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Anne Ray ‘Horizontal Enrichment: Avoiding the “Why Do I Have to do More Work?” Question’
International School of Islamabad Islamabad, Pakistan.
Advanced Math Project
STEP ONE……… 1st, begin by deciding what kind of project you wish to do. Some possibilities include: PEOPLE of MATH Study a famous mathematician and strive to understand both what he or she discovered and why it is important. The math department has biographical “starter packets.” PLACES of MATH Investigating mathematics is done differently part in some other region of the world or how the focus of mathematics might be different from the focus of math with which you are familiar. The library has a few books on the math of other regions and there is a lot of information on the web. Also, there is a book titled Math Elsewhere that you might be able to find. IDEAS of Math Consider some major concept of math, such as: zero, or coordinate graphing, or the Golden Ratio or pi, or logarithms, or the use of unknowns; and try to follow the history of this concept back in time and understand how it evolved and why it became important to the future progress of math. This is a research project, that can be pursued both on the internet and in popular math literature. CONNECTIONS to Math Investigate how math relates to some other field of interest, such as art, music, or sports. Design a project that will help you better understand the connection between mathematic and some other interest of yours, and help you gain the skills necessary to become more proficient at both. For example, your might wish to better understand sports statistical analysis and how the “handicapping” works, or you might wish to learn how a computer program animates a figure and write such a program, or consider the question of how music might motivates mathematical reasoning… Step Two………… 2nd, Complete enough preliminary investigation to confirm that the topic is appropriate for your level of math understanding . Will you learn new concepts or at least new approaches to concepts that are important? If the topic is appropriate, begin developing a list of the questions you will be considering as you continue with the project. Some of these should be “essential questions.” You should write out these questions and prioritize them. Step Three……….Now, begin your research and/or investigation. Decide how you would like to demonstrate what you gain from this experience. Will you create a movie, a Power point, a Smart board interactive lesson, a physical model or something else.
Write out a clear description of how you wish to share what you learn and by what date you will complete the project. Step Four……..Proceed with your research and/or investigations, modifying your questions and your goals as necessary. Be sure to discuss all modifications to your goals with your teacher in a timely manner. Do not wait until the due date. Step Five……..Complete you project with the goal of making the enthusiasm with which you pursued your questions, contagious. Teach what you have learned and/or discovered in an interesting and motivational way! After you’ve finished, congratulate yourself on your proven ability to work independently!
Advanced Math ……..1
Proposal a
Program for Advanced Middle Level
Math Students at The International School of Islamabad
Anne C Ray
Advanced Math ……..2
Math education, especially prior to calculus, in accordance with the principles of
NCTM, and my personal beliefs about math education, be taught in a constructivist way.
Wherever it is meaningful and possible, the separate strands of math, as well as math and
all other subjects should be integrated. Authentic learning and real problem solving
encourages a greater depth of understanding than the mere manipulation of memorized
algorithms.
Identification of the Need for a Program
Small schools often face the challenge of providing appropriate courses for all
students, while seeking to integrate certain components of the curriculum, and
maintaining minimum class sizes. This is a particularly challenging situation when
certain students’ needs are well met in all but one subject area, but that subject area
happens to be where their strongest abilities resides. In these cases, students, their parents
and the school administration, have to determine placement in consideration of the
scheduling limitations of the school, as distinct from the individual needs of particular
students. It is beneficial, according to generally accepted educational theory, that schools
such as The International School of Islamabad strive to help students synthesize their
learning in separate subject areas, especially before the secondary level, by offering
integrated classes, such as math and science, and that the school emphasizes
constructivist modes of learning. Unfortunately, this also has the affect of weakening the
appropriateness of what certain advanced math students are offered. Providing an
individualized program in math can
Advanced Math ……..3
ameliorate this problem. For this reason, I have designed an Advanced Math Standing
Program for Middle Level students at The International School of Islamabad.
Middle Level students at The International School of Islamabad are now placed in
heterogeneous math classes in both sixth grade and seventh grade. In eighth grade, they
are placed in General Math or Algebra I, but this greatly hinders the eighth grade
teacher’s ability to integrate math and science. It should be noted that each year several
transfer students have had Prealgebra in seventh grade, or in rare cases, in sixth grade,
and these students are challenging to place appropriately. The curriculum of what is
labeled “Prealgebra” varies greatly from one school to another and without appropriate
testing it impossible to know if a student in adequately prepared to begin Algebra I. (As
a placement test for algebra I, we presently use the Eighth Grade General Math Final
Exam.) Added to this is the near impossibility of scheduling seventh and eighth grade
math at the same time.
Our present curriculum of math education has many positive benefits in terms of
integration and constructivist exploration, but we are not at present providing adequate
challenge to our most able math students, and middle level is a time in educational
development when students need to be stretched and encouraged to begin teaching
Advanced Math ……..4
themselves how to pursue answers to their own questions. Establishing a well structured,
but ultimately self-directed, program of advanced math standing, with clear, but flexible
requirements, could serve to provide some of this needed intellectual stimulation, while
also serving as a system of recognition of talents.
Proposed Advanced Math Standing Entrance Requirements
The program I propose will be designed for those students who demonstrate all
three components of the enrichment triad – above average abilities, task commitment and
creativity, but admission into the program will be based on self-selection. Teachers can
encourage certain students to apply and discourage others, but ultimately, it will be a
student’s individual choice to seek this status or not.
Enticements to apply will include: special recognition on the student’s transcript
when and if all requirement are met, the privilege of taking pretests and potentially
beginning excused from most of the regular assignments connected when students
successfully “test out,” the freedom to work on project(s) of the student’s own choice, an
optional semiweekly lunch session with other advanced math students to discuss their
projects, and the honor of presenting the results of individual research projects at a
special “Math Night” for parents and other community members.
In my experience, students with the ability to work more independently and at an
advanced level leap at opportunities for greater freedom in what they learn and how they
learn it. If students hesitate to accept the additional challenges and responsibilities
involved, their math teacher and/or advisor should approach them, and parents can also
Advanced Math ……..5
be enlisted to provide additional encouragement. If a student still does not want to
participate, despite having an exceptional mathematical ability, their choice will be
honored. Likewise, students who seem unlikely to succeed at completing all the
requirements, but wish to try for this honor, will be permitted to do so, without any fear
of embarrassment if they select to leave the program before accomplishing all of the
goals. Their attempts to do so will have no negative affect on their grade or class status,
and all efforts they make while participating will be of obvious benefit to them.
Designing Individualize Programs (IAP)
Clarity and flexibility are the keys to this program. Students might excel in their
geometric reasoning, while moving less confidently with symbolic algebraic reasoning,
or visa versa. They may seek an extremely abstract reasoning project, such as striving to
understand and expand on Buffon’s Needle (a theorem about Pi); or conversely, they
might investigate the slope of the entrance stairways around the city by measuring the
rise and run and then calculating the rate of change, in order to understand the importance
of slope in architecture. Along with designing a project, they will also be required to
maintain a high average, and use their talents to serve their community by tutoring others,
creating learning tools or representing the school in math competitions. (See Appendix A
– Requirements for Advanced Math Standing.)
