, and philosophy of mathematics

Mathematics unbound: the evolution of the international research community, 1800-1945, Karen Hunger Parshall and Adrian C. Rice, editors, 2002 (408 pp.)"Global nature" of the mathematical community is relatively recent, having evolved over a period of roughly 150 years.The practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research  and cooperation transcended national boundaries. This includes developments within component national mathematical communities, such as the growth of societies and journals, but also more wide-ranging political, philosophical, linguistic, and pedagogical issues.The book will be of interest to mathematicians, historians of mathematics, and historians of science in general.

The honor class: Hilbert's problems and their solvers, Ben H. Yandell,  Petrs, 2002 (486 pp.) In 1900 David  Hilbert presented a list of 23 problems that have become an icon for the new century of math research. The author traces the life of each problem, with focus on the solvers. This reveals something of how  modern math happend.  Attractive rading  for all from undergraduates through faculty.

2.2 Biography

Archimedes What Did He Do Besides Cry Eureka? Sherman Stein

Diophantus and Diophantine Equations I.G. Bashmakova

Euler: The Master of Us All William Dunham, MAA:Dolciani Mathematical Expositions,  (192 pp.)
Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory
biographical sketch are chapters describing his contributions to eight different topics--number theory, logarithms, infinite
series, analytic number theory, complex variables, algebra, geometry, and combinatorics.

Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work G.H. Hardy,
AMS Chelsea, 1991 (254 pp., 429) Hardy collects twelve of his own lectures on topics stemming from Ramanujan's life and work. The topics include: partitions, hypergeometric series, Ramanujan's tau-function and round numbers.

Julia, a life in mathematics Constance Reid

The Man Who Loved Only Numbers Paul Hoffman

The Random Walks of George Pólya Gerald L. Alexanderson

The Search for E. T. Bell Constance Reid

Through A Reporter's Eyes - the Life of Stefan Banach Roman Kaluza
 
 

3. Psychology of mathematics.

The psychology of mathematics for instruction, Lauren B. Resnick and Wendy W. Ford, 1981 The book addresses psychologists, educators and mathematician who are interested in mental processes involving in learning mathematics. The book can be read as a history of psychological efforts to discover the nature of learning in math. Above all, it shows how instructions can enhance the process on elementary math learning.

Understanding in mathematics, Anna Sierpinska, 1994 The book draws together strands from mathematics, philosophy, logic, linguistics, the psychology of math education and continental European research. It primarily concerns with the question how real people understand mathemtics in real life.

The glass wall: why mathematics can be difficult, Frank Smith, NY: Teachers College Press, 2002 (176 pp.)
The book helps us to understand why some people find the world of mathematics so compelling while others find it so difficult. This original volume examines two different worllds : the physical world (our familiar world of objects and events) and the world of mathematics (a completely different domain of experience), and the glass wall that can exist between them. Smith argues that, because the language used to talk about these two worlds is not the same, many people find themselves behind the glass wall, on the outside looking in.

How to read and do proofs: an introduction to mathematical thought processes, Daniel Solow, NY: Wiley, 2002.
 
 
 
 

II . North American Journals
 
 

1. Mathematics education journals.

Journal for Research in Mathematics Education (http://www.nctm.org/jrme) is an official journal of the National Council of Teachers of Mathematics (NCTM). The JRME is devoted to the interests of teachers of mathematics and mathematics education at all levels--preschool through adult.

Mathematics Education Dialogues (http://www.nctm.org/dialogues/) is an open forum for the exchange of points of view about issues in mathematics education. It provides essays about compelling, complex, and timely topics in mathematics education that transcend grade levels. Dialogues does not present official policies of NCTM. The Editorial Panel strives to have many viewpoints represented.

The ComMuniCator (http://www.cmc-math.org/publications), a magazine published four times a year by California Mathematics Council, is a nationally recognized forum for mathematics educators. It discusses current issues, reports new developments, showcases innovative teaching and assessment techniques, and publicizes conferences, CMC services, and other professional opportunities.

Educational Researcher (http://www.aera.net/pubs/er/) contains scholarly articles of general significance to the educational R&D community from a wide range of disciplines.

Education Studies in Mathematics (http://www.wkap.nl/journalhome.htm/0013-1954) presents new ideas and developments of major importance to those working in the field of mathematical education. It deals with didactical, methodological and pedagogical subjects, rather than with specific programs for teaching mathematics.

