---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 here and/or by email; note that the weather-related cancellation of the February 8 class has pushed all classes back by one week--which is now reflect on this schedule)

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)
January 25	REGISTRATION; course organization; "pre-test" and demographics; Essential Dispositions for Educators	RH: Preface; "Dialogue with Laura"	history of mathematics review  history links
February 1	early ideas of philosophy of mathematics, to c. 1800	RH 6,7 history/philosophy links	favorite, special numbers  number links
February 8	no class due to the big snow
February 15	crises in philosophy of mathematics: non-Euclidean geometry, set paradoxes, Gödel; responses	RH 8,9 history/philosophy links	nominal numbers, gematria  number links
February 22	developing a philosophy of mathematics  ["Platonic/formalist ideas in school math" due]	RH 2-5	mathematical objects  objects links
March 1	humanist/socio-cultural philosophy of mathematics	RH 1, 10-13	folding paper  links for origami and hexaflexagons
March 8	ethnomathematics: ethnic mathematics	MA Intro, 1,3,4; P&F 11,15 ethnomathematics links	games I  games I links
March 15 note that this class will follow the PG County spring break and not that of Towson University	ethnomathematics: other cultures	MA 2,5,6,7; P&F (9?),10	networks
March 22	ethnomathematics political issues: diversity, equity, global education	P&F 7,13,14,18 socio-political links	games II  games II links
March 29	individual presentations:   "Mathematics in MY OWN Culture"	P&F 1,12,16,17
April 5	Spring Break
April 12	individual presentations:   "Mathematics in MY OWN Culture" [global essay due]
April 19	individual presentations:   "Mathematics in MY OWN Culture"	"Lockhart's Lament" and follow-up
April 26	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
April 21-24 National Council of Teachers of Mathematics Annual Conference, San Diego, California
May 3, 2010 Iyyar 19, 5770 Jumada-I 19, 1431 elder-metal Tiger: 4708-3-20	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
May 10	take home final exam  will be distributed in class; it will be due Monday, May 17, 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 February 22.(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.  March 29, April 12, or April 19 (topics and specific dates to be 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 April 26 (25% for presentation and paper)

Math in MY OWN Culture: topic selections

Carmichael, Susan---brain education(related to yoga)
Deterding, James
Fabré, Shelley---NCAA Basketball tournament
Engles, James---sabermetrics (in baseball)
Fiechuk, Christine
Frederick, Wendy---Bible numerology
Hayden, Dana
Hopper, Danielle
Jones, Elise
McNair, Gwendolyn---hair styles
Sarich, John---football
Velcenbach, Jacqueline---numerology in religion (incl. kabbalah)
Wintersteen-Kolb, Catherine
Wong Wing, Ashana
Yates, Candyce

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 March 22 and relates to  "Mathematics in Global Education Programs"  Also, check the related links.  Due April 12 (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 April 26 class.  Maybe some of these mathematics education links will assist you.  Due May 3 (15%)

FINAL EXAM

A take-home final exam will be distributed in class May 10 and by email attachment on May 11.  It will be due by Monday, May 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 Student Academic Integrity Policy [Word Document]  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  (no MCTM Annual Meeting in 2010, due to Regional NCTM meeting in Baltimore)
--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

--Number of the Day (from the Mathematical Association of America)
--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
---powers of ten--photos, video, etc. to show sizes of lengths and time
--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, use this version. Press the "Stereo" button twice.  You will see a double image. 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 examples and fractal of the day; zoom on Mandelbrot's plot;
--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 or phone 410-704-3500

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 ☺