Students will create the rubrics for their special projects with guidance from their
teachers. They will have to plan how to meet their specific goals. Prior to creating the
rubric, students will need to do some preliminary researching and formulate questions
Advanced Math ……..6
about the topic they are investigating. Students will be provided with pre–researching
tools, but also be allowed to explore outside of the topics and books listed. Some
students, who are unable to “test out” of a unit, will work on less complex special
projects, or read and review a math book. Students who successful “test out” of units
will have the time to explore more complex topics and do so in greater depth. (See
Appendix B – Topics, Questions, and Resources and also see Appendix C – Interesting
Math Books)
Evaluation of the Program
As with all enrichment programs, Advanced Math Standing should be formally
evaluated each semester, but it will be several years before the benefits can be clearly
determined. Some of the aspects of this assessment process should include:
A) How well do the names of students petitioning for this program correlate with the
results of standardized tests, teacher recommendations, parents’ expectations? (If
a student who is “highly able” did not sign up, why not?)
B) Is the number of students petitioning for Advanced Math Standing increasing? (Is
this program gaining in popularity among the students and serving to motivate an
increased interest in the study of math?)
C) What percentage of students is meeting the requirements and earning this special
standing? (Are any of the requirements causing a stumbling block?)
Advanced Math ……..7
D) Are the participating students demonstrating benefits from this program?
1) Are their standardized scores improving? (ISOI uses the MAPS )
2) In high school, do they sign up for appropriate high level math courses?
E) Are the Math Nights successful? Are the students excited about them and are
they preparing well? Are other students, parents and community members
attending these events?
F) Are the teachers of the participating students seeing benefits to the students in the
program? How are the teachers finding the extra mentoring? Is it interesting? Is
the extra time excessive or manageable?
The success of this program, and possible alterations to be considered,
should be determined after the first year, and every year thereafter, by a
committee composed of math teachers, an administrator, at least one student and
a parent of a student who is participating in the program.
Although no set of options is likely to meet the needs of every child, I
sincerely believe that this kind of an Advanced Math Program would improve our
ability to attract, retain and meet the needs of highly able math students.
Appendix A - Requirements for Advanced Standing in Middle Level Math
There will be four separate components to ADVANCED MATH STANDING
at The International School of Islamabad. A student must meet all of the numbered
requirements. Alternative specifics can be proposed, but must be approved in advance If
these are not met, advanced standing will not be granted, but may reapplied for the next
semester.
A student must……
1) Write a letter to her/his math teacher within the first three weeks of the semester
petitioning the Math Department to be considered for ADVANCED MATH
STANDING. This letter, read and signed by the petitioner’s parent(s) and advisor,
must clearly express an understanding of and commitment to the requirements involved
in achieving this status.
2) Consistently demonstrate a commitment to excellence
All of the following are required:
a) Achieve a homework average of at least 3 (after timely revisions)
b) Earn “B” or better on each Unit Test (after timely revisions)
c) Maintain an average at or above “B+” on all tests (after timely revisions)
d) Maintain a meaningful and clear notebook with daily notes, all returned
work, and vocabulary
e) Be consistently focused in class and contribute meaningfully to class
discussions and investigations when in the class
f) Correctly complete extension problems (in place of easier assignments) at
least twice each unit.
3) Be a “Math Scholar” within the school community
A student must successfully meet at least two of these challenges each semester
a) Consistently participate in Math League or similar math competition
b) Become trained as a Peer Tutor, and tutor ten or more sessions within a
semester (training sessions count towards total)
c) Participate in a math-related activity or committee, such as chess club,
logic games, student survey committee, or others which might be formed
4) Accomplish math work above and beyond the basic course assignments
Students must propose, design and successfully meet at least one of these
challenges each semester
a) Pretest out of at least one unit and successfully complete a special project
b) On her/his own, collect and create packets of additional resources such as
math puzzles and riddles, lists and abstracts of relevant internet site for
lovers of math and math problems, with commentaries on each site.
c) Prepare and arrange to teach a lesson to her/his class or that of a lower
grade. This includes collecting or creating all necessary materials and
becoming “an expert” both on the concept and on various ways of
explaining it. This must be done in close coordination with the teacher of
the class they will be teaching
d) Read a math book relevant to a topic discussed at their grade and be
prepared to demonstrate mastery of some math concept presented within it
by writing a review and/or creating a informative poster to encourage
others to read the math book.
Appendix B - TOPICS, QUESTIONS, AND RESOURCES ***KEY I=investigations, In=information, H=history R= resources T=tutorials ABACUS (also see Soroban)
Can you learn to do all arithmetic operations on the abacus? How does the abacus deal with place value? Can abacuses be used to represent operations in other bases? Why might different cultures have developed different abacuses?
Dilson, Jesse; The Abacus; St. Martin’s Press; 1995 ISBN ISBN 0-312-10409-X
http://www.ee.ryerson.ca:8080/~elf/abacus/ I, In www.ideafinder.com/history/inventions/abacus.htm In , R
ALGEBRA Is there a difference between formal and informal representations of algebra and how can I learn to translate words into equations? How can I determine the fewest number of symbols needed by reading a situation?
Tahan, Malba; The Man Who Counted: a Collection of Mathematical Adventures; WW Norton ISBN 0-393-30934-7 Also see the algebra chapter from Ambitious Horse from Key Curriculum Press http://www.algebra.com/algebra/about/history/ In, H, http://illuminations.nctm.org/index_d.aspx?id=619 I (functions) http://illuminations.nctm.org/index_d.aspx?id=376 I (orbital debris – adv) http://illuminations.nctm.org/index_o.aspx?id=137 I (decay model) http://illuminations.nctm.org/index_d.aspx?id=288 I (recursive sequence)
ALGORITHMS * Has mathematics always had algorithms? What is the history of algorithms?
* How has the concept of algorithms taken on new meanings in the age of computers?
* Do all calculations potentially follow algorithms?
Berlinski, David; The Advent of the Algorithm: The Idea That Rules the World; Harcourt; ISBN 0-15-100338-6 http://www.ewh.ieee.org/soc/es/May2001/14/Begin.htm I (in genetics) http://www.wolfram.com/solutions/highered/use/tandr.html In and I
ARITHMETIC How does a number system influence a culture’s operational math?
What might math have been before numbers were abstracted? Urton, Gary; The Social Life of Numbers: A Quechua Ontology of
Numbers and Philosophy of Arithmetic; University of Texas ISBN 0-292-78534-8
ART and MATHEMATICS Which qualities of art can be quantified and how? How has the study of proportion and perspective gained from and contributed to mathematical theory? Are there differences between aesthetics based on Euclidian Geometry and NonEuclidian Geometries? What is the math of light in color and in perspective? How prevalent is the Golden Ratio in art ?
