CULTURAL AND PHILOSOPHICAL BACKGROUND OF MATHEMATICS
MATH 602.330 Shanghai cohort section (see Class Photo)

Summer 2009

professor: Dr. Lawrence Shirley
phone: +1-410-704-3500 in U.S. (Shanghai hotel office phone: +86-21-63522000)
fax: +1-410-704-3434 in U.S.
e-mail: lawrencehshirley@gmail.com  [or LShirley@towson.edu  this may not work]
personal web-page: http://pages.towson.edu/shirley
consultation hours: immediately before or after class (in the classroom) or by appointment
class meetings:  Mondays, Tuesdays, Thursdays, Fridays, (12:20 - 3:10 pm) July 27 - August 14 (exam due August 26)
at Xuhui District Teachers Institute of Continuing Education (room 305), 800 Zhongshan Road, South-2, Shanghai (Map)
program director: Dr Wei Sun [wsunmd2002@yahoo.com]; program: M.S. in Mathematics Education
incoming mathematics education program director: Dr Maureen Yarnevich [myarnevich@towson.edu]
Towson China program coordinator: Dr Lijun Jin [ljin@towson.edu]

Catalog Course description:  Meanings and origins of mathematics and fundamental mathematical concepts, schools of philosophical thought on mathematics, cultural basis of mathematics, ethnomathematics, mathematics in the real world, philosophy and purpose of mathematics education, current issues in the direction of mathematics and mathematics education, role of the mathematics teacher in current debates. Prerequisite: Admission to Master's in Mathematics Education program. (G) (3 units)

A full (hard-copy) syllabus and a bibliography is distributed in class.  This webpage partially duplicates and supplements the syllabus and bibliography, and, in addition, includes relevant links .

Scroll down or jump immediately to:
Objectives, Texts, Topic Outline, Assignments, Final Exam,  Bibliography, Class Regulations, Links, Roster/Seating Chart,  Class Photo, and Contacts .

COURSE OBJECTIVES / LEARNING OUTCOMES

Students in this course should:

1. gain greater insight into the philosophical and logical foundations underlying the fields of mathematics and mathematics education.

2. recognize sources of mathematics from cultures and human activity

3. become familiar with aspects of the culture of mathematics

4. fit current issues of mathematics and mathematics education into the structures of logical foundations, philosophies, and cultures.

5. gain competence to discuss and deal with issues of mathematics and mathematics education.

6. recognize the important role of mathematics teachers in discussions of curriculum, instruction, and assessment issues of mathematics education.

TEXTS

Required (links go to the listing in Amazon.com; or for comparison shopping, try Campus Books4Less)

---(portions to be supplied) Ascher, Marcia (1991) Ethnomathematics: a multicultural view of mathematical ideas, Wadsworth. ISBN 0-412-98941-7 

ASSIGNMENTS (approximate percentage weightings for grading are given)

1. Read assigned chapters and other readings and be ready for discussion and questions (10%)  (participation in discussion will be taken into account)

2. Write between one and two pages (200-400 words), describing where you see Platonic and formalist philosophies of mathematics being applied in school mathematics curricula and/or instructional practices (especially in your own school). Due July 31.(20%)

3. Prepare a presentation of about 10-20 minutes on the mathematics of some area of your own cultural heritage and/or your non-professional life. "Cultural heritage" may be defined very broadly: race, ethnicity, religion, geography of hometown, family customs, social class, hobbies, life experiences. The presentation should explain how the topic fits your personal culture, give information on the topic's details, and show some mathematics related to the topic.  Include any appropriate visuals, handouts, activities, etc.  August 10 and 11.
Schedule of Presentations
Monday, August 10
---Games/Activity
    Badminton:Lucy
    Minesweeper game: Shelley
    Movement: Jane
---Science
    Environmental Protection: Sean
    Pandas, other animals: Sunlight
    Calendar: John
    Stones to Cobblestones:Tony 2
Tuesday, August 11
---Daily Life
    Driving: David
    House Purchase: LiDa
    Shopping: Rachel
---Arts/Culture
    Literature: Star
    Painting: Tony 1
    Music: Amy
    Temple of Heaven: Mary

Also write up a five-to-eight page (roughly 1250-2000 words) summary of the presentation, including materials and references. The paper is due via email September 14 (30% for presentation and paper)

4. Write a one-to-two page essay (200-400 words) on how you could show a global perspective in a mathematics class at the level where you teach by using global and multicultural content in class. Note: The content of this paper is based on the class discussion and activities of August 7 and relates to  "Mathematics in Global Education Programs"  Also, check the related links.  Due August 14 (20%)


