**
CULTURAL AND PHILOSOPHICAL BACKGROUND OF MATHEMATICS
MATH 602.241**

*
notes on course offerings:*

--Check with the

--This webpage is intended for Dr Shirley's class sections, but may be useful for other offerings.

** Fall
2014
**
Scroll down or jump immediately to:
Course Information,
Catalog Description,
Objectives,
Texts,
Topic Outline,
Assignments,
Schedule of Oral Presentations,
Final Exam,
Bibliography,
Class Regulations,
Links,
Roster,
Seating Chart,
References for NCATE and
Contacts.

*professor:* Dr. Lawrence Shirley

*phone:***
**
410-704-3500

*fax:* 410-704-4149 (Mathematics Dept)

*e-mail:*
LShirley@towson.edu

*personal web-page:*
http://pages.towson.edu/shirley

*office:* room 333, 7800 York Road Building, Towson University

*office hours:* MWF 10:00-11:00 am, by appointment, or
before/after class

*class meeting times:* Tuesdays, 5:00 - 7:40 pm (starting September
2, 2014)

*class meeting location:*Southampton Middle School(directions)(tentatively,
Room 212)

*graduate program director:* Dr Maureen Yarnevich [myarnevich@towson.edu
or 410-704-2988];
*program:* M.S. in Mathematics Education

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 credits)

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

**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.

[Note: Students will also be introduced to
Towson University's *Essential Dispositions for Educators* at the level
of Pre-assessment (Candidate Self-Evaluation)]

**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) |

September 2 | 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 |

September 9 | Southampton's Back-to-School night: no class | ||

September 16 |
issues, mysteries | ML 1 history/philosophy links |
favorite, special
numbers number links |

September 23 | Platonism, (Pythagoras to Kant) up to 1800 | ML 2, 4 (ML 3 for Oct 7) history/philosophy links | nominal numbers, gematria number links |

September 30 | Crises, formalism (Non-Euclidean geometry to Gödel |
ML 6,7( ML 5 optional) history/philosophy links | mathematical objects objects links |

October 5-11 National Metric Week | |||

October 7 |
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 |

October 14 | ethnomathematics: ethnic mathematics | MA Intro, 1,3,4; P&F 11,15 ethnomathematics links | games I games I links |

October 17--Annual Conference of the Maryland Council of Teachers of Mathematics at Baltimore Polytechnic Institute. This year's theme is "Journey to the Center of the Core." | |||

October 21 |
ethnomathematics: other cultures | MA 2,5,6,7; P&F 10,17 ethnomathematics links |
networks |

October 28 | ethnomathematics political issues: diversity, equity, global education |
P&F 7,13,14,18 (optional 3,4,5) socio-political links |
games II games II links |

November 4 | Election Day--building is closed: no class | ||

November 11 |
individual presentations: "Mathematics in MY OWN Culture" | P&F 1,12,16,17 | |

November 18 | individual presentations: "Mathematics in MY OWN Culture" [global essay due] | "Lockhart's Lament" and follow-up | |

November 25 | building closed: no class | ||

December 2 | 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 |

December 9 17/18 Kislev 5775 17/18 Safar, 1436; 18/10/4712, Horse (elder, wood) | applying philosophy: issues in mathematics education [philosophy essay due] --Review and summary |
NCTM-PSSM: Chap 2
"Principles" (log-in required) links to organizations and issues |
calendars calendar links |

December 10 |
take home final exam distributed via email | jokes math jokes & literary math | |

December 16 | 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 October 7.(15%)

3. Prepare a presentation of about 25-30 minutes on the mathematics of some area of your own cultural heritage and/or your

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:
approximate individual topic selections will be listed here *

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 October 28 class and relates to __
__
__
__
__
____"Mathematics
in Global Education Programs"__
Also, check the related
__
links__. Due November 18 (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 December 2 class. Maybe some of these

**
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. Large numbers of absences will be reflected in the "participation" part of the course grade calculation and possibly in other scores that are hurt by missed material.

--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.

Any student who needs an

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. Suspicious
material may be checked electronically.
Any academic dishonesty will normally result in a grade of zero for that
work and may result in greater sanctions. For details, see the
**
Student Academic Integrity Policy****Diversity Statement:** In accordance with the Towson University Strategic Plan, the Fisher College of Science and Mathematics
Diversity Action Plan, and the Department of Mathematics Diversity
Action Plan, everyone participating in this course is expected to be
respectful of each other without regard to race, class, linguistic background,
religion, political beliefs, sex, gender identity or expression, sexual
orientation, ethnicity, age, veteran’s status, or physical ability. If you feel
these expectations have not been met, please speak with your instructor or the
designated diversity liaison, Dr. Elizabeth Goode,
egoode@towson.edu, 410-704-4981.