Atalay, Bulent; Math and The Mona Lisa: The Art and Science of Leonardo da Vinci; Huntley, H.E. ; The Divine Proportion; Dover; ISBN 0-486-22254-3 Peterson, Ivars; Fragments of Infinity: A Kaleidoscope of Math and Art; John Wiley & Sons; ISBN 0-471-16558 http://math.albany.edu:8000/artmath/ In http://math.haifa.ac.il/mathasart.html R http://kandid.sourceforge.net/gal_voroni_1.html T, I (an art project) http://www.newshoes.net/artmathematicalframeset.htm Examples
CALCULUS How did calculus evolve and from what concepts did it evolve? How is calculus different from other kinds of calculating?
Berlinski, David; A Tour of the Calculus; Vintage, ISBN 0-679-74788-5
http://www.chipola.edu/instruct/math/mathlab/calculus.htm R http://www.mathsnet.net/omnigraph/investigations.html I
CALENDARS also see Mayan, Jewish, Aztec, etc calendars How was the length of the year calculated by different cultures and how precise are these calculations? How does the number base of a culture relate to the calendar? (For example, why do weeks have seven days?) How you learn to determine the week day of any future or past event by a simple calculation? When several different numbering systems are used how can you efficiently determine where they over lap? Brimner, Larry Dane; The Official M&M’s History of the Calendar; Charlesbridge; ISBN 1-57091-432-x
http://physics.nist.gov/GenInt/Time/ancient.html In, H CHESSS and MATHEMATICS
Petkovi´c, Miodrag; Mathematics & Chess; Dover; 0-486-29432-3
CLOCK ARIMETIC see Aschers’ Mathematics Elsewhere,& Gallois, Noether How and when is modal math applied to real life situations? How is modal math used in divination?
http://illuminations.nctm.org/index_o.aspx?id=125 I (paper pool simulation)
COMPUTING How does symbolic logic relate to computing? Does the history of calculators and computers parallel the development of mathematical concepts? How did mechanical calculators work?
Eglash, Ron; African Fractals: Modern Computing and Indigenous Designs; Rutgers; ISBN 0-8135-2614-0
http://www.rpi.edu/~eglash/csdt.html I
CONIC SECTIONS also see Apolonious, ellipse, hyperbola, parabola What are the equations of conic sections and can you use them? Why are these important to the development of mathematical concepts? From what other concepts were these developed?
http://hsc.csu.edu.au/maths/ext2/conics/ T, I, R http://mathforum.org/library/topics/conic_g/ R (I, H. In) http://www.keypress.com/sketchpad/javasketchpad/links.php I (using sketchpad)
CRYPTOGRAPHY AND CIPHERS also see Flannery, Kovalevsky Nash How is it safe to use credit card numbers on the internet? How can hackers hack? What is the difference between “hackers” and “crackers?”
Flannery, Sarah; In Code:A Young Woman’s Mathematical Journey; Algonquin Books of Chapel Hill ISBN 1-56512-377-8
* Use COMAP #73 Secret Codes Activities to simple codes http://www.vcaa.vic.edu.au/prep10/csf/support/sampleunits/Codes.pdf In ,I, R,
E What is e? Why is it important and does it have practical applications?
How and where was e first discovered?
http://www.math.utoronto.ca/mathnet/answers/ereal.html In , Ap
FIBONACCI NUMBERS Does the Fibonacci sequence really exist in nature? If so where? What is the relationship between the Fibonacci sequence and the Golden Ratio?
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html I,
In,R
FICTION Has math become more or less important in fiction over the years? Is math and mathematical brilliance portrayed differently in the fiction of
different cultures? Enzensberger, Hans Magnus; The Number Devil; ISBN 0-8050-6299-8 Papachristos, Petro; Uncle Petros & Goldbach’s Conjecture;
Bloomsbury; ISBN 1-58234-128-1 Tahan, Malba; The Man Who Counted: a Collection of Mathematical
Adventures; WW Norton ISBN 0-393-30934-7
FRACTALS also see Mandelbrot What are fractional dimensions and how do they exist in the real world? Is geometry, fractal or Euclidian, or some combination of these and a function of culture?
Eglash, Ron African Fractals: Modern Computing and Indegenous Designs; Rutgers; ISBN 0-8135-2614-0 {also see his web site with culturally designed simulations}
Introducing Fractal Geometry ; Tetem Books, ISBN 1840461233 * Use COMAP # 76 Iteration and Chaotic Dynamics – Iteration activities using a calculator to develop concepts of fixed points, periodic points and chaotic behavior MS-PC http://www.gwfa.de/ In and examples in art http://www.rpi.edu/~eglash/csdt.html I
FRACTIONS When did fractions become necessary and why? How do fractions relate to the concept of infinity? Why did the Egyptians only use fractions with 1 in the numerator? What are the benefits of the Egyptian method of representing fractions?
http://www.visualfractions.com/ I www.nrich.maths.org.uk/mathsf/journalf/may99 and /jun99 In (continued fractions)
GEOMETRY What are the differences between Euclidian and Non Euclidian geometry and why is this difference significant? What kinds of Non Euclidian Geometry are relevant to calculations in the real world?
Mlodinow, Leonard; Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace; A Touchstone Book Simon & Schuster ISBN 0-684-86524 Stewart, Ian; Flatterland; Perseus; ISBN 0-7382-0675-x * Use COMAP #1 Viewing Earth from Space – Uses Geometry and Trigonometry to find the distance from a satellite to the earth’s horizon, and surface area viewed by the satellite at a given altitude IM3 - PC *Use COMAP #5 Mathematics and Global Positioning – Explains the need of three measurements to find a location Uses 3-D coordinate system and some algebra IM3 – PC http://www.ics.uci.edu/~eppstein/geom.html In (with applications) http://illuminations.nctm.org/index_d.aspx?id=379 I http://illuminations.nctm.org/index_o.aspx?id=166 I
GOLDEN RATIO see Phi and Fibonacci How does the Golden Ratio relate to music? Is the Golden Ratio pleasing in all cultures?
Livio, Mario; The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number; Broardway Books ISBN 0-7679-0815-5 http://www.perseus.tufts.edu/GreekScience/Students/Tim/Golden.html In http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html In, I
HARMONOGRAMS also see Lissajous, trigonometry
Ashton, Antony; Harmonograph: A Visual Guide to the Mathematics of Music;Wooden Books ISBN 0-8027-1409-9
Bourke, Paul. Harmonograph. July, 2002. 5/15/05. astronomy.swin.edu.au
O’Connor, JJ and Robertson, EF. Jules Antoine Lissajous. December, 1996. University of St Andrews, Scotland. 5/15/05. www-groups.dcs.st-and.ac.uk Purdam, Andrew. The Physics of the Harmonograph. 5/15/05.
www.pcug.org.au
HISTORY How has math changed history? Has the most powerful nations always been the most advanced mathematically and how can you prove or disprove your opinion?