FINAL EXAM

A take-home final exam (English and Mandarin versions) will be distributed by email attachment on August 16.  It is due by Wednesday, August 26, at 8 pm (Shanghai time).  It may involve additional research in the library and/or the Web. (20%) It can be submitted by fax (+1-410-704-3434) or as e-mail ( lawrencehshirley@gmail.com) (email preferred)

CLASS REGULATIONS AND EXPECTATIONS

--Attendance is expected at all classes and assignments are due on the date announced. Potential absences or late submissions need to be discussed with the instructor ahead of time and unexpected absences need documentation..  Infringements may result in loss of credit.
--Plagiarism is, of course, not acceptable. Any use of the material of others must be documented, including Web-based material. Documentation does not sanction direct copying of text or ideas except in indicated quotations.  See the University policy statement.  Any academic dishonesty will normally result in a grade of zero for that work and may result in greater sanctions.
--Grading will be based on quality of written work and participation in class, weighted as indicated above.  Grades are A (90), B (80), C (70), and F(fail).
--Any student who needs an accommodation due to a disability should make an appointment to discuss the accommodation.

LINKS

MATHEMATICS CONTENT AND HISTORY (especially relevant to philosophy)

--Notes on the history of mathematics from the webpage of the MATH 301 History of Mathematics course; also with many history-related links.
--Biographies of historical Western mathematicians (nearly 1800 names!) and other topics
----including Pythagoras, Aristotle, Plato, Euclid, Ptolemy, Descartes, Newton, Leibniz, Bolyai, Lobachevsky, C. Peirce, Poincaré, Cantor, Frege, Russell, Hilbert, Gödel, Pólya, Lakatos, Erdös and hundreds more!
--links to topics of the history of Chinese mathematics
--Biographies of historical Chinese mathematicians (nearly 50 names)
----including Liu Hui, Jia Xian, Yang Hui, Zhu Shijie (Chu Shi Chieh), Zu Chongzhi (Tsu Chung Chi); more recent: Wen-Tsun Wu, Sun-Yung Alice Chang, Fan Chung Graham, Shing-Tung Yau
--Analysis of a Chinese astronomy map from the early Tang dynasty (7th century)--the oldest known star map
--Euclid's Elements, complete with dynamic linking cross-references
--Non-Euclidean geometry
--Hilbert's 23 problems and their disposition; and another similar list; and another list, with more references.
-- Gödel's Proof
--The Clay Mathematics Institute offers $1 million prizes for the solution of each of the seven currently unsolved "Millennium Problems"
--MathWorld--a great site to look up math content and terminology
--current mathematics news: MathWorld Headline News
--Philosopher Immanuel Kant
--Piaget's educational theory
--Reuben Hersh: his own webpage, in Wikipedia

ETHNOMATHEMATICS, MATHEMATICS OF OTHER CULTURES, GLOBAL RESOURCES

--International Study Group on Ethnomathematics (North American Study Group on Ethnomathematics)
----ethnomathematics links
----syllabi of ethnomathematics courses elsewhere
--For future reference: the Fourth International Conference on Ethnomathematics (in Towson, 25-30 July 2010)
--counting to ten in more than 5000 languages
--play oware on-line (slightly different rules than those used in class)
--References to mu torere: description, more technical, a computer program in BASIC
--information on Marcia Ascher
--references on the mathematics of Islam and more Islamic math. Here is a conversion to the Islamic calendar. This is a more technical, scientific explanation of the Islamic lunar calendar.
--Jewish calendar; conversions
--information on the Chinese calendar and more Chinese calendar details; conversions
--School of the Seasons: information on traditional calendar, mostly Europe, especially Celtic
 --outline of a conference presentation on ethnomathematics
--a paper on "Mathematics in Global Education Programs" from ICEM-3 (full text and references)
--the International Studies Schools Association
--"Teaching Statistics with Social Justice"--a good argument with good resources
--Peace Corps,  National Peace Corps Association (the organization of returned Peace Corps Volunteers)
-----Global TeachNet (assistance for international education)  World Wise Schools (connecting with a Peace Corps Volunteer)
--data and statistics from The World Bank, the US Census Bureau, the Population Reference Bureau, and the United Nations
--UN Millennium Goals (eight development goals for 2015)
--WorldMapper--world maps with country areas proportional to measures of interest.
--A talk using amazing graphics to break myths about the developing world (a 20-minute video) (from TED.com); more at gapminder.org
--A data processing lesson for Statistics: reading a table or chart from WorldView, Special Issue on HIV/AIDS,18, 2, May 2005
--RadicalMath looks at blending mathematics content and issues of social justice. Similarly, the Algebra Project considers algebra and the opportunity to learn mathematics as civil rights.  Rethinking Schools--a nonprofit educational publisher on school reform (including mathematics), with a focus on issues of equity and social justice
--the life and work of Paolo Freire, Brazilian philosopher and educator
--Not as course reading, but for general awareness, I highly recommend Thomas Friedman's 2005 book The World is Flat. (revised in 2006; third edition may now be available)

