Math 107 Math in Society: Ethnomathematics
Syllabus
#5947 Section A 12:30p-1:20p Daily Room 8-2 5 credits
Instructor
John Kellermeier
Office
Bldg. F1, Room 57
Phone
253-566-5303
Email
jkellermeier@tacomacc.edu
Office Hours
11:30-12:20 Daily
Course Introduction
Course
Description
A general education course investigating quantitative reasoning and its applications and role in society.
Topics may include graph theory, statistics, coding, game theory, symmetry, and geometric and numerical
patterns. Mathematical theory combined with quantitative skills will be used in applications to a variety of
problems encountered in mathematics and the world.
This section will be taught with the theme of ethnomathematics: an investigation of the use and
development of quantitative reasoning within various cultural contexts arising in response to problems,
struggles, and endeavors of human survival and development. The cultural contexts to be studied will be
taken from around the globe both historically and contemporarily.
Course
Overview
Math 107 is offered as a quantitative skills course for students whose majors have no specific mathematical
requirements. Although some topics taught in the course will require algebra and graphing skills at the
Intermediate Algebra level, the emphasis of the course will be applications that are not highly algebraic in
nature.
This section offers a unique opportunity for students to gain a multicultural perspective on mathematics.
Ethnomathematics studies how people within various cultures develop techniques to explain and
understand their world in response to problems, struggles, and endeavors of human survival, including not
only material needs and concerns but also such endeavors as art and spirituality. In this course we will use a
variety of modes of learning including reading, writing, hands-on activities, and problem solving.
Teaching
Philosophy
My teaching philosophy is based upon the concept of connected teaching where learning begins with the
student and teachers are to be midwives helping students to give birth to their own knowledge. I strive to
develop an atmosphere where students feel comfortable and respected while at the same time challenged
and engaged in their own learning. This involves creating a classroom environment where students feel free
to risk asking questions, making mistakes, taking guesses and using their intuition to learn the material.
My classroom technique is dominated by the problems approach. This syllabus contains a daily schedule of
topics to be covered, along with reading assignments and exercises. Students are expected to read the
assignment before coming to class and to have at least attempted some assigned problems. Then in class,
students will be asked to volunteer to write their solutions to problems on the board. As an incentive, you
will be given extra credit for doing so. Your solutions do not have to be correct to be written on the board.
In fact, I encourage you to present the problems for which you have not gotten a complete solution.
The problems written on the board will serve as the basis for discussion of the material. I will ask you to
explain what have written on the board. As instructor, my job will be to oversee the ensuing discussion and
any revisions required in the presented solutions, to ensure that all necessary topics are covered in sufficient
depth. In particular, I will draw attention to the thinking processes that you use in solving problems and the
way in which these solutions are written. These discussions will give an example of how to think
mathematically about the material covered and how to arrive at a well-reasoned and well-written solution.
Time permitting we will end class by working in groups on additional problems. On most days this
approach means that I will do little or no lecture. Instead, you will generate their own learning. This does
not mean that you will be asked to teach yourself. Rather, this approach is designed to create a community
of learners working together with the teacher as the central guide of this community.
For more information see "Feminist pedagogy in teaching general education mathematics: Creating
the riskable classroom."
Course
Objectives
The Math Department Program Learning Outcomes referred to in the course learning objectives below are:
1.
2.
3.
4.
5.
Create, interpret, and analyze graphs and charts that communicate quantitative or relational
information.
Determine, create, and use appropriate and reasonable mathematical constructs to model,
understand, and explain phenomena encountered in the world.
Determine and carry out an appropriate algorithm to solve problems that are amenable to
mathematical solutions.
Communicate mathematical information formally, using appropriate math notation and
terminology, and informally by using everyday language to express ideas.
Use technology to analyze and solve mathematical problems and to effectively communicate
solutions to problems, particularly those that cannot be solved efficiently by other means.
Upon successful completion of Math 107, the student should be able to:
1.
2.
Discern and appreciate the use of mathematics in many facets of society. (1,2)
State concrete examples of how quantitative reasoning and mathematical techniques can and have
been used to model and solve real world problems. (2,3,4)
3. Demonstrate the use of quantitative reasoning skills and problem solving in areas they can be
expect to encounter in their own lives and cultures. (2,3)
4. Use logic and critical thinking skills to read, organize and analyze technical information. (4,5)
5. Identify appropriate algorithms and correctly perform them in order to solve elementary problems
that emulate some of society's problems. (3)
6. Demonstrate knowledge of some topics of current interest in mathematics. (2)
7. Create and interpret mathematical graphs and charts. (1)
8. Solve problems, organize and write clear descriptions of how these problems are solved and how
mathematics is used in solving problems including correct mathematical notation. (3,4,5)
9. Use a calculator and/or computer software as appropriate. (5)
10. Work in small groups on group problems or projects. (4)
In addition upon successful completion of the Ethnomathematics section of Math 107, the student should be
able to:
1.