Ball, W.W. Rouse; A Short Account of the History of Mathematics; Dover; ISBN 0-486-20630-0 Darling, David The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes; Wiley; ISBN 0-471-27047
Ifrah, Georges; From One to Zero: A Universal History of Numbers;Viking; ISBN 0-670-37395-8 Kaplan, Robert; The Nothing that Is: A Natural History of Zero; Oxford
ISBN 0-19-514237-3 McLeish, John; The Story of Numbers: How Mathematics Has Shaped
Civilization;….ISBN 0-449-90938-7 McLeish, John; NUMBER: From Cave People to Computers, a Revolutionary
View of Ourselves; http://history-of-mathematics.ask.dyndns.dk/ IMAGINARY NUMBERS
What are imaginary numbers and where/when do they exist? What is different about the mathematics of imaginary numbers and that of real numbers?
Mazur, Barry; Imagining Numbers (Particularly the Square Root of minus fifteen); …… ISBN 0-312-42187-7 Nahin, Paul J; An Imaginary Tale: The Story of the Square Root of -1; ISBN 0-691-02795-1 INFINITY
Does infinity exist in nature? How has the concept of infinity influenced the development of art? What are the different infinities?
Aczel, Amir; The Mystery of the Aleph : Mathematics, the Kabbalah, and the Search for Infinity; Washington Square Press; ISBN 0-7434-2299-6 Bunch, Bryan; The Kingdom of Infinite Number; W.H. Freeman and Company; ISBN 0-7167-4447-3 Kanigel, Robert; The Man Who Knew Infinity: A Life of the Genius Ramanujan; Washinton Square Press ISBN 0-671-75061-5
Kaplan, Robert and Ellen Kaplan; The Art of the Infinite; Oxford; ISBN 0-19- 517606-5
KNOTS What is knot theory and why is it relevant to real world mathematics? Does every physical entity have a value in knot theory?
Sossinsky, Alexei; Knots: Mathematics with a Twist; Harvard University Press ISBN 0-674-01381-6
http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html
LANGUAGE AND MATH also see numbers and multicultural math topics
How do the words for numbers and mathematical concepts facilitate the mathematical development of a culture? Do the words for numbers and operations have the same meaning/significance in different languages?
LITERATURE AND MATH Can mathematical reasoning be found in every story? How does math relate to humor in literature?
Paulos, John Allen; Once Upon a Number: The Hidden Logic of Stories; Fadiman, Clifton (editor); Fantasia Mathematica: Being a Set of Stories…..; Copernicus; ISBN 0-387-94931-3
LOGARITHMS What is logarithmic growth and where does it occur in nature? What are some of the ways logarithmic growth can be represented?
http://mathforum.org/library/drmath/view/52469.html In
http://www.physicsforums.com/archive/t-50984_Logarithm_Investigation_Help.html I
http://www.mansw.nsw.edu.au/members/reflections/vol21no1coupland.htm SA
MAGIC SQUARES AND MAGIC TRIANGLES http://mathworld.wolfram.com/MagicSquare.html I and In http://mathforum.org/alejandre/magic.square.html I, Ac, In, R http://www.geocities.com/~harveyh/ In, R
MATHEMATICIANS General questions …..
How did this mathematician’s contributions influence the development of math? What was his/her most significant contribution and why was this most significant? Who were the greatest influences on this mathematician? What conceptual limitation did this mathematician need to overcome to make the discoveries he/she made? What new concepts were outgrowth of this mathematicians influence? How is the practical world we live in different because this person lived?
Henrion, Claudia; Women in Mathematics:The Addition of Difference;
Muir, Jane; Of Men & Numbers: The Story of the Great Mathematicians; Dover; ISBN 0-486-28973-7
Perl, Teri; Woman and Number: Lives of Women Mathematicians; World Wide
Publishing Tetra, ISBN 0-933174-87-x Turnbull, Herbert Westren; The Great Mathematicians; Barnes & Noble, ISBN
0-7607-1673-0
ABEL
AGNESI also see isoperimetric figures
AL-KHWARIZMI How did Al-Khwarizmi’s development of algebra contribute to the Islamic religion? How did Al-Kwarizmi ‘s use symbols and how is this different from modern algebra?
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html In,H http://www.algebra.com/algebra/about/history/Al-Khwarizmi.wikipedia In,H http://www.math.umd.edu/~czorn/hist_algebra.pdf In, H http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html In, H
APPOLONIUS see conic sections http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Apollonius.html ARCHIMEDES see lever, screw, etc
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html
BABBAGE also see analytical engine and calculators
BANNEKER also see Black American mathematicians (and architects)
BLUME
BOOLE also see number theory, square numbers CANTOR also see infinity
Aczel, Amir; The Mystery of the Aleph : Mathematics, the Kabbalah, and the Search for Infinity; Washington Square Press; ISBN 0-7434-2299-6
CARDANO
DESCARTES (father of analytical geometry) http://www.groups.dcs.stand.ac.uk/~history/Mathematicians/Descartes.html DODGSON also see logic puzzles EINSTEIN also see relativity ERATOSTHENES also see primes, measure of earth,
ERDOS Hoffman, Paul; The Man Who Loved Only Numbers: Paul Erdos; Hyperion ISBN 0-7868-6362-5 Schechter, Bruce; My Brain is Open < >: The Mathematical Journeys of Paul Erdos; A Touchstone Book Simon and Schuster ISBN 0-684-85980-7
http://www.usna.edu/Users/math/meh/erdos.html In,R
ESCHER also see tessellations http://www.mcescher.com/ In (includes gallery) http://www.mathacademy.com/pr/minitext/escher/ In R (mathematical art)
EUCLID What did Euclid have to go on and what did he really contribute to mathematics? What is the difference between a postulate and a axiom?
Euclid, The Elements, Dover http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html In,H, R
EULER What are the practical uses of Euler circuits and can you make one? Why was the bridge problem important?
http://leonhard-euler.ask.dyndns.dk/ In H,R (incl. explanations of discoveries) http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html In (quotes)
FERMAT Aczel, Amir; Fermat’s Last Theorem: Unlocking the Secret of the Ancient Mathematical Problem; Four Walls, Eight Windows; ISBN 1-56858-077-0
Singh, Simon; Fermat’s Enigma; Anchor-Random House; ISBN 0-385-49362-2
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fermat.html In,H,R
FIBONACCI also see Fibonacci numbers http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Fibonacci.html In,R http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html I, In, R http://www.fibonaccisecrets.com/?PHPSESSID=214d6c9036bec7415369255fb640a7bd In
FLANNERY What did Sarah Flannery know that you don’t? What questions did she ask to make the discoveries she made?
