M326K PROJECT: HISTORY OF NUMBERS TIMELINE Spring 2004
Final Project Due Date: Thursday, February 19
Progress Report Due Date: Thursday, February 5
Note: Standard VI of the Texas State Board for Educator Certification states: "The mathematics teacher understands the historical development of mathematical ideas, the interrelationship between society and mathematics, the structure of mathematics, and the evolving nature of mathematics and mathematical knowledge." This standard is the basis for the UTeach Portfolio requirement to "Illustrate knowledge of the history and cultural context of mathematics; in particular, the evolution of mathematical concepts." This project should give UTeach students a good start on this portfolio requirement.
Overview: This project is to be done in groups of three students. (If the class size is not evenly divisibly by 3, then one or two groups of two will be allowed.)
Your assignment is to create a timeline of the development of number concepts and notations. The format of your timeline is up to you. It might be a paper, a scroll, an accordion fold, a notebook with some fold-out pages, a web site, or some combination of these. The only constraint on format is that it must be something I can readily carry to my office or access on the computer. In particular:
Progress Report: You will need to turn in a progress report on Thursday, February 5. Each group member should have researched at least one print source by then. Your progress report should include
1. In your timeline, you must include the first use (time and place) in Western culture of each of the following. (You may not be able to pinpoint all of these exactly, but should be able to give approximate dates and places.) For our purposes, "Western culture" is defined as including Mesopotamia, Egypt, Europe , and North America after European influence. (This definition is intended to include the development of the mathematics taught today in North America, Europe, and many other parts of the world.)
2. Since one purpose of this project is to become familiar with a variety of resources in the history of mathematics, you are required to use the following variety of resources in researching your project:
-> See more information below on what references are or are not acceptable.<-
3. You must give a reference for each fact you mention.
-> See more information below on how to do this.<-
4. Exact quotes must be placed in quotation marks. (A long quote may be indented from surrounding text, with an introduction clearly indicating that it is a quote.) An exact reference (including page numbers) must be provided for each quote. Copying material without providing proper indications that it is a quote or without giving the source(including page number) is plagiarism and is considered academic dishonesty.
5. You must include a list of the references you used.
-> See more information below on the appropriate format for references.<-
6. You must also include in your project or hand in with it a discussion of the implications of what you have learned in your project for teaching and learning mathematics.
7. One project is to be turned in for the entire group. In addition, each group member must write and turn in individually the following items:
In most cases, all students in a group will receive the same grade. However, in cases where there is convincing evidence of very uneven participation, different students may be given different grades. Also, a student who omits their individual part described in item 7 , or whose individual report is below par, may receive a lower grade than the other students in the group
A "C" project will satisfy all of the minimum requirements (items 1 - 7 above) adequately, with at most 3 omissions or errors in the twenty-five required "first uses", and will be organized and written well enough to convey information clearly without distracting additions, errors or sloppiness.
An "A" project will meet all the requirements for a "C" grade and in addition include at least two of the following features in substantial amounts:
A "B" project will be between a C and an A project.
A "D" or "F" project will not meet the minimum requirements. In particular, a project involving plagiarism will receive a grade of D or F.
MORE ABOUT REFERENCES
A. The following books have been put on reserve at the PMA library (fourth level of RLM) for this class. They may be checked out overnight. Please do not check out too many of these books at once, so others may use them. If you have difficulty checking out some books on this list, please let me know, so I can change them to library use only.
Bashmakova and Smirnova, The Beginnings and Evolution of Algebra
Berlinghoff and Gouvea, Math through the Ages; A Gentle History for Teachers and Others
Cajori, History of Elementary Mathematics
Cajori, History of Mathematical Notation, Vol. 1
Cajori, History of Mathematics
Danzig, Number: The Language of Science
Eves, Great Moments in Mathematics
Eves, Introduction to the History of Mathematics
Gazale, Number: From Ahmes to Cantor
Gillings, Mathematics in the Time of the Pharoahs
Gittlen, History of Mathematics
Joseph, The Crest of the Peacock: Non-European Roots of Mathematics
Katz, A History of Mathematics
Martzloff, A History of Chinese Mathematics
NCTM, Historical Topics for the Mathematics Classroom
Smith, History of Mathematics, Vols. 1,2
Swetz, Frank, Capitalism and Arithmetic
Swetz, Frank, From Five Fingers to Infinity
Wilder, Evolution of Mathematical Concepts
B. The following additional sources are also on reserve at the UT libraries indicated:
Companion encyclopedia of the history and philosophy of the mathematical sciences.