Educause Quarterly (formerly Cause/Effect) is a practitioner's journal about planning, developing, managing, using, and evaluating information resources and technology in higher education. Written by campus practitioners, articles are peer-reviewed prior to publication.

Journal on Excellence in College Teaching (http://ject.lib.muohio.edu/) is a peer-reviewed journal by and for faculty at universities and two- and four-year colleges to increase student learning through effective teaching, interest in and enthusiasm for the profession of teaching, and communication among faculty about their classroom experiences.

Mathematics Teacher (http://my.nctm.org/eresources/journal_home.asp?journal_id=2) includes activities, lesson ideas, teaching strategies, and problems through in-depth articles, departments, and features. It is devoted to improving mathematics instruction in grade 8 through two-year and teacher-education colleges.

Ohio Journal of School Mathematics (http://www.ohioctm.org/ojsm01.htm) is the official journal of the Ohio Council of Teachers of Mathematics.

Primus (http://www.dean.usma.edu/math/pubs/primus/) is a rich forum for the exchange of ideas in mathematics education at the college level. The journal is a refereed quarterly devoted to dialog among those interested in teaching undergraduate mathematics.

Teaching Mathematics and its Applications (http://www3.oup.co.uk/teamat/) provides a forum for the exchange of ideas and experiences which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. A distinctive feature of the journal is its emphasis on the applications of mathematics and mathematical modeling within the context of mathematics education world-wide.

Educational Technology  Review (ETR)  originally a print journal, has been transformed into anonline publication to not only increase timeliness of content but also to enhance every issu with the current and future electronic resources and tools available on the AACE website.
 

2. Research journals for professional mathematicians.

Bulletin of the American Mathematical Society (http://www.ams.org/bull/): This journal is devoted to articles of the following types: Bulletin articles, which may be of two types: (1) papers that present a clear and insightful exposition of significant aspects of contemporary mathematical research, and (2) brief, timely reports on important mathematical developments, which are normally solicited and often written by a disinterested expert. Book Reviews are accepted for publication by invitation only. Unsolicited manuscripts will not be accepted.

Proceedings of the American Mathematical Society (http://www.ams.org/proc): This journal is devoted to shorter research articles (not to exceed 10 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Longer papers may be submitted to the Transactions of the American Mathematical Society.

Electronic Research Announcements (http://www.ams.org/era): This electronic-only journal publishes research announcements (up to about 10 journal pages) of significant advances in all branches of mathematics. A research announcement should be designed to communicate its contents to a broad mathematical audience and should meet high standards for clarity as well as mathematical content. Papers with complete proofs may be published in exceptional cases if the results are substantial enough to meet the criteria.

Journal of the American Mathematical Society (http://www.ams.org/jams): This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

Transactions of the American Mathematical Society (http://www.ams.org/tran): This journal is similar to the Proceedings, but accepts papers of greater length.

Canadian Journal of Mathematics (http://journals.cms.math.ca/CJM/)

Canadian Mathematical Bulletin (http://journals.cms.math.ca/CMS/CMB/)
 

3. Journals adopted for students of mathematics.

American Mathematical Monthly (http://www.maa.org/pubs/monthly.html) publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of Monthly readers.

The College Mathematics Journal (http://www.maa.org/pubs/cmj.html) emphasizes the first two years of the college curriculum. The journal contains a wealth of material for teachers and students. A wide range of topics will keep you current, stimulated, and entertained.

Communications in Visual Mathematics (http://www.maa.org/news/cvm.html) is the first electronic journal featuring articles that cannot be published in the traditional printed form.

Mathematics Magazine (http://www.maa.org/pubs/mathmag.html) presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. Mathematics Magazine is published five times per year.

Crux Mathematicorum (http://journals.cms.math.ca/CRUX/) is a solely electronic journal

4. Journals on the history of mathematics.

Historia Mathematica (http://www.chass.utoronto.ca/hm/) is the official journal of the International Commission on the History of Mathematics and publishes research articles in all areas of the history of mathematics; book reviews; and miscellaneous items of interest to historians of mathematics.

Isis (http://www.journals.uchicago.edu/Isis/home.html) has featured scholarly articles, research notes and commentary on the history of science, medicine, and technology, and their cultural influences.

