CULTURAL AND PHILOSOPHICAL BACKGROUND OF MATHEMATICS
MATH 602.101
notes on course offerings:
MATH 602 is offered on campus in Spring 2013: Wednesdays, 5:00 - 7:40 pm
in room YR 106.
(It was offered in Fall 2011 at the Laurel College Center,
but it was not offered in Spring or Fall 2012. We expect to offer the
course in Fall 2013
for a Howard County cohort, and in Spring 2014 in Southern Maryland)
--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.
Spring
2013
GRADES HAVE BEEN SUBMITTED
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 367, 7800 York Road Building, Towson University
office hours: Tuesdays, 2-4 pm, Wednesdays 2-3 pm, by appointment, or
before/after class
class meeting times: Wednesdays, 5:00 - 7:40 pm (starting January
30, 2013)
class meeting location: room 106, 7800 York Road Building, Towson University
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)
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)
GRADES HAVE BEEN SUBMITTED
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)
--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
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%)
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).
GRADES HAVE BEEN SUBMITTED
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. 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.
--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":
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
--"ten coolest
math results" For all kinds of lists (not just
math), see listverse.com
--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]
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
(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: (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)
--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):
"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 29 May 2013
All links checked on 4 January 2013 (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
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]
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.
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.
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 February 2013] see ten-week webpage for updates
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ROSTER Spring 2013 (as of 6 February 2013)
Adams, Jason Lamar |
Alshahrani, Wafa Saad Saeed |
Dondzila, Katie |
Engles, James |
Grant, Heather |
Hahn, Maureen Annette |
Mariano, Alison Diana |
Nikamooz, Alireza |
Olunuga, Foluke Grace |
Stanmyer, Hilary Patricia |
YR 106
Wafa Alshahrani |
Hilary Stanmyer | XXX | James Engles | Foluke Olunuga |
Maureen Hahn | Ali Nikamooz | XXX | Katie Dondzila | Heather Grant |
Alison Mariano | Jason Adams | XXX |
DOOR DR SHIRLEY