---Hersh, Reuben (1997) What is Mathematics, Really?  Oxford University Press.  ISBN 0-19-511368-3

---Powell, Arthur and Frankenstein, Marilyn (editors) (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education, State University of New York Press  ISBN 0-7914-3352-8

----also, handouts are distributed and references are made to Links below.

Recommended:

---Davis, Philip, and Hersh, Reuben (1981) The Mathematical Experience, Birkhauser. ISBN 0-395-92968-7
---National Council of Teachers of Mathematics (2000) Principles and Standards of School Mathematics, NCTM [available on-line to NCTM members] ISBN 0-87353-480-8

----Also, students should consult  links given below and books from the bibliography (paper copy distributed in class) as necessary

BIBLIOGRAPHY (click here)

TOPIC OUTLINE
(subject to possible changes--including weather- or flu-related--which will be announced)

date	general topic [Due dates for assignments are noted in  brackets; assignments are described below] (also see related Links below)	reading (to be completed before class) the code for the texts is: RH=Hersh MA=Ascher P&F=Powell & Frankenstein NCTM=Principles and Standards)	math culture topic   (see related Links below)
September 2	REGISTRATION; course organization; "pre-test" and demographics; Essential Dispositions for Educators	RH: Preface; "Dialogue with Laura"	history of mathematics review  history links
Monday, September 7, Labor Day
September 9 @YR 218a, TU campus map	early ideas of philosophy of mathematics,          to c. 1800	RH 6,7 history/philosophy links	favorite, special numbers  number links
September 16	crises in philosophy of mathematics: non-Euclidean geometry, set paradoxes, Gödel; responses	RH 8,9 history/philosophy links	nominal numbers, gematria  number links
September 23	developing a philosophy of mathematics  ["Platonic/formalist ideas in school math" due]	RH 2-5	mathematical objects  objects links
September 30	humanist/socio-cultural philosophy of mathematics	RH 1, 10-13	folding paper  links for origami and hexaflexagons
October 7	ethnomathematics: ethnic mathematics	MA Intro, 1,3,4; P&F 11,15 ethnomathematics links	games I  games I links
October 14	ethnomathematics: other cultures	MA 2,5,6,7; P&F (9?),10	networks
Friday, October 16 Maryland Council of Teachers of Mathematics Annual Meeting, Northwest High School in Germantown, MD
October 21	ethnomathematics political issues: diversity, equity, global education	P&F 7,13,14,18 socio-political links	games II  games II links
Monday, October 26   Graduate Lecture Series: “Me the Media” by Eric van Ommeren ------reception at 6:30, talk at 7:00; Potomac Lounge, University Union on the TU campus
October 28	individual presentations:   "Mathematics in MY OWN Culture" Sports, physical activity Barnaba, Elizabeth--FOOTBALL Davis, Dave--ARCHERY Westervelt, Sarah--RUNNING Technology Meagher, Debra--EARLY COMPUTERS Moore, Christine--AN ENGINEERING FAMILY Religion and Heritage Lee, Spring--BIBLICAL NUMEROLOGY Neuman, Suzanne--GERMANY	P&F 1,12,16,17
Friday, October 31 Halloween!  (Boo!)  (actually, this is related to the math culture topic for December 2)
November 4	individual presentations:   "Mathematics in MY OWN Culture" Home Life Obenschain, Andrea-ARMY LIFE Schrengost, Barry--BABY CARE Six, Tracie--HOLIDAY COOKING Spilman, Stefanie--HEALTHY LIVING Games Bradley, Joshua--GAMBLING Rohner, Cybil--PINOCHLE Tabor, Pamela--ROOK [global essay due]	"Lockhart's Lament" and follow-up
November 11	individual presentations:   "Mathematics in MY OWN Culture" Music Baublitz, Tiffany--ELEMENTARY MUSIC Campbell, Kathryn--ROCK and other music Crafts and Design Craig, Elizabeth--CROCHET Fager, Amanda--POTTERY Gregory, Stephanie--SCRAPBOOKING Viton, Diana--LANDSCAPING ----- Neuman, Suzanne--GERMANY (more)
Nov 13-14	Mathematical Association of American, MD/DC/VA Section Fall meeting, Goucher College, Towson
Nov 16-20	International Education Week (fits in with the "Global" memo assignment)
November 18	philosophy of mathematics education [Math in MY Culture write-up due]	NCTM-PSSM: Chap 2 "Principles"; review RH 2,13(criteria for philosophy)	magic squares (lo shu)  magic square links
November 25	no class, Thanksgiving holiday
December 2, 2009 Kislev 15, 5770 DhulOi'dah 15, 1430 (younger-earth 0x-4707-10-16)	applying philosophy: issues in mathematics education     [philosophy essay due]	NCTM-PSSM: Chap 2 "Principles" "Math Wars" handout via e-mail links to organizations and issues	calendars  calendar links
December 9 @ room 102, Southampton MS	review distribute  take home final exam   due Wednesday, December 16, 5 pm		jokes!  links to math jokes & literary math