2.
3.
4.
5.
6.
7.
State concrete examples of how quantitative reasoning and mathematical techniques have been
used to model and solve real world problems by a variety of peoples both historically and globally.
Describe the way in which mathematics is developed by all people in response to the problems,
struggles, and endeavors of human survival and development including not only material needs
and concerns but also such endeavors as art and spirituality.
Recognize and appreciate the use and development of mathematics within a variety of cultural
contexts including subordinate cultures.
Demonstrate the use of quantitative reasoning skills in their own lives and the use and
development of mathematics within their own cultures.
Demonstrate an understanding of implicit and explicit mathematical concepts found in various
world cultures. Such concepts may correspond to western topics such as, but not limited to, logic,
geometry, probability, combinatorics and graph theory.
Analyze the effect of culture on the development of mathematical ideas including the detrimental
effects dominant cultures have had on the mathematics of subordinate cultures.
Identify, evaluate, and present information on those people and groups outside of the mainstream
image of mathematicians who have contributed to the development of mathematics and
ethnomathematics.
8. Solve problems, organize and write clear descriptions of how problems are solved and
mathematics is developed.
Prerequisites
Before taking Math 107 you must have
1.
MATH-095 or TMATH-100 with a "C" or better or assessment above MATH 095, and
2. Completed READ 095 or ENGL 095 with a "C" or better or assessment above READ-095 or
ENGL 095.
Materials
Required
No textbook is required. All readings for this course will be found online through links in the Course
Schedule
A scientific or graphic calculator is required
Course Requirements and Assignments
Attendance and
Participation (1
point per day)
This class is highly interactive. Attendance is essential.
Students are expected to be in class and to participate in all discussions and activities each day.
Students will receive one point each day (excluding exam days) for arriving to class on time, staying to
the end of class, and participating in all activities.
Each class will end when students are given a form asking for their name, the date and answers to the
two following questions:


What is the most important thing you learned in class today?
What is the main question you still have?
Students must fill out and hand in this form to be counted as present.
Reading Quizzes
(3 points each)
Each class with a reading assignment will begin with a five-to-seven-minute quiz covering the readings
for the day. Notes may be used but not the readings themselves. Quizzes will contain eight matching
questions; six correct answers will earn a perfect score. Students arriving after the quizzes have been
passed out must request a reading quiz. Late arrivals will not be given extra time. The lowest quiz
score will be dropped. There are no make-up reading quizzes.
Study Groups
Students are required to form study groups consisting of 2 to 4 students. These groups must be formed
by the fourth day of class. Each group must then notify the instructor of their group name and the
names of the members of the group. Students will not be able to receive credit for Group Quizzes or
Projects without being a member of a study group.
Group Quizzes
(20 points each)
There will be a take home group quiz approximately once a week. Group quizzes will be due on the
first class following the class in which they are assigned. Group quizzes are posted on the Course
Schedule. It is the responsibility of each study group to print a copy of this quiz, complete all
problems, and hand it in collectively. In order to receive credit, each student must author at least one
problem on each Group Quiz.
Exams (100
points each)
There will be three exams. One 8-1/2 X 11 inch sheet of notes may be used.
Group Biography
Project (50
points)
Each study group must choose two mathematician at least one of which is not a white male and
research their lives and work. A five to ten minute presentation will be required comparing their lives
and work. The choice of mathematicians must be approved by the instructor. No two groups may
choose the same persons. Each group must hand in a paper copy of their presentation. In addition, each
student must complete and hand in a Group Evaluation Form. This will be used in determining the
grade each student earns for the project. Failure to hand in a Group Evaluation Form will result in a
grade of zero. More information can be found on the Projects page.
Group Problem
Project (60
points)
Each study group will choose a problem that requires the development of a mathematical solution.
Each group will then derive a solution which will be presented during the final exam period. The
presentation must include visual aids and must involve every member of the study group. In addition,
each group will write a paper describing their group problem solving process. Note that only one paper
is required for each group. In addition, each student must complete and hand in a Group Evaluation
Form. This will be used in determining the grade each student earns for the project. Failure to hand in
a Group Evaluation Form will result in a grade of zero. More information can be found on the Projects
page.
