Work Session #1: Create a Website
Work Session #1 completed.
Work Session #2a: Add One Reference In Each Bibliographic Category
History of Mathematics:
Boyer, C. B. (1968) History of Mathematics. John Wiley and Sons, Inc.
Focusing primarily on the development of European mathematics -- while not totally ignoring that of the
Chinese, Indian and Arabic civilizations -- this book chronicles the way numbers have been used, from their simple beginnings
to the complexities of modern use of mathematics. While there is an attempt to make this vast history "make
sense," that is, in compiling coherent stories of development, the author interjects copious amounts of facts and number-examples
to provide a seemingly thorough history of the subject.
Multicultural Mathematics:
Joseph, G. G. (1991) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton
University Press.
The author of this book examines the oft deep-seated notion that euro-centric methods are the best
and most effective way of "doing" mathematics, and shows how such prejudice leads to the perception that differing methods,
both in history and the present (taking Ramanujan as an example), are inferior and thus "ignored, devalued or distorted" to
an unjustifiable degree. The book explores the "roots and shoots" of mathematics throughout ancient civilizations, showing
how these peoples and their various methods of thinking prove highly capable of complex and creative mathematical
ideas, despite their often fundamental differences with current European structures.
Activities and Other Educational Resources:
Haven, K. (1998) Marvels of Math: Fascinating Reads and Awesome Activities. Teacher Ideas Press.
This book, intended for teachers, attempts to make the history of mathematics more interesting for students.
Themes covered include the concept of zero, negative numbers, algebraic equations, and more. Each story includes a vocabulary
section, discussion questions, and suggestions for projects and activities.
Work Session #2b: Purchase References
Three references purchased; Work Session #2b completed.
Work Session #2c: Explore Websites
Notes on Websites:
"A Time Line of Mathematicians": Divides the history of mathematics into seven time periods, and for each time period
provides a time line showing the lives of significant mathematicians of that era.
"History Topics Index": Provides a large amount of quality links to articles pertaining to mathematics in various cultures
as well as other math topics; a very rich web-based reference tool.
"A History of Pi": Details the history of the search for the value and meaning of pi, from its nearly untraceable roots
in prehistory to contemporary squabbles that highlight the social influences, sometimes repressive, toward the acceptance
of new mathematical truths.
Two New Websites:
"A History of Mathematics in Africa": An extensive resource on the history of mathematics in Africa.
"Abacus: The Art of Calculating with Beads": Provides an introduction to the ancient calculating machine, its history,
how to use it, as well as several interesting articles on abacus vs. computer (or man) competitions, abacus analysis,
and links to just about everything else to do with an abacus on the world wide web.
Bibliography:
Boyer, C. B. (1968) History of Mathematics. John Wiley and Sons, Inc.
Joseph, G. G. (1991) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton
University Press.
Menninger, K. (1969) Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications, Inc.
Work Session #3: A History of Math Timeline
To see the timeline, please click on "Timeline" on the Navigation Bar to your upper left.
Bibliography for "A History of Math Timeline"
Books
Boyer, C. B. (1968) History of Mathematics. John Wiley and Sons, Inc.
Joseph, G. G. (1991) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton
University Press.
Menninger, K. (1969) Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications, Inc.
Websites
Work Session #4: Diversifying the History of Math Timeline
To see the diversified timeline, please click on "Timeline" on the Navigation Bar to your upper left.
Other examples of references relative to a multiculturally diverse understanding of mathematics:
Books
Joseph, G. G. (1991) The Crest of the Peacock: Non-European Roots of Mathematics. Princeton
University Press.
Menninger, K. (1969) Number Words and Number Symbols: A Cultural History of Numbers. Dover Publications, Inc.
Websites
Work Session #5: Developing Instructional Applications: Historical Contributions in their
Social Context
Please click on "Three Lesson Plans" on the Navigation Bar to your upper left to view the lesson plans created in
this work session.