**
LINKS
**

--

--

--

--In the year 2000, the Clay Mathematics Institute offered $1 million prizes for the solution of each of the seven significant unsolved

--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 Millennium problems, 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

--

--current mathematics news:

--Philosopher Immanuel Kant

--Piaget's educational theory

--The author of

--The author of

__
__ (it was in
Towson in 2010); the 5th one was in Mozambique in July 2014; the 6th will be in Colombia in 2018

ETHNOMATHEMATICS, MATHEMATICS OF OTHER CULTURES, GLOBAL RESOURCES

--International Study Group on Ethnomathematics (North American Study Group on Ethnomathematics)

----ethnomathematics links

----the Fourth International Conference on Ethnomathematics

--counting to ten in more than 5000 languages

--play oware/mancala on-line (slightly different rules than those used in class)

--References to

--author of

--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

--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)

--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 (2015 Annual Meeting in Boston, April 15-18, 2015)

-----Principles and Standards of School Mathematics on-line (log-in required)

--Maryland Council of Teachers of Mathematics; the 2014 annual conference is on October 17, 2014.

--Common Core State Standards (pages 3-8 are general information, pages 9-45 focus grade-by-grade from kindergarten to grade 6)

--Maryland State Department of Education

--The Math Forum @ Drexel

--The Mathematics Curriculum Center

--The Eisenhower National Clearinghouse

--Mathematically Correct

--Mathematically Sane

--Report of the

**
OTHER CULTURE OF MATHEMATICS
**

**
**
--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 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)
We are awaiting the 49th!

--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: (use A=1, B=2,...Z=26; find words whose
letters add up to 100) examples and calculating (and more details).

--details on
Kaprekar's routine (6174 trick)

--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 (this site may be down) and
for
sale

--
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 (

--some classic math jokes, and more good math jokes; top-ten lists, joke definitions, etc

--three math/geek humor blogs: Math-Fail, xwhy

--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.
**
**

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

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):

"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**
****☺**

"Mathematics
consists in proving the most obvious thing in the least obvious way."

George
Polya (1887-1985) **☺**

"A mathematician is a device
for turning coffee into theorems"

Paul Erdos (1913-1996) **☺**

**
**

*
All links checked on 28 July 2014
(if you find a bad link, please
inform
Dr. Shirley)*

**
[
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)

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.

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 Gardner's 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

Greenwald, Sarah and Thomley, Jill (editors) (2011) *Encyclopedia of Mathematics and Society*, Salem Press.(includes
8 articles by LHS)

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.[recommended text]

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.

Joseph, George Gheverghese (1991) *The Crest of the
Peacock: Non-European Roots of Mathematics*, Penguin.

Kaplan,
Robert (1999) *The Nothing that Is: A
Natural History of Zero*,

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

Katz, Victor J. (editor) (2007) *The Mathematics of Egypt, Mesopotamia,
China, India, and Islam: A Source Book*, Princeton University Press

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.

_____ (2009) *
Is God a Mathematician*? Simon
& Schuster.[required text]

**
**
______
(2013)

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

Mukhopadhyay, Swapna, and
Roth, Wolff-Michael (editors) (2012)
*Alternative Forms of Knowing (in)
Mathematics: Celebrations of Diversity of Mathematical Practices*, Rotterdam,
The Netherlands: Sense Publishers

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 [required 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.

_____ (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://pages.towson.edu/shirley/global.htm )

_____ (2008)
“Ethnomathematics Looks Back and Looks Forward” Discussion Group 18--Ethnomathematics
at the 11^{th} International Congress of Mathematical Education,
Monterrey, Mexico.
http://pages.towson.edu/shirley/ethnomath%20looks%20back,%20forward.htm
**
**

_____ (2011) eight
articles in Greenwald and Thomley (eds)
*(see above)*

Singh, Simon (1997) *Fermat's 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.

Stinson, David, and Wager, Anita (editors) (2012) *
Teaching Mathematics for Social Justice*, National Council of Teachers
of Mathematics.

Taylor, Alan D.(2005) *Social Choice and the Mathematics of Manipulation,*
Cambridge University Press.

Tippett, Krista (2010) *Einstein's God: Conversations about Science and
the Human Spirit*, Penguin.

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.

Wager, Anita A., and Stinson, David
W. (editors) (2012) *Teaching Mathematics for Social Justice: Conversations with *
*Educators*, NCTM.

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.

* [bibliography updated August 2013]*

Erica Charvat

Tina Hartman

expected, but not yet registered: Patricia Chamberlin, Gina Heidel, Jessica Knott, Dennis Lehr, Susan Pinder, Natalia Seets,

**
SEATING CHART
**(to be added after the first class)