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 (200-500 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 September 23.(15%)

3. Prepare a presentation of about 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.  October 28, November 4, or November 11 (specific dates shown below).

Also write up a five-to-eight page (roughly 1250-2000 words) summary of the presentation, including materials and references. The written paper is due November 18 (25% for presentation and paper)

Math in MY OWN Culture: topic selections and presentation dates
Section 241 (Harford County Cohort)
Barnaba, Elizabeth-- FOOTBALL--Oct 28
Baublitz, Tiffany--     ELEMENTARY MUSIC--Nov 11
Bradley, Joshua---     GAMBLING--Nov 4
Campbell, Kathryn--  ROCK and other music--Nov 11
Craig, Elizabeth        CROCHET--Nov 11
Davis, Dave--             ARCHERY--Oct 28
Fager, Amanda---      POTTERY--Nov 11
Gregory, Stephanie-- SCRAPBOOKING--Nov 11
Meagher, Debra--      EARLY COMPUTERS--Oct 28
Moore, Christine        AN ENGINEERING FAMILY--Oct 28
Obenschain, Andrea-ARMY LIFE--Nov 4
Rohner, Cybil            PINOCHLE--Nov 4
Schrengost, Barry-     BABY CARE--Nov 4
Six, Tracie                HOLIDAY COOKING--Nov 4
Spilman, Stefanie---  HEALTHY LIVING--Nov 4
Tabor, Pamela--        THE GAME OF "ROOK"--Nov 4
Westervelt, Sarah--    RUNNING--Oct 28

Section 242 (non-cohort)
Lee, Spring               BIBLICAL NUMEROLOGY--Oct 28
Neuman, Suzanne    GERMANY--Oct 28 & Nov 11
Viton, Diana              LANDSCAPING--Nov 11

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 21 and relates to  "Mathematics in Global Education Programs"  Also, check the related links.  Due November 4 (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 18 class.  Maybe some of these mathematics education links will assist you.  Due December 2 (15%)

FINAL EXAM

A take-home final exam will be distributed at the class meeting on December 9 and by email attachment on December 11.  It is due by Wednesday, December 16, 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.
--H1N1 note: Students should not attend classes or other university events from the onset of flu-like symptoms until at least 24 hours after the fever subsides without the use of fever reducing medications. Such absences will be considered excused absences; however, students are responsible for the material covered during the period of their absence.

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" (one has now been solved)
--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
----the Fourth International Conference on Ethnomathematics (in Towson, July 25-30, 2010)
--counting to ten in more than 5000 languages
--play oware/mancala 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
--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 (2010 Annual Meeting in San Diego, California)
-----Principles and Standards of School Mathematics on-line
--Maryland Council of Teachers of Mathematics  (Annual Meeting, October 16, 2009, Northwestern HS, Germantown)
--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 (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.
--mathematical origami; Lang=a leading origamist; more origami links and some origami basics
--hexaflexagons and more hexaflexagons
--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 (lo shu): 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.

NCATE REFERENCES

As part of the accreditation requirements of Towson University's Teacher Education program, 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 personal homepage, where you will find his biography with many 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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[ Top ]

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
:-)