Mathematical Connections (http://www.aug.edu/dvskel) seeks to provide a forum for exploring the interplay between mathematics and the humanities. Classroom applications of these topics, such as the use of history in the teaching of mathematics, also fall within scope of this periodical.

The Mathematical Intelligencer (http://link.springer.de/link/service/journals/00283/index.htm) publishes articles about mathematics, about mathematicians, and about the history and culture of mathematics.
 
 

III. Websides.

0. Sites containing general info and links

http://camel.math.ca. Camel is the official website of the Canadian Mathematical Society.

http://www.ams.org. Official webside of The Mathematical Association of America

http://www.maa.org. Official webside of American Math Society

http://www.ams.org/mathweb. Math on the Web

http://www.mathworld.wolfram.com . Mathworld is a comprehensive and interactive math encyclopedia intended for students, educators, and researchers. This side is constantly updated to include new material an incorporate new discoveries

http://www.nctm.org. Official website of the National Council of Teachers of Mathematics.

http://mathforum.org/math.topics.html. Math Forum at Drexel University. List of resources organized by topic.
 
 

1. Teaching of mathematics.

http://archives.math.utk.edu/materials.html. The goal of the Mathematics Archives is to provide organized Internet access to a wide variety of mathematical resources. The primary emphasis is on materials which are used in the teaching of mathematics. Currently the Archives is particularly strong in its collection of educational software. Other areas, ranging from laboratory notebooks and problem sets to lecture notes and reports on innovative methods, are growing. A second strength of the Archives is its extensive collection of links to other sites that are of interest to mathematicians. Resources available through these links include electronic journals, preprint services, grant information, and publishers of mathematical software, texts, and journals. These educational resources and the organized collection of links combine to make the Mathematics Archives a comprehensive site for mathematics on the Internet.

http://www.ericse.org/. Educational Resources Information Center (ERIC) comprises 16 clearinghouses that have created the world's largest bibliographic database of over one million records related to education.

http://www.prel.org Pacific Resources for Education and Learning (PREL) is an independent, nonprofit corporation that serves schools across the U.S. and its affiliates from Rhode Island to Palau. PREL seeks to bridge the gap between research, theory, and practice in education and works collaboratively with schools and school systems to provide services that range from curriculum development to assessment and evaluation.

http://www.math.uic.edu/MER/pages. The Mathematicians and Education Reform (MER) Forum seeks the effective participation of mathematicians in mathematics education reform at the K-12, undergraduate, and graduate levels, and the recognition of the importance of these efforts to the well-being of the mathematics community.

http://MTL.math.uiuc.edu. Math Teacher Link is a website designed to deliver professional development opportunities and classroom resources to teachers of mathematics, statistics, and related subjects at the high school and lower division college levels. This site includes course modules for teachers of mathematics, showing them how to integrate current electronic applications into the classroom.

http://www.bham.ac.uk/ctimath/talum/talum1.html. Teaching and Learning Undergraduate Mathematics (TaLUM) is a group that is widely representative of mathematical interests and experience in higher education. Groups work in areas of (i). learning, (ii) content of undergraduate mathematics, and (iii) difficulties at the school/university interface.

http://www.pkal.org/. Project Kaleidoscope (PKAL) is an informal national alliance of individuals, institutions, and organizations committed to strengthening undergraduate science, mathematics, engineering, and technology education.

http://www.comap.com/ COMAP, the Consortium for Mathematics and Its Applications, is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students and business people to create learning environments where mathematics is used to investigate and model real issues in our world. COMAP develops curriculum materials and teacher development programs that are multidisciplinary, academically rigorous, and fun for teachers to teach and students to learn. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems. Our products are developed in print, video, and multi-media formats.

http://www.maa.org/t_and_l/sampler/research_sampler.html. This site contains brief expositions of research on undergraduate mathematics education and is linked to a bibliography, a glossary, and a list of research questions.

http://problems.math.umr.edu/index.htm. Compilation of various mathematical problems.
 