MATHEMATICS EDUCATION: ORGANIZATIONS AND "MATH WARS"

--an outline of the history of mathematics education in the 20th century
--International Congress of Mathematical Education (ICME-11) was in Mexico, July, 2008; ICME-12 will be in Seoul, Korea, July 8-15, 2012.
--National Council of Teachers of Mathematics
-----Principles and Standards of School Mathematics on-line
--The Math Forum @ Drexel (issues, resources, problems, etc.)
--The Mathematics Curriculum Center of the Educational Development Center
--The Eisenhower National Clearinghouse: info on curriculum development and implementation (a subscription site)
--Mathematically Correct
--Mathematically Sane
--an MAA group trying to settle disagreements by finding common ground
--Math is More A group looking for a coordinated effort to improve mathematics education nation-wide.
--Report of the National Mathematics Advisory Panel, March 2008 [press release]

OTHER CULTURE OF MATHEMATICS

--conference presentation on numbers (with interesting links)
--BIG numbers by counting pennies (Also, follow the links at the end for terminology and more sense of BIG numbers)
--a suggestion for names for big numbers
--a great index of terms for sizes, units, time, numbers, etc.
--primes, Mersenne primes, and perfect numbers (general information); updates on the search for more; and how YOU can join the search)
--repunits (1,11,111,1111, etc.)
--dollar words and gematria calculations
-- minimal surfaces (with average curvature of zero); Costa surface
--Virtual Math Museum
--four-dimensional hypercube (tesseract) in 3-D (note: If you have red-blue 3-D glasses, you can use them. Otherwise, press the"stereo" button twice to get a double image. Then cross your eyes to produce a third image between the two. Watch that one. The page also has some instructions and other "cool" images below the tesseract. Enjoy!)
--Klein bottle pictures and for sale
-- fractals, and fractint, which is software for playing with fractal images.
--hexaflexagons and more hexaflexagons
--mathematical origami; Lang=a leading origamist; more origami links and some origami basics
--Play tic-tac-toe in 3-D (4x4x4) or 4-D (3x3x3x3)
--information and links about the game of Hex.  Here you can play it.
--a page on Nine Men's Morris. Here you can play it.
--lo shu (magic squares): for educational use and more; more technical details (with many links)
--some classic math jokes, and more good math jokes
--more broadly, here is a page of mathematical fiction.
-- Martin Gardner's collected columns (available on CD-ROM)

As I find more interesting links, I'll put them up. See also my personal home page mathematics links.
If you find good webpages related to any aspect of this course, let me know.

CONTACTS
If you have questions or comments, send e-mail to Dr. Shirley

You are also invited to visit Dr. Shirley's homepage, where you will find his biography with related links, his phone and other contacts, and a collection of other interesting links (including some other links on mathematics, mathematics culture, and mathematics education).

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but, contrary to the premise of this course....here's a quote from the French mathematician Henri Lebesgue (1875 - 1941):

"In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy--an opinion, moreover, which has been expressed by many philosophers."  quoted in Scientific American 211 (September 1964)
:-)  

also--

"A good mathematical joke is better, and better mathematics, than a dozen mediocre papers."
John Littlewood (1885-1977) A Mathematician's Miscellany, 1953
:-)

This webpage was last updated on 24 August 2009

All links checked on 4 June 2009 (if you find a bad link, please inform Dr. Shirley)

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BIBLIOGRAPHY [required course texts are in bold]

African Americans in Science, Mathematics, Medicine, and Invention (1993), Peoples Publishing.

Ascher, Marcia (1991) Ethnomathematics: a Multicultural View of Mathematical Ideas, Brook-Cole Publishing Company.

Ascher, Marcia (2002) Mathematics Elsewhere: An Exploration of Ideas across Cultures, Princeton University Press.

Atkins, Peter (2003) Galileo's Finger: The Ten Great Ideas of Science, Oxford: Oxford University Press

Barrow, John D. (1992) Pi in the Sky: Counting, Thinking, and Being, Clarenden Press, Oxford.