Flannery, Sarah; In Code:A Young Woman’s Mathematical Journey;
Algonquin Books of Chapel Hill ISBN 1-56512-377-8
GALOIS
http://galois-theory.ask.dyndns.dk/ In,R
GAUSS GODEL Smullyan, Ramond; Forever Undecided: A Puzzle Guide to Godel; Alfred Knopf; ISBN 0-394-54943-0 http://www.usna.edu/Users/math/meh/godel.html In
GOLDBACH Papachristos, Petro; Uncle Petros & Goldbach’s Conjecture;
Bloomsbury; ISBN 1-58234-128-1 HARDY
Which is more important, practical or theoretical mathematics? What was Hardy’s “field “?
Hardy, G. H. ; A Mathematician’s Apology; Cambridge University or more recently, Dover; HERON HYPATIA also see ellipse, parabola)
KOVALEVSKY also see prime numbers) LAGRANGE also see four square metrics) http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Lagrange.html
LEIBNIZ
LISSAJOUS also see harmonograms/harmonographs LOVELACE also see number theory, computer programming MANDELBROT also see fractals
MOBIUS http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mobius.html
MONTALVO NASH Nasar, Sylvia; A Beautiful Mind; Touchstone; ISBN 0-684-85370-1 NEWTON NOETHER also see abstract algebra, clock arithmetic PAISANO also see statistics
PAPPAS
PASCAL http://mathforum.org/workshops/usi/pascal/ I http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html H
http://mathforum.org/workshops/usi/pascal/pascal_intro.html In http://www.bath.ac.uk/~ma2aap/project2.html In http://ptri1.tripod.com/ In http://a415software.com/matti/PascalsTriangle.html I
PENROSE http://www.nationmaster.com/encyclopedia/Roger-Penrose In http://haides.caltech.edu/~lifshitz/symmetry.html In http://www.geom.uiuc.edu/apps/quasitiler/about.html I POLYA
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Polya.html In, H
PYTHAGORAS See chapters from
Muir, Jane, Of Men and Numbers Smith, Sanderson; Agnesi to Zeno http://dtp.epsb.net/ict/students/gr8/pyth/task3.htm I http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Pythagoras.html In,H www.utm.edu/research/iep/p/pythagor.htm In http://www.cut-the-knot.org/Curriculum/Algebra/PythagoreanTriples.shtml I www.aboutscotland.com/harmony/prop.html In
RAMANUJAN Kanigel, Robert; The Man Who Knew Infinity: A Life of the
Genius Ramanujan; Washinton Square Press ISBN 0-671-75061-5 http://scienceworld.wolfram.com/biography/Ramanujan.html In,H,R http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ramanujan.html
In,R
RIEMANN Derbyshire, John; Prime Obsession: Bernard Riemann and the Greatest Unsolved Problem in Mathematics; A Plume Book Penguin ISBN 0-452-28525-9 Rockmore, Dan; Stalking the Riemann Hypothesis; Pantheon Books; ISBN 0-375-42136-x Sautoy, Marcus du; The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics; Perennial HarperCollins ISBN 0-06- 093558-8 http://www.groups.dcs.stand.ac.uk/~history/Mathematicians/Riemann.html In,R SOMERVILLE also see star shapes, multiples THALES
VENN How do Venn diagrams facilatate logical reasoning? Can all logic be demonsttated with Venn diagrams??
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Venn.html
In,H http://illuminations.nctm.org/index_d.aspx?id=384 I
WOMEN Flannery, Sarah; In Code:A Young Woman’s Mathematical Journey; Algonquin Books of Chapel Hill ISBN 1-56512-377-8 Henrion, Claudia; Women in Mathematics: The Addition of Difference; Perl, Teri; Women and Number: Lives of Women Mathematicians; World Wide Publishing Tetra, ISBN 0-933174-87-x http://www.awm-math.org/articles/notices/199107/henrion/ In, H MOBIUS STRIPS also see Mobius
MULTICULTURAL MATH BY CULTURE General Questions
How does the religion or philosophy of this culture influence the math and visa versa and how can this be seen in the representations of mathematical concepts in words or symbols?
In what ways is mathematical understanding dictated by the culture one is born into and how can this be seen in ?
What aspects of mathematical understanding might be easier for non-westerners to learn and understand and which might be more difficult?
What determines the number base that a culture develops? Ascher, Marcia; Mathematics Elsewhere: An Exploration of Ideas Across Cultures; Princeton Press ISBN ? Joseph, George Ghverghese; The Crest of the Peacock: Non-European Roots of Mathematics; Princeton Paperbacks ISBN 0-691-00659-8 Nelson, David and Joseph, George and Williams, Jullian; Multicultural Mathematics; Oxford; ISBN 0-19-282241-1
http://www1.eboard.com/eboard/servlet/BoardServlet?ACTION=BOARD_SHOW&SITE_NAME=cesp&BOARD_NAME=MultiMath&SESSION_ID=skpqgb43ak3r82w6081 (This is the e-board that Anne Ray created for Rutger’s Center for Effective School Practices)
http://www.enc.org/features/focus/archive/mathroots2/ In, R http://www.ethnomath.org/ In, H, R
AZTEC ARAB also see Islamic
How is the artistic sense of beauty represented in Arabic mathematics?
What are some of the ways Arab mathematics influences Arab music http://64.233.179.104/search?q=cache:rK2BWfl_EtoJ:math.unipa.it/~grim/Conf_
mahdi_1.ppt+algebra+Arab+%22history+of%22+-lessons&hl=en H http://www-gap.dcs.st-
and.ac.uk/~history/HistTopics/Arabic_mathematics.html#49 In
AFRICAN Eglash, Ron African Fractals: Modern Computing and Indigenous Designs; ISBN 0-8135-2614-0 Zaslavsky, Claudia; Africa Counts: Number and Pattern in African Culture; Lawrence Hill Books ISBN 1-55652-350-5 http://www.rpi.edu/~eglash/csdt.html I, In T
CHINESE How does the Chinese language facilitate the learning of mathematics? In what ways is the approach to mathematics different in the orient from the Western hemisphere?
Swienciki, Lawrence W; The Ambitious Horse: Ancient Chinese Mathematical Problems; Key Curriculum Press; ISBN 1-559-53461-3 http://www.roma.unisa.edu.au/07305/pythag.htm (Chinese “pythagorian”) In,H,R http://www.groups.dcs.stand.ac.uk/~history/Mathematicians/Zhu_Shijie.html In,H http://www.roma.unisa.edu.au/07305/chin.htm In,H
EGYPIAN http://www.saxakali.com/COLOR_ASP/history,af5.htm H, R
INDIAN also see Vedic Kanigel, Robert; The Man Who Knew Infinity: A Life of the Genius Ramanujan; Washinton Square Press ISBN 0-671-75061-5 http://members.tripod.com/~INDIA_RESOURCE/mathematics.htm H
ISLAMIC also see Arab
Tahan, Malba; The Man Who Counted: a Collection of Mathematical Adventures; WW Norton ISBN 0-393-30934-7
http://www.groups.dcs.stand.ac.uk/~history/HistTopics/Arabic_mathematics.html In, H http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html
In,H, R
http://www.hellam.net/twinsite/ In, H
JAPANESE LATIN AMERICAN - also see Quechua and Inca Urton, Gary; The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arthimetic; University of Texas ISBN 0-292-78534-8 MAORI MAYAN http://www.saxakali.com/historymam2.htm In, T
NATIVE AMERICAN Closs, Michael P (editor); Native American Mathematics; University of Texas ISBN 0-292-71185-9 ORIENT http://mathforum.org/geometry/rugs/ In MULTICULTURAL MATH BY TOPIC ABACUS see Abacus above KOLAM
How do Kolams relate to Euler circuits? What is the mathematics of Kolams and what “powers” does this have ?
