Towson University---Mathematics Department

CULTURAL AND PHILOSOPHICAL BACKGROUND OF MATHEMATICS
MATH 602.241

notes on course offerings:
--Check with the
Mathematics Education Graduate Program Director, Dr Maureen Yarnevich or the Mathematics Department for information on any course offerings in this program.
--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)(room to be announced)
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
issues, mysteries ML 1
history/philosophy links
 favorite, special numbers
 number links
September 16 Platonism, (Pythagoras to Kant) up to 1800 ML 2, 4 (ML 3 for Feb 7)  history/philosophy links nominal numbers, gematria
 number links
September 23 Crises, formalism
(Non-Euclidean geometry to Gödel)
ML 6,7( ML 5 optional) history/philosophy links  mathematical objects
 objects links
September 30
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 5-11 National Metric Week 
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 10,17
ethnomathematics links
 networks
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 political issues:
diversity, equity, global education
P&F 7,13,14,18 (optional 3,4,5)
 socio-political links
games II
 games II links

October 28

 individual presentations:
  "Mathematics in MY OWN Culture"
P&F 1,12,16,17  
November 4 individual presentations:
  "Mathematics in MY OWN Culture"

[global essay due]
 "Lockhart's Lament"
and follow-up
 
November 11 individual presentations:
  "Mathematics in MY OWN Culture"
  
November 18  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
November 25
3/4 Kislev 5775
3/4 Safar, 1436;
04/10/4712, Horse .
 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
December 2 Review and summary
take home final exam  
distributed via email on December 3
  jokes
math jokes & literary math
December 9 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 September 30.(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. October 28, November 4, or November 11 (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 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 21 class 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 November 25 (15%)

FINAL EXAM

A take-home final exam will be distributed by email attachment on December 3.  It will be due by Tuesday, December 9, at 5 pm.  It may involve additional research in the library and/or the Web. (20%) It can be submitted by fax (410-704-4149) or as e-mail ( LShirley@towson.edu) or in hard-copy to room 333, 7800 York Road Building (postal: Lawrence Shirley, Mathematics Department, Towson University, 8000 York Road, Towson MD 21252-0001).

CLASS REGULATIONS AND EXPECTATIONS

--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.
--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.

--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.
--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

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 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":
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 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
--
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
----the Fourth International Conference on Ethnomathematics
(it was in Towson in 2010); the 5th one was in Mozambique in July 2014; the 6th will be in Colombia in 2018
--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, 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 CorpsNational 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 (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)
--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
(this page may not be up)
--Mathematically Sane
--Math is More A group looking for a coordinated effort to improve mathematics education nation-wide.
--Report of the National Mathematics Advisory Panel (2008)

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 (
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: Math-Fail, xwhy
--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.

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--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):

"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)

 
This webpage was last updated on 28 July 2014

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

Barrow, John D. (1992) Pi in the Sky: Counting, Thinking, and Being, Clarenden Press, Oxford.

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.

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, Oxford University Press.

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) Brilliant Blunders, Simon & Schuster.

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 11th 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]

[ Top--return to syllabus ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ROSTER  Fall 2014

SEATING CHART  (to be added after the first class)

 

 

[ Top--return to syllabus ]