Bazin, Maurice, Tamez, Modesto, and the Exploratorium Teacher Institute (2002) Math and Science Across Cultures: Activities and Investigations from the Exploratorium, The New Press (Norton).

Bishop, Alan (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics Education, Kluwer.

DAmbrosio, Ubiratan (1992, English translation by Patrick B. Scott, 1998) Ethnomathematics: The Art or Technique of Explaining and Knowing, International Study Group on Ethnomathematics.

Davis, Philip (2006) Mathematics and Common Sense: A Case of Creative Tension, A.K. Peters.

Davis, Philip, and Hersh, Reuben (1981) The Mathematical Experience, Birkhauser. [recommended text]

Dehaene, Stanislas (1997) The Number Sense, Oxford University Press.

Devlin, Keith (2002) The Millennium Problems, Basic Books.

Eglash, Ron (1999) African Fractals: Modern Computing and Indigenous Design, Rutgers University Press.

Ernest, Paul (1991) The Philosophy of Mathematics Education, Falmer Press.

_____(editor) (1994) Mathematics, Education, and Philosophy: An International Perspective, Falmer Press.

Everybody Counts (1989) National Academy Press (for National Research Council).

Fadiman, Clifton (1957, 1997) Fantasia Mathematica, Springer-Verlang.

_____ (1962, 1997) The Mathematical Magpie, Springer-Verlang.

Frankenstein, Marilyn (1994) "Critical Mathematics Education: Bringing multiculturalism to the mathematics classroom" in M.M. Atwater, K. Radzick-March, & M. Strutchens (eds) Multicultural Education: Inclusion of All, The University of Georgia.

Friedman, Thomas L. (2005) The World is Flat: A Brief History of the Twenty-First Century, Farrar, Straus and Giroux.

Freudenthal, Hans (1973) Mathematics as an Educational Task, D. Reidel Publishing Company.

_____ (1978) Weeding and Sowing: Preface to a Science of Mathematical Education, D Reidel Publishing Company.

Gardner, Martin  many articles and books on recreational (but substantive!) mathematics; now his monthly columns are collected in (2005)Martin Gardners Mathematical Games: The Entire Collection of his Scientific American Columns (CD format), Mathematical Association of America.

Gay, John and Cole, Michael (1967) The New Mathematics and an Old Culture (A Study of Learning among the Kpelle of Liberia) Holt, Rinehart and Winston.

Gold, Bonnie and Simons, Roger (editors) (2008) Proofs and Other Dilemma: Mathematics and Philosophy, Mathematical Association of America.

Gowers, Timothy (editor) (2008) The Princeton Companion to Mathematics, Princeton University Press

Gutstein, Eric and Peterson, Bob (editors) (2005) Rethinking Mathematics: Teaching Social Justice by the Numbers, Rethinking Schools, Ltd.

Hersh, Reuben (1997) What is Mathematics, Really? Oxford University Press. (selected pages as handout)

Hofstadter, Douglas (1979) Gödel, Escher, Bach: An Eternal Golden Braid, Vintage Books.

Ifrah, Georges (1994) The Universal History of Numbers, Wiley.

Irons, C., Burnett, J., & Hoo Foon, S.W. (1993) Mathematics from Many Cultures, Mimosa Publications.

Kaplan, Robert (1999) The Nothing that Is: A Natural History of Zero, Oxford University Press.

Kasner, Edward, and Newman, James (1940) Mathematics and the Imagination, Penguin Books.

Kline, Morris (1953) Mathematics and Western Culture, Oxford University Press.

_____ (1962) Mathematics: A Cultural Approach, Addison-Wesley.

Kuhn, Thomas (1962) The Structure of Scientific Revolutions, University of Chicago Press.

Lakatos, Imre (1976) Proofs and Refutations, Cambridge University Press.

Lerman, Stephen (editor) (1994) Cultural Perspectives on Mathematics Classrooms, Kluwer.

Livio, Mario (2002) The Golden Ratio: The Story of Phi, the Worlds Most Astonishing Number, Random House.

Mazur, Barry (2003) Imagining Numbers (particularly the square root of minus fifteen), New York: Farrar Straus Giroux

Multiculturalism in Mathematics, Science and Technology: Readings and Activities (1993) Addison-Wesley.