ORIGAMI
Which geometric concepts are represented in origami What are the mathematical theorems of origami/
Franco,Betsy. Unfolding Mathematics With Unit Origami. Emeryville: Key Curriculum Press. 1999 Mitchell, David; Mathematical Origami; ISBN 1-899618-18-X Olson, A., Mathematics Through Paper Folding, National Council of Teachers of Mathematics, Reston, Virginia, 64 pp. (1975). http://www.geocities.com/snowflakegame/ I
http://www.mathworld.wolfram.com/Origami.html In,R http://www.merrimack.edu/~thull/OrigamiMath.html In, T http://www.paperfolding.com/math/ In ,H R http://cgm.cs.mcgill.ca/~athens/cs507/Projects/2002/ChristianLavoie/maths.html I (adv) TANAGRAM see separate listing QUIPUS
How might quipus have been used to represent numbers and prerform mathematical operations? Could quipus represent everything that written symbols can represent by using color, length and position ?
Ascher, Marcia and Robert Ascher; Mathematics of the Incas: Code of the Quipu; Dover; ISBN 0-486-29554-0 http://www.spanish.sbc.edu/MMLatAm/Quipus.html I, R MUSIC AND MATH
In what ways is music mathematical? Why do cultures have different scales and how does this relate to their mathematics ? Can math be heard musically? How is the symbolic representation of music related to the symbols of math Does the relative importance of rhythm and melody have any connection to the mathematics of a culture? What is the math of instrument making? What is the math of sound?
Ashton, Anthony; Harmonograph: A Visual Guide to the Mathematics of Music; Wooden ; ISBN 0-8027-1409-9 www.aboutscotland.com/harmony/prop.html In http://www.math.niu.edu/~rusin/uses-math/music/ In http://illuminations.nctm.org/index_d.aspx?id=489 I (computer sound waves) PENROSE TILES PHI see Golden Ratio
Livio, Mario; The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number; Broardway Books ISBN 0-7679-0815-5 http://ccins.camosun.bc.ca/~jbritton/ goldslide/jbgoldslide.htm>
http://www.slot-1.com/Foundation/default
PI (π) What are some of the applications of pi beyond the circle? To what decimal position is pi meaningful and what can be gained from going beyond this degree of exactitude?
Beckman, Petr; A History of Pi; St. Martin’s Griffin; ISBN 0-312-38185-9 Posamentier, Alfred & Ingrmar Lehmann; π A Biography of the World’s Most Mysterious Number; Prometheus ISBN 1-59102-200-2 The Joy of Pi; ISBN 0-8027-7562-4 http://dtp.epsb.net/ict/students/gr7/pi/task4.htm I www.joyofpi.com R, In http://members.tripod.com/egyptonline/history.htm H
POPULATION GROWTH *Use “Population Connection” disk – investigative simulation activities for MS and higher *Use COMAP #63 – A dynamical system that models fish populations. Uses calculator and MAPLE PC, Calc, IB http://illuminations.nctm.org/index_d.aspx?id=255 I
PRIME NUMBERS Derbyshire, John; Prime Obsession: Bernard Riemann and the Greatest Unsolved Problem in Mathematics; A Plume Book Penguin ISBN 0-452-28525-9 Rockmore, Dan; Stalking the Riemann Hypothesis; Pantheon Books; ISBN 0-375-42136-x Sautoy, Marcus du; The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics; Perennial HarperCollins ISBN 0-06-093558-8 http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html#55 H,R
PROBABILITY What are some important applications of probability? What is conditional probability?
Paulos, John Allen; Innumeracy: Mathematical Illiteracy and Its Consequences; Farrar, Strauss and Giroux ISBN 0-8090-5840-5
Peterson, Ivars; The Jungles of Randomness: A Mathematical Safari; John Wiley & Sons; ISBN 0-471-16449-6 Shaffner, George; The Arithmetic of Life and Death; Ballantine Books
ISBN 0-345-42645-2 Stewart, Ian; Does God Play Dice?; Blackwell; 0-631-23251-6 *Use COMAP #4 The Big Texas Lottery – Uses permutations to calculate
probabilities for winning combinations of numbers *Use COMAP #60 Polling Pitfalls – a lesson in conditional probability –
Introduction to conditional probability. PC- AP Stats *Use COMAP #70 Simple probability model for population genetic make up MS-
PC *Use COMAP #79 Imperfect Testing – Activities involving conditional
probability http://illuminations.nctm.org/index_d.aspx?id=290 I (chance in games) http://illuminations.nctm.org/index_d.aspx?id=377 I (stick or switch) http://illuminations.nctm.org/index_d.aspx?id=386 I (voting scenario)
PROPORTIONALITY http://illuminations.nctm.org/index_d.aspx?id=584 I http://illuminations.nctm.org/index_o.aspx?id=125 I (paper pool simulation)
RANDOM NUMBERS What are the defining characteristic of a series of random numbers? Can one number be “random?” What is the connection to probability?
* Use COMAP # 12 The Monte Carlo Method and Random Number Generators – Explores random number generators and soimple basics of Monte Carlo Method
REGRESSION *Use COMAP #66 Alcohol and Your Body – Calculate amount of alcohol in blood over time plus elimination factor Uses rations function and asymptotes MS – PC * Use COMAP #71 – correlation and regression modeling from data Activities MS – IM3 http://illuminations.nctm.org/index_o.aspx?id=135 I
SCIENCE AND MATH Cole, K.C.; The Universe and The Teacup: The Mathematics of Truth and Beauty; Harcourt Brace ISBN? Davis, Philip J & Reuben Hersh; Descartes’ Dream: The World According to Mathematics; Houghton Mifflin Paperbacks; ISBN 0-395-43154-9
Hersh, Reuben; What is Mathematics, Really?; Oxford Paperbacks; ISBN 0-19- 513087-1
Peterson, Ivars; The Jungles of Randomness: A Mathematical Safari; John Wiley & Sons; ISBN 0-471-16449-6 *Use COMAP #67 Testing for Steriod use Activities with short programs for simulations MS – PC
http://www.enc.org/ R In I http://www.sciencegems.com/math.html R (many connecting links by math
topic)
STATISTICS Shaffner, George; The Arithmetic of Life and Death; Ballantine
BooksISBN 0- 345-42645-2 * Use COMAP # 2 The 1992 Election - Uses statistics to generate confidence
intervals based on polling data. Cities several cases where errors were made. AP Stats * Use COMAP #62 Mathematics abnd the City Water Tower Data collection,
augmented matrices, used to study the flow of water from a container http://www.york.ac.uk/depts/maths/histstat/lifework.htm In, H, R
http://www.math.yorku.ca/SCS/Gallery/ (principals of graphic display) http://illuminations.nctm.org/index_o.aspx?id=136 I (cardiac output) http://illuminations.nctm.org/index_o.aspx?id=143 I (rational functions )
SYMMETRY What are the different kinds of symmetries and what mathematic operations relate to each of them? How many flat symmetries are there and what are they? Can artistic symmetry be represented mathematically? How does the meaning of symmetry change when discussing more than two dimensions?
