4. Write a one-to-two page essay (200-500 words) on the values of incorporating a global perspective into mathematics classes at the level where you teach. Organize the essay as though it were a memo to your principal or department head, urging greater global and multicultural content in classes--especially mathematics (with justification and suggestions) Note: The content of this paper is based on the class discussion and activities of October 22 and relates to  "Mathematics in Global Education Programs"  Also, check the related links.  Due November 5 (15%)

5. Write a one-to-two page essay (200-500 words) on your own philosophy of mathematics education and teaching, reflecting our review of philosophies of mathematics and mathematics education and their implementation. This should grow out of the discussion of the November 19 class.  Maybe some of these mathematics education links will assist you.  Due December 3 (15%)

FINAL EXAM

A take-home final exam will be distributed at the class meeting on December 10 and by email attachment on December 11.  It is due by Wednesday, December 17, at 5 pm.  It may involve additional research in the library and/or the Web. (20%) It can be submitted by fax (410-704-3434) or as e-mail ( LShirley@towson.edu) or in hard-copy to 218-E in 7800 York Road (postal: Lawrence Shirley, College of Graduate Studies and Research, Towson University, 8000 York Road, Towson MD 21252-0001).

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
--Any student who needs an accommodation due to a disability should make an appointment to discuss the accommodation.  A memo from Disability Support Services authorizing the accommodation is required.

LINKS

MATHEMATICS CONTENT AND HISTORY (especially relevant to philosophy)

-- Notes on the history of mathematics from the webpage of the MATH 301 course; also with many history-related links.
--Biographies of historical 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!
--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

ETHNOMATHEMATICS, MATHEMATICS OF OTHER CULTURES, GLOBAL RESOURCES

--International Study Group on Ethnomathematics
----ethnomathematics links
----syllabi of ethnomathematics courses elsewhere
--For future reference: the Fourth International Conference on Ethnomathematics (in Towson, late 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
--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
--HIV/AIDS data in a data-processing lesson Lesson Plans for WorldView Magazine, 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 (2009 Annual Meeting in Washington DC)
-----Principles and Standards of School Mathematics on-line
--Maryland Council of Teachers of Mathematics  (Annual Meeting, October 17, 2008)
--Maryland State Department of Education
--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 (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.
--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.
--The film "Proof" (with Gwyneth Paltrow and Anthony Hopkins) shows some of the back-side of mathematics.
-- 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.

NCATE REFERENCES

As Towson University's Teacher Education program faces renewal of its accreditation, the following items demonstrate compliance with various standards of the National Council for Accreditation of Teacher Education (NCATE)

--Essential Dispositions for Educators--Advanced Programs: The Dispositions are introduced in the first class meeting and students do a self-evaluation.
--Assessment literacy components: Assessment issues are included in the discussion of mathematics education issues.
--Signature assessments: Pre-test, three short papers, one oral presentation with paper, final exam
--Reference to standards: National Council of Teachers of Mathematics: Principles and Standards of School Mathematics(2000), Chapter 2 (used as assigned reading); and Professional Standards for Teaching Mathematics (1991) "Standards for the Professional Development of Teachers of Mathematics" Standard 2 (bullets 4, 7, 8) and "Standards for the Support and Development of Mathematics Teachers and Teaching"  Standard 2 (generally)
--Reference to Voluntary State Curriculum and Maryland Core Learning Goals:   This course for experienced teachers does not cover PK-12 content as described in the VSC or Core Learning Goals, but the philosophical and cultural background of mathematics should help the teachers see mathematics from a deeper and more sophisticated point of view, thus broadening and strengthening their ability to cover all mathematical topics.  
--Towson University's Conceptual Framework for Professional Education: MATH 602 fits into the Mission to "inspire, educate and prepare facilitators of active learning for diverse and inclusive communities of learner in environments that are technologically advanced" by satisfying several of integrated themes of the Vision: The reflective view of the philosophy of mathematics helps ensure academic mastery; the review of ethnomathematics helps prepare educators for diverse and inclusive classrooms; applying philosophy helps develop professional conscience and provide leadership through scholarly endeavors.
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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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