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:
4107043500
fax: 4107044149 (Mathematics Dept)
email:
LShirley@towson.edu
personal webpage:
http://pages.towson.edu/shirley
office: room 333, 7800 York Road Building, Towson University
office hours: MWF 10:0011:00 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 4107042988];
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 (hardcopy) 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 Preassessment (Candidate SelfEvaluation)]
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 0412989417
Livio, Mario (2009) Is God a Mathematician?, Simon & Schuster. ISBN 074329405X (or 9780743294065)
Powell, Arthur and Frankenstein, Marilyn (editors) (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education, State University of New York Press ISBN 0791433528
also, handouts are distributed and references are made to Links
below.
Recommended:
Davis, Philip, and Hersh, Reuben (1981)
The Mathematical
Experience, Birkhauser. ISBN 0395929687
Hersh, Reuben (1997) What is Mathematics, Really?
Oxford University Press. ISBN 0195113683
National Council of
Teachers of Mathematics (2000) Principles and Standards of School Mathematics,
NCTM
[available online to NCTM members] ISBN 0873534808
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 changesincluding
weather or flurelatedwhich 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;
"pretest" 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 BacktoSchool 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
(NonEuclidean geometry to
GödelML 6,7( ML 5 optional)
history/philosophy links
mathematical objects
objects links
October 511 National Metric Week
October 7
Continuing issues; sociocultural 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 17Annual 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 educationP&F 7,13,14,18 (optional 3,4,5)
sociopolitical linksgames II
games II links
November 4
Election Daybuilding is closed: no class
November 11
individual presentations:
"Mathematics in MY OWN Culture"
recreational activities
Tricia Chamberline living with a disabled child
Tina Hartman baseball
Jessica Knott pool (as in billiards,
not swimming!)
Natalia Seets travel
P&F 1,12,16
November 18
individual presentations:
"Mathematics in MY OWN Culture"
family heritage
Erica Harvey multinational
family
Will Marbury Hungarian
mathematics heritage
Sue Pinder snowball business
[global essay due]
November 25
building closed: no class
December 2
philosophy of
mathematics education
[Math in MY Culture writeup due]
NCTMPSSM: Chap 2 "Principles" (login 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
NCTMPSSM: Chap 2
"Principles" (login 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 (200500 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 2530 minutes on the
mathematics of some area of your own cultural heritage and/or your
nonprofessional 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. November 11 or November 18
(topics and specific dates shown above).
Also write up a fivetoeight page (roughly 12502000 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
Patricia Chamberline sailing navigation
Tina Hartman baseball
Erica Harvey multinational
family
Jessica Knott pool (as in billiards,
not swimming!)
Will Marbury Hungarian
mathematics heritage
Susan Pinder snowball business
Natalia Seets travel
4. Write a onetotwo page essay (200500 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 classesespecially 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 onetotwo
page essay (200500 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
mathematics education links will
assist you. Due December 9 (15%)
FINAL EXAM
A takehome final exam will be distributed by email
attachment on December 10. It will be due by
Tuesday,
December 16, at 5 pm. It may
involve additional research in the library and/or the Web. (20%) It
can be submitted by fax (4107044149) or as email
(
LShirley@towson.edu) or in hardcopy to room 333, 7800 York Road
Building (postal: Lawrence Shirley, Mathematics Department, Towson University, 8000 York Road, Towson MD 212520001).
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. 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 flulike 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 accommodation
due to a disability should make an appointment to discuss the accommodation. A
memo from
Disability Support Services: authorizing the accommodation is required.
Plagiarism is, of course, not acceptable. Any use of the material of others must
be documented, including Webbased 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, 4107044981.
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
historyrelated 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 crossreferences

NonEuclidean 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
Livio briefly explaining
Platonism and formalism
(6minute video)
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
online (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 ICEM3 (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 update of world statistics at
Worldometers
UN Millennium Goals (eight development goals for 2015)
WorldMapperworld
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 Schoolsa 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
ICME12 was in Seoul, Korea, July, 2012.The Thirteenth Congress
ICME13 will be in Hamburg, Germany, July 2431, 2016
National Council of Teachers of
Mathematics (2015 Annual Meeting
in Boston, April 1518, 2015)
Principles and Standards of
School
Mathematics online (login required)
Maryland Council of Teachers of
Mathematics; the
2014 annual conference is on October 17, 2014.
Common Core State Standards
(pages 38 are general information, pages 945 focus gradebygrade from kindergarten to grade 6)
Common Core Standards, Math and English, K12
(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 nationwide.
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 tenphotos, 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)
fourdimensional hypercube (tesseract) in 3D
Note: If you have
redblue 3D 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 tictactoe in
3D (4x4x4) or
4D (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; topten lists, joke definitions, etc; from GoodRiddlesNow.com
three math/geek humor blogs:
MathFail,
xwhy
more broadly, here is a page of
mathematical fiction.

Martin Gardner's collected columns
(available on CDROM) (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 EducatorsAdvanced Programs: The Dispositions are introduced in the first class meeting
and students do a selfevaluation.
Assessment literacy components: Assessment issues are included in the discussion of
mathematics education issues.
Signature assessments: Pretest, 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
readinglogin 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 PK12 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 email to
Dr. Shirley or phone 4107043500
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 philosophyan 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
(18851977) A Mathematician's Miscellany, 1953
☺
"Mathematics
consists in proving the most obvious thing in the least obvious way."
George
Polya (18871985) ☺
"A mathematician is a device
for turning coffee into theorems"
Paul Erdos (19131996) ☺
This webpage was last updated on 20 November 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, BrookCole 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, SpringerVerlang.
_____ (1962, 1997) The Mathematical Magpie, SpringerVerlang.
Frankenstein, Marilyn (1994) "Critical Mathematics Education: Bringing multiculturalism to the mathematics classroom" in M.M. Atwater, K. RadzickMarch, & 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 TwentyFirst 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: NonEuropean 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, AddisonWesley.
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, WolffMichael (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) AddisonWesley.
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 onlyonline
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), 278285.
_____ (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 18Ethnomathematics
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]
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