Weyl, Hermann; Symmetry; Princeton Science; ISBN 0-691-02374-3 http://math.rice.edu/~lanius/Patterns/design2.html I In http://mathworld.wolfram.com/Symmetry.html In, R http://britton.disted.camosun.bc.ca/jbsymteslk.htm I http://mathforum.org/geometry/rugs/ In http://illuminations.nctm.org/index_o.aspx?id=138 I (rotations) http://illuminations.nctm.org/index_o.aspx?id=139 I (reflections) http://illuminations.nctm.org/index_d.aspx?id=474 I (translations) http://illuminations.nctm.org/index_d.aspx?id=475 I (glide reflections)
TANAGRAMS How does the Pythagorean theorem relate to tanagrams What new concepts are represented in supertanagrams?
TESSELLATIONS also see Escher
How are tessellations represented algebraically? How do three dimensional tessellations differ from two dimensional ones mathematically?
http://www.hellam.net/twinsite/ I http://mathforum.org/sum95/suzanne/whattess.html In and R http://mathworld.wolfram.com/Tessellation.html In and R http://www.geom.uiuc.edu/software/tilings/ R for I and In
TOPOLOGY http://topology.ask.dyndns.dk/ In , H, R
http://www.shef.ac.uk/nps/Wurble.html In (with applications) http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Topology_in_mathematics.html H,R http://geometrygames.org/ I, (games) http://mathworld.wolfram.com/Topology.html In,R
TRIGONOMETRY
Maor, Eli; Trigonometric Delights; Princeton Paperbacks ISBN 0-691-095 * Use COMAP #1 Viewing Earth from Space – Uses Geometry and Trigonometry to find the distance from a satellite to the earth’s horizon, and surface area viewed by the satellite at a given altitude IM3 - PC * Use COMAP #8 Latitude and Longitude – Uses Law of Cosines for a spherical triangle to find distance between two points on the surface of the earth Adv IM3 -PC *Use COMAP #65 Mathematics and Apollo 11 flight to the moon – Circular and elliptical orbits of satellites Trig, physics Adv IM3, PC http://www.groups.dcs.stand.ac.uk/~history/HistTopics/ In, H http://illuminations.nctm.org/index_d.aspx?id=383 I
VEDIC MATH How is Vedic math used in India? What are the benefits of learning Vedic math?
http://www.hinduism.co.za/vedic.htm In, H, T http://www1.ics.uci.edu/~rgupta/vedic.html In, R
http://www.mcs.drexel.edu/~gpmahesh/ved.html In,R
VORONOI REGIONS * Use COMAP #69 – Voronoi regions used to estimate rain fall (3 activities) MS, IM1 IM2, IM3 www.ics.uci.edu/~eppstein/gina/scot.drysdale.html In, T, I, R http://kandid.sourceforge.net/gal_voroni_1.html T, I (an art project)
WOMEN Flannery, Sarah; In Code:A Young Woman’s Mathematical Journey; Algonquin Books of Chapel Hill ISBN 1-56512-377-8 Henrion, Claudia; Women in Mathematics:The Addition of Difference; Perl, Teri; Woman and Number: Lives of Women Mathematicians; World Wide Publishing Tetra, ISBN 0-933174-87-x http://www.agnesscott.edu/lriddle/women/women.htm R, In http://www.math.umd.edu/~wim/#wim R
ZERO Why is zero so important? How has it’s representation and meaning developed What does the symbol allow us to do that the concept alone did not?
Kaplan, Robert; The Nothing that Is: A Natural History of Zero; Oxford ISBN 0-19-514237-3
Seife, Charles; Zero: The Biography of a Dangerous Idea; A Penguin Book; ISBN 0-14-029647-6
http://mathworld.wolfram.com/Zero.html In, R (including limits) http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html H, R http://mathforum.org/dr.math/faq/faq.0.to.0.power.html In ( 0^0)
Appendix C – Interesting Math Books (alphabetically arranged by author)
Aczel, Amir; The Mystery of the Aleph : Mathematics, the Kabbalah, and the Search for Infinity Washington Square Press; ISBN 0-7434-2299-6 Fermat’s Last Theorem: Unlocking the Secret of the Ancient Mathematical Problem; Four Walls, Eight Windows; ISBN 1-56858-077-0 Ascher, Marcia; Mathematics Elsewhere: An Exploration of Ideas Across Cultures; NJ, Princeton Press ISBN 0-91-07020-2 Ascher, Marcia and Robert Ascher; Mathematics of the Incas: Code of the Quipu; Dover; ISBN 0-486-29554-0 Ashton, Anthony; Harmonograph: A Visual Guide to the Mathematics of Music; Wooden; ISBN 0-8027-1409-9 Atalay, Bulent; Math and The Mona Lisa: The Art and Science of Leonardo da Vinci;
NY, Smithsonian Books ISBN 10-06-085119-8 Ball, W.W. Rouse; A Short Account of the History of Mathematics; Dover; ISBN 0-486-20630-0 Beckman, Petr; A History of Pi; St. Martin’s Griffin; ISBN 0-312-38185-9 Berlinsky, David; A Tour of the Calculus; Vintage; ISBN 0-679-74788-5 The Advent of the Algorithm; Harcourt ISBN 0-15-601391-6 Bunch, Bryan; The Kingdom of Infinite Number; W.H. Freeman and Company; ISBN 0- 7167-4447-3 Casti, John L; Five Golden Rules: Great Theories of 20th Century Mathematics – and Why They Matter; John Wiley & Sons; ISBN 0-471-19337-2 Closs, Michael P (editor); Native American Mathematics; University of Texas ISBN 0-292-71185-9 Cole, K.C.; The Universe and The Teacup: The Mathematics of Truth and Beauty; Harcourt Brace ISBN 0-15-100323-8 Darling, David The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes; Wiley; ISBN 0-471-27047 Davis, Philip J & Reuben Hersh; Descartes’ Dream: The World According to Mathematics; Houghton Mifflin Paperbacks; ISBN 0-395-43154-9 Also The Mathematical Experience