Homework
Problems and
Extra Credit
Assigned homework problems from the Worksheets will not be collected. However, they should be
attempted before class they are assigned. We will often base our discussion of the day's topic on the
homework problems that students present or put on the board. Consequently, it is up to the members of
the class to be sure that problems they wish to discuss have attempted solutions written on the board.
This means that each student should attempt some problems from throughout the assignment and not
just the first few.
Any student who writes an attempted solution to a homework problem on the board receives 1 extra
credit point. This means 1 extra credit point for a solution regardless of whether the solution is correct
or not. In fact, it is the incorrect solutions from which we will learn best.
Be prepared to spend a minimum of two hours a day on work outside of the classroom.
No Questions
Asked Coupon
Each student will be given one No Questions Asked Passes for use during the quarter. This pass will
allow a student to turn in one assignment late after the due date. To make use of the No Questions
Asked Pass for a late assignment, simply write NQA at the top of the first page of the assignment when
it is handed in. Include the name of the person using the NQA pass if the assignment is a Group Quiz.
At the end of the quarter, an unused No Questions Asked Pass will automatically earn the student five
extra credit points.
Grading
The grading of each individual assignment or exam will be based on your ability to demonstrate and
communicate your understanding of a given concept or skill. Accordingly all work and steps must be
shown as well as the final answer. Correct answers with no back-up work will receive no credit.
Letter Grades
Grades will be determined according to the following scale:
Grade
A
A-
B+
B
B-
C+
C
C-
D+
D
Percent
93
90
87
83
80
77
73
70
67
63
Course Policies
Withdrawals
The procedures for dropping this class are in accordance with the rules outlined in the TCC Catalog.
Students may drop a course during the first 10 calendar days of the quarter and no grade will appear on
their transcript. After that, through the 50th calendar day, a student may withdraw with a grade of W.
After the 50th day you must request an instructor withdrawal (a grade of WI) from the instructor. No
requests will be considered after the 9th week of classes.
Incompletes
Incompletes are not given except under very unusual circumstances, which must be discussed with the
instructor. Typically an incomplete is only given when a student who is doing well in the class misses a
small amount of work (such as the final) due to an emergency.
Disruptive
Behavior
Disruptive behavior and hostility will not be tolerated either in class or in communication with the
instructor outside of class. To foster a positive learning environment, students are expected to maintain
a respectful attitude toward classmates, the instructor, and opinions that differ from their own. Those
who are disruptive or hostile or fail to participate in a respectful manner will be told to leave class and
be counted as absent. The student may not return to class until she or he has made an appointment with
the instructor and come to an agreement with the instructor as to how to improve the behavior.
Cell Phones and
Mobile Devices
All cell phones and mobile devices must be put into silent mode before class begins. Having a cell
phone or mobile device that rings in class may be considered disruptive behavior (see above). Any use
of a cell phone or mobile device in the classroom must be related to learning. This does not include
sending or reading text messages but does include accessing the course web site mobile menu.
Students with
Special Needs
All students are responsible for all requirements of the class, but the way they meet these requirements
may vary. If you need specific auxiliary aids or services due to a disability, please contact the Access
Services office in Building 7 (253-566-5328). They will require you to present formal, written
documentation of your disability from an appropriate professional. When this step has been completed,
arrangements will be made for you to receive reasonable auxiliary aids or services. The disability
accommodation documentation prepared by Access Services must be given to me before the
accommodation is needed so that appropriate arrangements can be made.
Academic
Dishonesty
As stated in the TCC Catalog, "Students are expected to be honest and forthright in their academic
endeavors. Cheating, plagiarism, fabrication or other forms of academic dishonesty corrupt the learning
process and threaten the educational environment for all students."
Students who engage in behaviors that may be interpreted as academic dishonety will receive a zero
score on the assignment in question. A second offense will result in a grade of E for the course.
Late Work
All work to be handed in such as Group Quizzes and Projects must be handed in on the day it is due
either in class or in the instructor's mailbox with a time stamp given by the faculty secretary. Late work
will be accepted only with a No Questions Asked Pass.
Visitors in Class
If you intend to bring visitors to class (including children), you must get the permission of the instructor
first. Permission will not automatically be given.
Food and
Beverages
Students may bring food and beverages to class as long as they do not distract other students and clean
up after themselves.
Classroom
Concerns or
Disputes
If you have questions or concerns about this class or your instructor, please talk to your instructor about
your concerns. If you and your instructor are unable to resolve your concerns, you may talk with the
Department Chair of the Mathematics Department, Carol Avery, Building F2 Room 7 (253-460-44297).