National Council of Teachers of Mathematics (1989) Curriculum and Evaluation Standards for School Mathematics, NCTM

_____ (1990) Teaching and Learning Mathematics (1990 Yearbook), NCTM.

_____ (1991) Professional Standards for Teaching Mathematics, NCTM.

_____ (1995) Assessment Standards for School Mathematics, NCTM.

_____ (1995) Connecting Mathematics Throughout the Curriculum (1995 Yearbook), NCTM.

_____ (1997) Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (1997 Yearbook), NCTM.

_____ (2000) Learning Mathematics for a New Century (2000 Yearbook), NCTM.

_____ (2000) Principals and Standards for School Mathematics, NCTM.
[recommended text](full text is available to members only--on-line at http://standards.nctm.org )

______(2006) Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics NCTM.

Nelson, D., Joseph, G.G., Williams, J. (1993) Multicultural Mathematics, Oxford University Press.

Newman, James (editor) (1956) The World of Mathematics (4 volumes), Simon & Schuster.

Omnès, Roland (2005) Converging Realities: Toward a Common Philosophy of Physics and Mathematics, Princeton University Press.

Papert, Seymor (1980) Mindstorms: Children, Computers and Powerful Ideas, Basic Books.

Paulos, J.A. (1988) Innumeracy: Mathematical Illiteracy and its Consequences, Vintage Books.

Pickover, Clifford (2005) A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality, Wiley.

Pólya, George (1945) How to Solve It, Princeton University Press.

_____ (1962) Mathematical Discovery (two volumes), John Wiley & Sons.

Powell, Arthur, and Frankenstein, Marilyn (eds) (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education, State University of New York Press.[recommended text]

Shirley, Lawrence (1995) "Using Ethnomathematics to Help Find Multicultural Mathematical Connections" in National Council of Teachers of Mathematics (1995) Connecting Mathematics Across the Curriculum (1995 Yearbook), NCTM. (handout)

_____ (2000) "Twentieth Century Mathematics: A Brief Review of the Century" Mathematics Teaching in the Middle School, 5,5 (January 2000), 278-285.

_____ (2001) "Ethnomathematics as a Fundamental of Instructional Methodology" Zentralblatt fr Didaktik der MathematikInternational Reviews on Mathematical Education, issue 2001/3 (handout to be distributed).

_____ (2006) "Ethnomathematics in Global Education Programs" Third International Conference on Ethnomathematics, Auckland, New Zealand (proceedings forthcoming)(also http://www.towson.edu/~shirley/global.htm  )

Singh, Simon (1997) Fermats Enigma, Walker and Company.

Sriraman, Bharath (editor) (2007)  International Perspectives on Social Justice in Mathematics Education, Information Age Publishing

Steen, Lynn Arthur (editor) (1992) On the Shoulders of Giants: New Approaches to Numeracy, National Academy Press (for National Research Council).

_____ (editor) (1997) Why Numbers Count: Quantitative Literacy for Tomorrows America, The College Board.

Stewart, Ian (1975, 1995) Concepts of Modern Mathematics, Penguin Books (reissued by Dover).

_____ (1996) From Here to Infinity, Oxford University Press,

Taylor, Alan D. Social Choice and the Mathematics of Manipulation, Mathematical Association of America.

Tobias, Sheila (1978, 1993) Overcoming Math Anxiety, W.W. Norton & Company.

Tymoczko, Thomas (editor) (1998) New Directions i the Philosophy of Mathematics, Princeton University Press.

Wilder, Raymond L. (1965) The Foundations of Mathematics, John Wiley & Sons.

Zaslavsky, Claudia (1973, 1999) Africa Counts: Number and Pattern in African Culture, Lawrence Hill Books.

_____ (1996) The Multicultural Mathematics Classroom, Heinemann.

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MATH 602.330 Summer 2009
Roster
Cao Hua Song--Sean
Ji Wei--David
Lu Haiyan--Lucy
Peng Benxin--Star
Tang Lin--Tony 1
Tang Xuechuan--Tony 2
Xiao Jun--Jane
Xie Xiaoli--LiDa
Yang Guang--Sunlight
Yu Qiang--John
Zhang Yu--Amy
Zhao Yumei--Mary
Zhou Ke--Rachel
Zhou Xiaolei--Shelley

seating chart

Rachel	Tony 1	Tony 2	Star	Sean	Sunlight
Mary (Camilla)	John	David	Amy	Shelley	Lida
	Lucy	Jane
					Louise
		Xue Li Ren

class photo (xie xie, Lida!):
front row: Louise (TA), Lida, Shelley, Amy, Mary
second row: Rachel, Lucy, Dr Shirley (Xue Li Ren), Jane, Sunlight
third row: Sean(standing), Star, John, Tony 2, Tony 1 (standing), David