TEXTS
Required (available in the University Store; links go to the listing in Amazon.com; or for comparison shopping, try Campus Books4Less)
---Ascher, Marcia (1991) Ethnomathematics: a multicultural view of mathematical ideas, Wadsworth. ISBN 0-412-98941-7
---Livio, Mario (2009) Is God a Mathematician?, Simon & Schuster. ISBN 074329405X (or 978-0743294065)
---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
---Hersh, Reuben (1997) What is Mathematics, Really?
Oxford University Press. ISBN 0-19-511368-3
---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
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:
ML = Livio
MA = Ascher
P&F=Powell &
Frankenstein
NCTM=Principles and Standards)
math culture topic
(see related Links
below)
January 30
course organization;
"pre-test" and
demographics; Essential Dispositions for Educators"Dialogue with Laura" (preface
to the Hersh book, copy to be distributed in class)
history of mathematics review
history links
February 6
issues, mysteries
ML 1
history/philosophy links favorite, special
numbers
number links
February 13
Platonism, (Pythagoras to Kant) up to 1800
ML 2, 4
(ML 3 for Feb 7) history/philosophy links
nominal numbers, gematria
number links
February 20
Crises, formalism
(Non-Euclidean geometry to
GödelML 6,7( ML 5 optional)
history/philosophy links
mathematical objects
objects links
February 27
Continuing issues; socio-cultural philosophy "Platonic/formalist
ideas in school math" due]
ML 3,8,9
history/philosophy links
folding paper
links for origami and hexaflexagons
March 6
NO CLASS
ӿӿ
SNOW (but really not much) ӿӿ
March 13
ethnomathematics: ethnic mathematics
MA Intro, 1,3,4;
P&F 11,15
ethnomathematics links
games I
games I links
March 14--Pi Day
http://en.wikipedia.org/wiki/Pi_Day
March 20
NO CLASS
SPRING BREAK
March 27
ethnomathematics: other cultures
MA 2,5,6,7; P&F 10,17
ethnomathematics links networks
Mathematics
Awareness Month
comes every April. For 2013, the theme is "Mathematics
and Sustainability".
April 3
ethnomathematics political issues:
diversity, equity, global educationP&F 7,13,14,18 (optional 3,4,5)
socio-political linksgames II
games II links
April 10
individual presentations:
"Mathematics in MY OWN Culture" (activities)
Adams, Jason
giving back to the community
Engles,
James gambling
Grant,
Heather restaurants
Hahn, Maureen accordion
Dondzila, Katie rainbowsP&F 1,12,16,17
April 17
individual presentations:
"Mathematics in MY OWN Culture" (heritage/religion)
Stanmyer, Hilary Celtic
Mariano, Alison Bible
Alshahrani, Wafa Islam/Arab
Nikamooz, Ali Iranian architecture
Olunuga, Foluke Yoruba
[global essay due] "Lockhart's Lament"
and
follow-up
April 17-20
NCTM Annual Conference in Denver, Colorado
April 24
philosophy of
mathematics education
[Math in MY Culture write-up due]
NCTM-PSSM: Chap 2 "Principles" (log-in required)
magic squares
(
洛书 lo shu)
magic square links
1 May, 2013
21/22 Iyyar 5773
21 Jumada II, 1434;
Snake 
(younger water)
22/03/4711
applying philosophy:
issues in mathematics education
[philosophy essay due]
NCTM-PSSM: Chap 2
"Principles" (log-in required)
links to organizations and issues calendars
calendar links
May 8
Review and summary
take home final exam
distributed
in class
(and via email on May 9)
jokes
math jokes
& literary math
May 15
no class meeting, but the
exam is due by 5 pm
(via
email or other means)
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 27.(15%)
3. Prepare a presentation of about 25-30 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, etc. 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. April 10 or 17
(topics and specific dates shown above).