The Chair can assist with information about additional steps, if needed.
Changes
The instructor reserves the right to make changes to this syllabus during the quarter. Any changes made
will be announced in class and incorporated into this course website.
Schedule
All readings are from the Internet and can be accessed by clicking on the title of the reading. Students are expected to do the assigned
readings before the day it is to be discussed and come to class prepared to take a short reading quiz.
In addition, homework problems in the daily worksheet should be attempted before class as well. We will often base our discussion of
the day's topic on the homework problems that students present or put on the board. Consequently, it is up to the members of the class
to be sure that problems they wish to discuss have attempted solutions written on the board. This means that each student should
attempt some problems from throughout the worksheet and not just the first few. Remember, any student who writes an attempted
solution to a homework problem on the board receives 1 extra credit point.
A majority of the problems should be completed after the topic is discussed. Any remaining problems should be completed as a means
of studying for exams.
Date
Topic
Reading
Mar 30
Introduction
Course Syllabus and Schedule
Mar 31
Defining Ethnomathematics
Culture and Mathematics
Ethnomathematics Examples
Apr 1
How People Count
How Menstruation Created Mathematics
Tally Sticks
Apr 2
Number Words
Number Words from Around the World
Apr 3
Biography Project Research Day
Work Due
Apr 6
Number Words (continued)
Apr 7
Egyptian Number Symbols
Egyptian Hieroglyphic Numerals
Apr 8
Aztec and Mayan Number Symbols
Aztec Tribute Record Numerals
Mayan Numerals
Apr 9
Aztec and Mayan Number Symbols (continued)
Apr 10
Babylonian and Hindu-Arabic
Number Symbols
Babylonian Numerals
Hindu-Arabic Numerals
Apr 13
Chinese Number Symbols
Chinese Numerals
Biography Project Part One
Due
Apr 14
Chinese Number Symbols (continued)
Apr 15
Chinese Number Symbols (continued)
Apr 16
Roman Numerals
Roman Numerals
Apr 17
Incan Quipu
Incan Quipu
Apr 20
Review for Exam 1
Apr 21
Exam 1
Apr 22
Traceable Graphs
Apr 23
Biography Project Research Day
Apr 27
Mirror Curves
Shongo Networks
More Network Designs
Mirror Curves
Page of Dots
Apr 28
Mirror Curves (continued)
Apr 29
Mathematical Principles in Art and
Craft
Mathematical Principles in Native
American Petroglyphs
Matryoshka doll, Wikipedia
History of Russian nesting dolls
Apr 30
Mathematical Principles in Art and
Craft (continued)
Mathematical Principles in Amish Quilts
Symmetry in Medieval Heraldry
May 1
Symmetric Strip Patterns
Symmetric Strip Patterns
Symmetric Strip Pattern Examples
Symmetric Strip Pattern Generator
May 4
Symmetric Strip Patterns (continued)
May 5
Biography Presentations
May 6
Biography Presentations (continued)
Video: Donald in Mathmagic Land
May 8
Kinship Structure
May 11
Kinship Structure (continued)
May 12
Kinship Structure (continued)
May 13
Review for Exam 2
Biography Project Part Two
Due
Cousins
Warlpiri Kinship
Problem Project Part One
Due
May 14
Exam 2
May 15
Games People Play
Three-in-a-Row Games from around the
World
May 18
More Games People Play
Games of Strategy
May 19
Games of Chance
Games of Chance: Dish
Games of Chance: Lu-lu
May 20
Games of Chance (continued)
May 21
Puzzles and Logic
Puzzles and Logic
Sudoku, Wikipedia
Sudoku
May 22
Geometry and Space
Mozambican Rectangles
Labyrinths
May 26
Geometry and Space (continued)
May 27
Synchronicity and Divination
Synchronicity and Divination
The I Ching
May 28
Tibetan Dice Divination and Runes
Mo
Runes
May 29
Everyday Cultures
Triathlon Ethnomathematics
Jun 1
Everyday Cultures (continued)
Mathematics and Rollerblades, Silverman
(read first article)
Mathematics in Traditional Women's
Work
American Grocery Shoppers
Jun 2
Review for Exam 3
Jun 3
Exam 3
Jun 4
Group Project Work Day
Jun 5
Group Project Work Day
Jun 8
Group Project Work Day
Final Exam
Period
Group Project Presentations
©2015 John Kellermeier
Meander Paper
Problem Project Parts Two
and Three Due