 

2. Research in mathematics.

http://www.ams.org/mathscinet. MathSciNet is a comprehensive database covering the world's mathematical literature of the past 61 years, providing Web access to the signed reviews and bibliographic data from Mathematical Reviews and Current Mathematical Publications, an early awareness journal. MathSciNet provides links to original articles and other original documents and by encouraging links from journal article references to MathSciNet. Offers world-wide access via multiple mirror sites.

http://www.math.psu.edu/MathLists/Journals.html. Links to electronic and printed journals dedicated to mathematics.
 
 

3. History of mathematics.

http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html. Website dedicated to the history of mathematics. Organization of mathematical information by region and subject. Also includes a bibliography and chronological list of all mathematicians starting in 1700 B.C.E.

http://www-groups.dcs.st-andrews.ac.uk/~history/BiogIndex.html. Index of biographies of mathematicians throughout history. Organized alphabetically and by date and includes an index of female mathematicians.

http://www-groups.dcs.st-andrews.ac.uk/~history/. MacTutor History of Mathematics Archive contains historical mathematics organized by culture, topic, mathematician, etc.

http://it.stlawu.edu/~dmelvill/mesomath/erbiblio.html. An extensive bibliography of monographs, reviews, and journal articles that discuss ancient Mesopotamian mathematics.
 

4. Psychology

http://www.members.tripod.com/~IGPME/. International Group for the Psychology of Mathematics Education. Promotes international contacts and the exchange of scientific information in the psychology of mathematics education. Stimulate interdisciplinary research in the aforesaid area, with the cooperation of psychologists, mathematicians and teachers; further a deeper insight into the psychological aspects of teaching and learning mathematics and the implications thereof.

http://www.edc.org/LTT/GAMT/. Gateways to Advanced Mathematical Thinking is a project funded by the National Science Foundation. The goal of the project is to research the ways in which high school and college mathematics students come to acquire flexible understandings of essential concepts needed for analytic and algebraic thinking.
 

5. Distance education in mathematics.

http://www.utexas.edu/world/lecture. World Lecture Hall contains links to course materials for university-level courses.

http://www.educause.edu. Educause is a nonprofit association whose mission is to advance higher education by promoting the intelligent use of information technology. While it has some useful information, it appears to be more directed toward business professionals, information technologists, and administrators, rather than teachers and professors.
 
 

IV. Videos.

1. Teaching mathematics.

Let Us Teach Guessing George Pólya. (1966, 61 min.) In a remarkable tour de force, Pólya shows us how to teach guessing. In this classic film, master teacher Pólya leads an undergraduate class to discover the number of parts into which 3-space is divided by five arbitrary planes. (color, $36.95).

Mathematically Motivated Designs, Howard Eves

The Moore Method: A Documentary on R.L. Moore

The Teachers Workshop This 28-minute tape, accompanied by a 90-page transcript contains excerpts from a two-day workshop held in 1991 for teachers who had successfully used project materials in their classrooms. ($34.90 for video and workbook)

Pedagogical Peeves and Other Complaints of Age: Crazy Al, Still Teaching Calculus after All These Years - Al Novikoff - AMS, 1992, 60 minutes, $49.95

The Teaching of Calculus: Careful Changes - Gilbert Strang - AMS, 1992, 60 minutes, $49.95

How Computers Have Changed the Way I Teach - John G. Kemeny - AMS, 1988, 60 minutes, ISBN 0-8218-8019-5, List: $51.95
 

2. Topics in mathematics.

MAA Calculus Films in Video Format: 3 tape collection (1960s, 60 min. each)

Pits, Peaks, and Passes, Parts 1 and 2, Marston Morse

Polynomials

To Prove and Conjecture: Excerpts from Three Lectures by Paul Erdös (Problems and Results on Combinatorial Number Theory, Open Problems in Random Graphs and Combinatorics, and Sixty Years of Mathematics: My Favorite Problems in Number Theory, Analysis, Combinatorics, Geometry, and Set Theory) $39.95.

Similarity

Sines and Cosines, Parts 1, 2, and 3

The Story of Pi: Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles. Animated sequences dissect a circular disk of radius r and transform it to a rectangle of base ¹r and altitude r. Animation shows how Archimedes estimated p using perimeters of approximating polygons. (24 min, $34.90 for video and workbook).