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
24 (25% for presentation and paper)
Math in MY OWN Culture:
approximate individual topic selections (not yet focused or confirmed)
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 the April 3 class and relates to
"Mathematics
in Global Education Programs"
Also, check the related
links. Due April 17 (15%)
CLASS REGULATIONS AND EXPECTATIONS
--Jason Adams giving back to the
community
--Wafa Alshahrani Islam/Arab culture
--Katie Dondzila rainbows
--James Engles gambling
--Heather Grant restaurants
--Maureen Hahn music: accordion
--Alison Mariano Bible
--Ali Nikamooz architecture in
Iran
--Foluke Olunuga Yoruba
--Hilary Stanmyer Celtic
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 24 class. Maybe some of these
mathematics education links will
assist you. Due May 1 (15%)
FINAL EXAM
A take-home final exam will be distributed in class May 8 and by email
attachment on May 9. It will be due by Wednesday,
May 15, at 5 pm. It may
involve additional research in the library and/or the Web. (20%) It
can be submitted by fax (410-704-3129) or as e-mail
(
LShirley@towson.edu) or in hard-copy to room 367, 7800 York Road
Building (postal: Lawrence Shirley, Mathematics Department, Towson University, 8000 York Road, Towson MD 21252-0001).
--The Graduate course grading system has grades of A (4.0), A- (3.67), B+
(3.33), B (3.0), C (2.0), and F (0.0). Depending on the spread of grades,
it is expected that the following lower boundaries will be used
approximately to translate course points into letter grades:
A: 95, A-: 90, B+: 85, B: 80, C: 70. Since this system is still fairly new, some adjustments
may be made.
--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.
Any academic dishonesty will normally result in a grade of zero for
that work and may result in greater sanctions.
--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.
--flu 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
--
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 2000 names!) and other topics
----including
Pythagoras,
Aristotle,
Plato,
Euclid,
Ptolemy,
Descartes,
Newton,
Leibniz,
Bolyai,
Lobachevsky,
Riemann,
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 a
similar list; and
another
list, more detailed and with more references.
--
Gödel's Proof that mathematics, as an axiomatic system, is
incomplete (i.e., that there exist true statements that cannot be proven)
--In the year 2000, the Clay Mathematics Institute
offered $1 million prizes for the solution of each of the seven significant unsolved
"Millennium
Problems" (one has now been solved)
----solution of "ABC Conjecture":
background (from 1997);
news story of September 2012;
article in Nature magazine
--in January 2013, a report was made at a conference that
the Invariant Subspace Problem (for Hilbert Spaces) had been solved. It has not been confirmed or published yet. This is not one of the
, but is still an important problem awaiting definitive solution.
--5 February 2013: confirmation of the finding of the 48th
Mersenne prime (and 48th perfect number)
http://www.mersenne.org/
--Remember
that the Goldbach Conjecture says all even numbers (>2) can be written as the
sum of two primes.
This suggests
all odd numbers (>5) can be written as
the sum of three primes (May 2013)
--The Twin Prime Conjecture says there are an infinite number of twin prime pairs—primes p and p+2, i.e., separated by 2.
This says there are an
infinite numbers of prime pairs separated by less
than 70 million (May 2013).
--The
Eleven Most Beautiful Mathematical Equations
--MathWorld:--a great site to look up math content and terminology
--current mathematics news: MathWorld Headline News (but it doesn't keep up to date very well)
--Philosopher Immanuel Kant
--Piaget's educational theory
--The author of Is God a Mathematician?: Mario Livio(links on that page for more); in Wikipedia
--The author of What is Mathematics, Really? : 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 (it was in Towson, July 25-30, 2010); the fifth one will be in Mozambique in July 2014
--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
--fractals in ethnomathematics: Ron Eglash website (see the links on the lower right section)
--author of Ethnomathematics: a multicultural view of mathematical ideas ;brief biography of Marcia Ascher
--references on the mathematics of Islam. 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 "Ethnomathematics in Global Education Programs" from ICEM-3 (full text and references)
--"Teaching Statistics with Social Justice"--a good argument with good resources
--Peace Corps, National Peace Corps Association (the organization of returned Peace Corps Volunteers)
-----Educational resources, 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
--estimated live up-date of world statistics at Worldometers
--UN Millennium Goals (eight development goals for 2015)
--WorldMapper--world maps with country areas proportional to measures of interest.