(QA 21 C645 1994), on permanent reserve in both the PCL and PMA libraries is
Suzuki, Jeff, A History of Mathematics, on reserve at UGL for M 315C.
C. You do not need to restrict yourself to the books listed above. However, the following books are not acceptable references, since they contain inaccuracies:
Bell, Men of Mathematics.
Boyer, Carl, A History of Mathematics
Ifrah, From One to Zero
Ifrah, The Universal History of Numbers
Menninger, Number Words and Number Symbols
II. Web sites
A. Here are some suggestions of web sites you may use:
David E. Joyce's History of Mathematics web site, http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html
The MacTutor History of Mathematics Archive,
Jeff Miller's Earliest Uses of Various Mathematical Symbols web site, http://members.aol.com/jeff570/mathsym.html
Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics web site
History of Negative Numbers web site, http://www.ma.utexas.edu/users/mks/326K/Negnos.html
B. Since web sites vary tremendously in quality, if you want to use a web site other than the ones above, you must check it out with me before you use it.
C. You may not use a web site written by a student as a reference for your project.
III. Professional Journals
Here are some examples of professional journals that you might use as references. If you wish to use other periodicals as sources, be sure to check them out with me for suitability first.
The Mathematics Teacher. This is the professional journal for secondary math teachers.
Mathematics Teaching in the Middle Grades. This is the professional journal for middle grades math teachers.
The College Mathematics Journal. This is a journal aimed at students and their teachers in the first two years of college.
Mathematics Magazine publishes articles related to college mathematics.
The American Mathematical Monthly. This contains a wide range of expository articles on mathematics
The Mathematical Intelligencer publishes expository articles about mathematics, mathematicians, and the history and culture of mathematics.
IV. How to List References . Use the format for references that is used in the publications of the National Council of Teachers of Mathematics. Here are some examples:
Book with Single Author:
Boyer, Carl, A History of Mathematics.
Book with More than One Author:
Boyer, Carl B. and Utta C. Merzbach. A History of Mathematics. 2nd ed. New York: John Wiley & Sons, 1989.
Book with Editor:
Calinger, Ronald, ed., Classics of Mathematics. Englewood Cliffs, N.J.; Prentice Hall, 1995.
Book with More than One Editor:
Swetz, Frank, John Fauvel, and Otto Bekken, eds. Learn From the Masters! Washington, D.C.: Mathematical Association of America, 1995.
Article from a Journal:
Espenshade, Pamela H. "A Text on Trigonometry by Levi Ben Gershon 1288 - 1344." Mathematics Teacher 60 (October 1967): 628 - 37.
Article from a Book:
Bowsher, Lester E. "History of the Terms 'Ellipse,' 'Hyperbola,' and 'Parabola.' " in Historical Topics for the Mathematics Classroom, pp. 222 - 24. Reston, Va.: National Council of Teachers of Mathematics, 1989
"The MacTutor History of Mathematics Archive." www-history.mcs.st-and.ac.uk/~history/
Book Also Available at a Website
National Commission on Excellence in Education. A Nation at Risk: The Imperative for Educational Reform. National Commission on Excellence in Education, 1983. Available at www.ed.gov/pubs/NatAtRisk. World Wide Web.
(You can find more examples at http://my.nctm.org/eresources/mt/reference_mt.asp or by looking in recent copies of the Mathematics Teacher.)
V. How to give references for facts. Use the format used in the publications of the National Council of Teachers of Mathematics. Example:
If you are stating that the first use of the word xirxium was in Austin, Texas on December 16, 1982, and your source for this information was p. 13 of the book by Jones published in 1984 that is listed in your list of references, you would write:
The first use of the word xirxium was in Austin, Texas on December 16, 1982 (Jones, 1984, p. 13).
If there are two books or articles listed in your list of reference that are both by Jones and both published in 1984, you need to list their dates in your list of references as 1984a and 1984b; then you refer to these books as (Jones, 1984a) and (Jones, 1984b)