Work Session #6: Securing Professional Feedback on Your Instructional Plans
To satisfy the requirements for this work session, I decided to contact Mr. Justin Rotter, a Mathematics Teacher at Rochester
High School, in Rochester, WA. Justin has lived and taught in Rochester, a small town in southern Thurston County, for
nearly his entire life. While Rochester is a small town, it is directly adjacent to the Chehalis Indian Tribe Reservation,
and thus is relatively diverse in ethnicity, in comparison to other school districts in Southwest Washington. Justin
has been teaching math at Rochester High School for five years, and in the opinion of all that I've talked to has excelled
in the process.
Justin reviewed my lesson plans, and delivered me the following letter:
Mr. Mano,
The lesson plans
you sent me to review seem very well planned and offer students a good look into the mathematical world away from simple arithmetic. They are ambitious lesson plans that might require a good deal of class time. Because of this I might use these as unit projects stretching over a couple of weeks,
or I might use them during WASL testing weeks when students tend to get burned out on traditional mathematics lessons.
The “Mathematics
in Social Context” lesson is a great way to introduce several theorems in mathematics that you might be working on in
the classroom. I would suggest using this lesson to introduce the importance
of formal proofs in Geometry, or you could use this lesson to discuss the difference between inductive and deductive reasoning. Also, I would try to find some particular topics or theorems in your curriculum that
were originally looked at skeptically by the mathematical community, but were ultimately proven to be true.
The “Women in
Mathematics” lesson is great way to break down some of the social myth that men are more suited to succeed in a mathematical
or scientific field. I would suggest telling students that they may use any notes
they take during the presentations on the exam at the end. This may keep students
more focused on the group presenting, and it will help foster the note taking skills needed to succeed in college. As far as women in Mathematics, be sure to take a look at Emmy Noether.
She was a remarkable figure in Mathematics around the turn of the 20th century.
The “Chaos Theory”
lesson seems to take a lot of the aspects of everyday life (i.e. weather) and relate them to Mathematics. Honestly, I don’t have much experience with teaching Chaos Theory, but the lesson seems well planned
with lots of hands-on learning. Depending on the experience of your students
with the complex number system, you could also look at the Mandelbrot Set, a set of complex numbers that produces chaotic
fractal images.
Justin Rotter
Rochester High School
Math Dept. Chair
Work Session #7: Reflection Paper
Reflection Paper:
As a student
in my pre-adult years, I had no idea the extent to which other cultures, across vast reaches of time and space, had contributed
to mathematics; or, in some cases, had devised different, and yet equally as valid, ways of doing mathematics than what I
had learned. Perhaps some of these historical roots of mathematics were presented
in little sidebar columns in my school math books. And yet, I remember nothing
of them, probably because they were skimmed over, if perused at all, by the teacher or myself.
I can recall no math lesson focused primarily on math history, let alone the multicultural roots of mathematics.
I first became
consciously aware of these roots while in the process of obtaining my Masters in Teaching degree, a few years ago, at City University. Their program did an excellent job of implementing diverse practices, and multicultural awareness, into
our teacher training. Thus, reinforced by this course, I feel very strongly about
introducing the history of mathematics with an emphasis on multiculturalism to prospective math students I may teach in the
future. Specifically, I would hope to, in the first few days of class, provide
students a broad scope of the history of mathematics; and then to introduce specific topics or persons as we begin studying
a type of mathematics appropriate to that topic or person. In so doing, I believe
students will gain a greater respect and appreciation for mathematics, and to see it as the foundation of much of what surrounds
us in this modern age.
The resources
I consulted for this course, The Multicultural History of Mathematics, all proved interesting to me. It is only a pity that I do not have time to read them all cover to cover, although I may be able to in
the future, and am glad I was able to purchase three of them for that purpose. However,
the internet proved to be my most valuable resource on this topic, and I was surprised at the large number of quality sites
on the history of mathematics that exist on the World Wide Web. I gained a greater
appreciation of the subject because of this; and certainly it also reinforced in me the vast abundance of resources on the
internet for any topic I might research in the future.
The independent
nature of this course worked well for me, as it has always worked well for me throughout my college years, beginning with
my time at The Evergreen State College in Olympia, WA, where self-initiative is an essential component to learning. I have no problem with working independently, or with others in a more traditional classroom, and frankly
just love learning, period.
I have no
suggestions to improve the course design.