Introduction to Geometric Probability, Gian-Carlo Rota (1999, 60 minutes, $54.95)

Fermat's Last Theorem, Barry Mazur (1995, 60 minutes, $54.95)

In Search of Symmetry, William Browder (1994, 90 minutes, $54.95)

Optimization of Extended Surfaces for Heat Transfer, J. Ernest Wilkins, Jr. (1994, 90 min, $54.95)

Fermat's Last Theorem-The Theorem and its Proof: An Exploration of Issues and Ideas, Will Hearst (1994, 90 min, )

Fermat's Last Theorem (Video and booklet set) Presented by the Mathematical Sciences Research Institute, Berkeley, CA; booklet edited by Robert Osserman. Washington: NCTM: 1993 (98 min.) Dynamic videotape and booklet on the most famous unsolved (until recently) problem in mathematics. Explores the issues and history of the theorem and its proof. Shows how new discoveries are made and how different parts of mathematics, such as geometry and algebra, are linked to each other and to areas outside mathematics, such as music. Includes 10-to-15-minute segments that can be viewed separately. Also shows excerpts from an interview with Andrew Wiles in Oxford, England, the day after he announced his proof.

Modular Elliptic Curves and Fermat's Last Theorem - Kenneth A. Ribet - AMS, 1993, 100 minutes, $49.95,

Some Mathematics of Baseball - Henry O. Pollak - AMS, 1993, 60 minutes, $54.95,

The Problem of Scale in Ecology - Simon Levin - AMS, 1993, 60 minutes, $54.95,

Compound Soap Bubbles, Shortest Networks, and Minimal Surfaces - Frank Morgan - AMS, 1992, 60 minutes, $49.95

Mathematics under Hardship Conditions in the Third World - Neal I. Koblitz - AMS, 1992, 60 minutes, ISBN 0-8218-8067-5, List $49.95,

The Mysteries of Space - Michael Atiyah, Trinity College - AMS, 1992, 60 minutes, ISBN 0-8218-8076-4, List: $49.95

A Century of Representation Theory of Finite Groups - Charles W. Curtis - AMS, 1991, 60 minutes, ISBN 0-8218-8038-1, List: $49.95,

Algebra as a Means of Understanding Mathematics - Saunders Mac Lane - AMS, 1991, 60 minutes, ISBN 0-8218-8057-8, List: $51.95,

Matrices I Have Met- Paul Halmos - AMS, 1986, 60 minutes, ISBN 0-8218-8017-9, List: $51.95

Hyperbolic Billiards - Yakov G. Sinai - AMS, 1991, 60 minutes, ISBN 0-8218-8054-3, List: $51

The Transition to Chaos: The Orbit Diagram and the Mandelbrot Set - Robert L. Devaney - AMS, 1990, 60 minutes, List: $56.95

Chaos, Fractals and Dynamics: Computer Experiments in Mathematics - Robert L. Devaney - AMS, 1989, 60 minutes, List: $56.95

The Beauty and Complexity of the Mandelbrot Set - John Hubbard - AMS, 1989, 60 minutes, List: $56.95
 
 

3. History of mathematics.

A Conversation with Paul Halmos

Courant in Göttingen and New York

Early History of Mathematics (2000, 30 min.) This program outlines some of the important developments in the early history of mathematics, from Babylonian calendars on clay tablets produced 5000 years ago to landmark events leading to the development of calculus in the 17th century. It describes number symbols developed in different cultures; how numerology gave birth to number theory; the Pythagorean Theorem; the multicultural search for estimating the number pi; how astronomy led to trigonometry; and efforts such as the creation of analytic geometry that accelerated the development of calculus. It presents computer-animated demonstrations of the Pythagorean Theorem, the irrationality of the square root of two (a new geometric proof), the formula for the area of a circular disk, and the method of Archimedes for estimating. A workbook/program guide to accompany this tape is also available (color, $34.90).