Derbyshire, John; Prime Obsession: Bernard Riemann and the greatest Unsolved Problem in Mathematics; A Plume Book Penguin ISBN 0-452-28525-9 Dilson, Jesse; The Abacus; St. Martin’s Press 1995 ISBN 0-312-10409-X Eglash, Ron African Fractals: Modern Computing and Indigenous Designs; Rutgers ISBN 0-8135-2614-0 {also see his web site with culturally designed simulations} Enzensberger, Hans Magnus; The Number Devil: A Mathematical Adventure; Henry Holt ISBN 0- 8050-6299-8 Fadiman, Clifton (editor); Fantasia Mathematica: Being a Set of Stories…..; Copernicus ISBN 0-387-94931-3 Flannery, Sarah; In Code:A Young Woman’s Mathematical Journey; Algonquin Books of Chapel Hill ISBN 1-56512-377-8 Franco, Betsy. Unfolding Mathematics With Unit Origami. Emeryville: Key Curriculum Press. 1999 Hardy, A Mathematician’s Apology; New York. Dover, 1950 Henrion, Claudia; Women in Mathematics:The Addition of Difference; Hersh, Reuben; What is Mathematics, Really?; Oxford Paperbacks; ISBN 0-19-513087-1 Hoffman, Paul; The Man Who Loved Only Numbers: Paul Erdos; Hyperion ISBN 0- 7868-6362-5 Archimedes’ Revenge:The Challenge of the Unknown The Joys and Perils of Mathematics; ISBN 0-393-02522-5 Higgins, Peter M; Mathematics for the Imagination; Oxford University press ISBN 0-19-860460-2 Huntley, HE; The Divine Proportion: A Study in Mathematical Beauty; Dover; ISBN 0-486-22254-3 Ifrah, Georges; From One to Zero: A Universal History of Numbers;Viking; ISBN 0-670- 37395-8 Joseph, George Ghverghese; The Crest of the Peacock: Non-European Roots of Mathematics; Princeton Paperbacks ISBN 0-691-00659-8
Kanigel, Robert; The Man Who Knew Infinity: A Life of the Genius Ramanujan; Washington Square Press; ISBN 0-671-75061-5 Kaplan, Robert; The Nothing that Is: A Natural History of Zero; Oxford ISBN 0-19-514237-3 Kaplan, Robert and Ellen Kaplan; The Art of the Infinite; Oxford; ISBN 0-19-517606-5 Livio, Mario; The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number; Broardway Books ISBN 0-7679-0815-5 Maor, Eli; Trigonometric Delights; Princeton Paperbacks ISBN 0-691-095 Mazur, Barry; Imagining Numbers (Particularly the Square Root of minus fifteen); …… ISBN 0-312-42187-7 McLeish, John; The Story of Numbers: How Mathematics Has Shaped Civilization;…. ISBN 0-449-90938-7 NUMBER: From Cave People to Computers, a Revolutionary View of Ourselves; Mlodinow, Leonard; Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace; A Touchstone Book Simon & Schuster ISBN 0-684-86524 Muir, Jane; Of Men & Numbers: The Story of the Great Mathematicians; Dover; ISBN 0-486-28973-7 Nasar, Sylvia; A Beautiful Mind; Touchstone; ISBN 0-684-85370-1 Nahin, Paul J; An Imaginary Tale: The Story of the Square Root of -1; ISBN 0-691-02795-1 Nelson, David and Joseph, George and Williams, Jullian; Multicultural Mathematics; Oxford; ISBN 0-19-282241-1 Papachristos, Petro; Uncle Petros & Goldbach’s Conjecture; Bloomsbury ISBN 1-58234-128-1 Paulos, John Allen; A Mathematician Reads the Newspaper; Beyond Innumeracy: Ruminations of a Numbers Man; Alfred A Knopf; ISBN 0-394-58640-9 Innumeracy: Mathematical Illiteracy and Its Consequences; Farrar, Strauss and Giroux ISBN 0-8090-5840-5 Once Upon a Number: The Hidden Logic of Stories
Perl, Teri; Women and Number: Lives of Women Mathematicians; World Wide Publishing Tetra, ISBN 0-933174-87-x Petkovi´c, Miodrag; Mathematics & Chess; Dover; 0-486-29432-3 Peterson, Ivars; The Jungles of Randomness: A Mathematical Safari; John Wiley & Sons; ISBN 0-471-16449-6 The Mathematical Tourist; WH Freeman; ISBN 0-7167-19533 Fragments of Infinity: A Kaleidoscope of Math and Art; John Wiley & Sons; ISBN 0-471-16558 Islands of Truth: A Mathematical Mystery Tour; WH Freeman; ISBN 0-7167- 2113-9 Posamentier, Alfred & Ingrmar Lehmann; π A Biography of the World’s Most Mysterious Number; Prometheus ISBN 1-59102-200-2 Rockmore, Dan; Stalking the Riemann Hypothesis; Pantheon Books; ISBN 0-375-42136-x Sautoy, Marcus du; The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics; Perennial HarperCollins ISBN 0-06-093558-8 Schechter, Bruce; My Brain is Open < >: The Mathematical Journeys of Paul Erdos; A Touchstone Book Simon and Schuster ISBN 0-684-85980-7 Seife, Charles; Zero: The Biography of a Dangerous Idea; A Penguin Book; ISBN 0-14- 029647-6 Shaffner, George; The Arithmetic of Life and Death; Ballantine Books ISBN 0-345-42645-2
Singh, Simon; Fermat’s Enigma; Anchor – Random House; ISBN 0-385-49362-2
Smullyan, Ramond; Forever Undecided: A Puzzle Guide to Godel; Alfred Knopf; ISBN 0-394-54943-0 Sossinsky, Alexei; Knots: Mateamatics with a Twist; Harvard University Press ISBN 0-674-01381-6 Steinhaus, H; Mathematical Snapshots; Oxford University Press ISBN ? Stewart, Ian; Does God Play Dice?; Blackwell ISBN 0-631-23251-6 Flatterland; Perseus ISBN 0-7382-0675-x From Here to Infinity: A Guide to Today’s Mathematics; Oxford; ISBN 0-19-283203-6
Swienciki, Lawrence W; The Ambitious Horse: Ancient Chinese Mathematical Problems; Key Curriculum Press; ISBN 1-559-53461-3 Tahan, Malba; The Man Who Counted: a Collection of Mathematical Adventures; WW Norton ISBN 0-393-30934-7 Turnbull, Herbert Westren; The Great Mathematicians; Barnes & Noble, ISBN 0- 7607-1673-0 Urton, Gary; The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic; University of Texas ISBN 0-292-78534-8 Wells, David; Prime Numbers: The Most Mysterious Figures in Math; Wiley ISBN 0-471-46234-9 Weyl, Hermann; Symmetry; Princeton Science; ISBN 0-691-02374-3 Zaslavsky, Claudia; Africa Counts: Number and Pattern in African Culture; Lawrence Hill Books ISBN 1-55652-350-5