--Creative presentations on world issues: from TED.com; from gapminder.org
--graphs of inequalities in the US
--RadicalMath looks at blending mathematics content and issues of social justice. Similarly, the Algebra Project (of Robert Moses) 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. (There are newer editions since 2005)
MATHEMATICS EDUCATION: ORGANIZATIONS AND ISSUES
--an outline of the history of mathematics education in the 20th century
--12th International Congress on Mathematical Education ICME-12 was in Seoul, Korea, July, 2012.The Thirteenth Congress ICME-13 will be in Hamburg, Germany, July 24-31, 2016
--National Council of Teachers of Mathematics (2013 Annual Meeting in Denver, April 17-20, 2013)
-----Principles and Standards of School Mathematics on-line (log-in required)
--Maryland Council of Teachers of Mathematics probably the 2013 annual conference will be Oct 18. Watch for announcements--and plan to be a speaker! (note: these webpages may not be updated yet)
--Common Core State Standards (pages 3-8 are general information, pages 9-45 focus grade-by-grade from kindergarten to grade 6)
--Common Core Standards, Math and English, K-12 (June, 2010)[more information]
--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]
--a short video about the the Museum of Mathematics in New York City (opened in 2012)
--a blog of mathematics culture, puzzles, curiosities, etc.: Alex Bellos
--numberphile (videos about interesting number facts)
--Number of the Day (from the Mathematical Association of America)
--What is your favorite number?
--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
---letters in the spelling of numbers (in English and in Roman numerals)
---powers of ten--photos, video, etc. to show sizes of lengths and time
--a great index of terms (currently off-line for reconstruction) 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) NEWS: 5 February 2013: confirmation of the finding of the 48th Mersenne prime (and 48th perfect number)
--repunits (1,11,111,1111, etc.)
--prime birthday(when you are a prime number of days old)
--nerdiversary (wierd celebrations you can observe)
--dollar words and gematria calculations
--details on Kaprekar's routine (6174 trick)
--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!
--Another resource on hypercubes: This also talks about making one (a 3D "shadow" of one) with a 3D printer
--A sample of M.C. Escher art
--Klein bottle pictures and for sale; knitting instructions for a Klein Bottle Pi hat
-- fractals, and examples and fractal of the day; zoom on Mandelbrot's plot; more zooms with images; making a Mandelbrot plot; biography of Mandelbrot; obituary of Mandelbrot [Here is story of people building a giant fractal from business cards]
--mathematical origami; Lang=a leading origamist; more origami links and some origami basics
--hexaflexagons; two short videos about hexaflexagons: #1 and #2
--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 (on a 7x7 board).
--a page on Nine Men's Morris. Here you can play it.
--magic squares (洛书 lo shu): for educational use and more; more technical details(with many links)
--some classic math jokes, and more good math jokes; top-ten lists, joke definitions, etc
--three math/geek humor blogs: Spiked Math, Math-Fail, xwhy, and GaussFacts
--more broadly, here is a page of mathematical fiction.
-- Martin Gardner's collected columns (available on CD-ROM) (Martin Gardner: 1914 - May 22, 2010)
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.
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--log-in required); 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.
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).
------------------------
[ Top ]
but, contrary to the premise of this course....here's a quote from the
French mathematician
Henri
Lebesgue (1875 - 1941):
also--
"A good mathematical joke is better, and better mathematics, than a
dozen mediocre papers." "A mathematician is a device
for turning coffee into theorems"
All links checked on 4 January 2013
(if you find a bad link, please
inform
Dr. Shirley)
"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)
John Littlewood
(1885-1977) A Mathematician's Miscellany, 1953
☺
George
Polya (1887-1985) ☺
Paul Erdos (1913-1996) ☺
[ Top ]
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
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.
_____ (2011) The Man of Numbers:
Fibonacci's Arithmetic Revolution, Walker & Company.
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.