John von Neumann, a Biography

Journey Through Genius

N is a Number: A Portrait of Paul Erdos

The Theorem of Pythagoras

The Tunnel of Samos: This video describes a remarkable engineering work of ancient times: excavating a one-kilometer tunnel straight through the heart of a mountain, using separate crews that dug from the two ends and met in the middle. How did they determine the direction for excavation? The program gives Hero's explanation (circa 60 AD), using similar triangles, as well as alternate methods proposed in modern times. (30 minutes, $34.90 for video and workbook)

Celebrating 100 Years of Meetings: History and Reminiscences (1995, 2 hours, $54.95)

Descartes and Problem Solving - Judith Grabiner - AMS, 1992, 60 minutes, $49.95

Oscar Zariski and His Work - David Mumford - AMS, 1988, 60 minutes, ISBN 0-8218-8022-5, List: $51.95

Harish-Chandra and His Work - Rebecca Herb - AMS, 1991, 60 minutes, ISBN 0-8218-8061-6, List: $51.95

The Art of Renaissance Science: Galileo and Perspective - Joseph W. Dauben - 1991, 45 minutes, List: $54.95

Georg Cantor: The Battle for Transfinite Set Theory - Joseph W. Dauben - AMS, 1989, 60 minutes, ISBN 0-8218-8015-2, List: $51.95,
 
 

4. Related topics.

Careers in Mathematics (2001, $15)

Preparing for Careers in Mathematics, Annalisa Crannell et al. (1997, 30 minutes, $15)

Case Studies of Political Opinions Passed Off as Science and Mathematics - Serge Lang - AMS, 1991, 60 minutes, ISBN 0-8218-8037-3, List: $51.95

The Flowering of Applied Mathematics in America - Peter D. Lax - AMS, 1989, 60 minutes, ISBN 0-8218-8020-9, List: $51.95

European Mathematicians' Migration to America - Lipman Bers - AMS, 1988, 60 minutes, ISBN 0-8218-8013-6, List: $51.95

Donald Duck in MathMagic Land. (30 min.)
 
 

IV. Societies.

1. For professional mathematicians.

International Mathematical Union (IMU):
c/o Phillip A. Griffiths, Secretary
Institute for Advanced Study
Einstein Drive, Princeton, NJ
USA 08540
Fax: (609) 683-7605
Email: imu@ias.edu
http://www.mathunion.org/

American Mathematical Society (AMS):
201 Charles Street
Providence, RI 02904-2294
800-321-4AMS (US and Canada)
401-455-4000 worldwide
Fax: 401-331-3842
Email: ams@ams.org
http://www.ams.org/

Canadian Mathematical Society (CMS):
577 King Edward, Suite 109
POB 450, Station A
Ottawa, ON
Canada K1N 6N5
(613) 562-5702
Fax: (613) 565-1539
Email: office@cms.math.ca
http://www.cms.math.ca/

The Mathematical Association of America (MAA):
1529 Eighteenth Street, NW
Washington, DC 20036-1385
800-741-9415
202-387-5200
Fax: 202-265-2384
Email: maahq@maa.org
http://www.maa.org/

National Association of Mathematicians (NAM):
c/o Scott W. Williams, Editor of NAM Newsletter
Department of Mathematics
State University of New York
Buffalo, New York 14214
Email: bonvibre@adelphia.net
http://www.math.buffalo.edu/mad/NAM/NAM-index.html

Association for Women in Mathematics (AWM):
4114 Computer & Space Sciences Building
University of Maryland
College Park, MD 20742-2461
(301) 405-7892
Fax: (301) 314-9363
awm@math.umd.edu
http://www.awm-math.org/

Society for Industrial and Applied Mathematics (SIAM):
3600 University City
Science Center
Philadelphia, PA 19104-2688
800-447-SIAM (US and Canada)
215-382-9800
Fax: 215-386-7999
E-Mail: service@siam.org
http://www.siam.org/

Canadian Applied and Industrial Mathematics Society (CAIMS)
http://www:caims.ca
 

2. For educators and teachers of mathematics.

National Council for Teachers of Mathematics (NCTM):
1906 Association Drive
Reston, VA 20191-9988
(703) 620-9840
Fax: (703) 476-2970
Email: infocentral@nctm.org
http://www.nctm.org/
 
 

V. Conferences.

1. For mathematicians.

The following mathematical meetings have sections on math education and history of mathematics.

Quadrennial Internation Congress of Mathematicians
Beijing, China, Aug 2002
Madrid, Spain, 2006

Joint Mathematics Meetings: Coincident meetings of the AMS, ASL, AWM, MAA, NAM and SIAM.
San Diego 2002, January 6-9,
Baltimore 2003, January 15 - 18,
Phoenix 2004, January 7 - 10,
Atlanta 2005, January 5 - 8,
San Antonio 2006, January 12 - 15,
New Orleans 2007, January 4 - 7,

First Joint International Meeting between the American Mathematical Society (AMS) and the Real Sociedad Matematica Espanola (RSME) , June 18-21, 2003 Seville, Spain

The Joint AMS-India Mathematics Meeting For educators in mathematics.
December 17-20, 2003, Bangalore, India

CMS: Semiannual National Meetings
CMS Winter 2002 Meeting , December 8-10, 2002 , University of Ottawa
CMS Summer 2003 Meeting , June 14-16, 2003 , University of Alberta
CMS Winter 2003 Meeting , December 6-8, 2003, Simon Fraser University
CMS Summer 2004 Meeting , Dalhousie University
CMS Winter 2004 Meeting , McGill University

16th Triennial International Congress on Mathematical Physics (http://icmp2003.net/),
Lisbon, Portugal, July 2003

2. For math teachers and educators.

NCTM:
October 2002: Semiannual Section meetings, Regina, Saskatchewan
April 2002: Annual National Meetings, Las Vegas, CA

Canadian School Mathematics Forum 2003 , May 16-18, 2003 , Montréal

Annual Meetings of the International groups for Psychology of Math Education
July, 2002, Norwich, United Kingdom
July 13-18, 2003 Honolulu, Hawaii
July 15-18, 2004, Bergen, Norway
 

Publishing Companies

Elsevier Science
360 Park Avenue South
New York, NY 10010-1710
USA
Phone: (212) 633-3730
Fax: (212) 633-3680
http://www.elsevier.com
Elsevier publishes original research, bibliographic data, and review and reference information, in the forms of traditional research journals, newsletters, review journals, major reference works, magazines and abstract journals. Elsevier's divisions include Academic Press, Mosby, Saunders, and other publishers; their coverage of mathematics includes algebra and number theory, analysis, applied math, discrete math, geometry and topology, logic, general math, and numerical analysis.

McGraw-Hill Companies
PO Box 182605
Columbus, OH 43218-2605
Phone: (800) 262-4729 (Students)
Phone: (800) 338-3987 (Instructors)
Fax: (614) 759-3644
http://www.mhhe.com/catalogs/sem
McGraw-Hill publishes instructional materials targeted at the higher education market, including texts, lab manuals, study guides and testing materials, and software and multimedia products.

Pearson Custom Publishing
75 Arlington Street, Suite 300
Boston, MA 02116
Phone: (800) 428-4466
Fax: (617) 848-6333
http://www.pearsoncustom.com/
Pearson Education is one of the world's leading textbook publishers, combining Prentice-Hall, Allyn & Bacon/Longman and Addison Wesley/Benjamin Cummings. Prentice-Hall publishes books in developmental mathematics, technical mathematics, teaching mathematics, and textbooks for advanced mathematics courses.

Springer-Verlag New York, Inc.
175 Fifth Avenue
New York, NY 10010
Phone: (212) 460-1500
Fax: (212) 473-6272
http://www.springer-ny.com
Springer-Verlag is one of the most prestigious international scientific publishers today, with publications ranging from medicine to all fields of life sciences, and from mathematics to engineering. Springer publishes annually over 2,400 new books and approximately 500 journals, also available in electronic form. A total of about 19,000 books are currently available, 60 percent of them in English.

Wiley Publishers
111 River Street
Hoboken, NJ 07030
Phone: (201) 748-6000
Fax: (201) 748-6088
http://www.wiley.com
Wiley has approximately 22,700 active titles and about 400 journals, specializing in scientific, technical, and medical books and journals; professional and consumer books and subscription services; and textbooks and other educational materials for undergraduate and graduate students as well as lifelong learner

Oxford University Press
University of Oxford,
Wellington Square, Oxford OX1 2JD, UK
Telephone: +44 1865 270000,
Fax: +44 1865 270708
http://www.oup.com/
Publishes: Academic & Professional Books and Journals; Humanities, Social Sciences, Law, Science, Medicine, Journals, Music, Bibles; Oxford World's Classics ; Teaching and Learning; English Language Teaching, School and FE Textbooks, Children's Fiction and Poetry, Higher Education Textbooks, Dictionaries and Reference.
 

Teachers College Press
 1234 Amsterdam  Av.
New York, NY 10027
Phone: (212) 678-3929
Fax: (212) 678-4149
http://www.teacherscollegepress.com/