Instructor: John Olive, 105F Aderhold, 542-4557, jolive@coe.uga.edu

Instructor: Brad Findell, 109B Aderhold, 583-8155, bfindell@coe.uga.edu

Teaching assistant: Samuel Obara, 502 Aderhold, 542-7715, sobara@coe.uga.edu

Office hours by appointment. Please call or e-mail.

**Course description**.
This course is about connections within and across mathematics
and about connections between mathematics and contexts outside
of mathematics. We will be looking in particular for opportunities
to think about middle and high school mathematics more deeply
and more broadly and in ways that take advantage of the undergraduate
mathematics courses you have taken or are taking.

**Course structure**.
The course will consist of assignments, two mid-course exams,
and a final project. The bulk of the course will be organized
around approximately five topics. For each topic, there will be
mathematical problem sets, research assignments such as exploring
the development of the topic in various textbooks, and reflective
writing assignments. Some of these assignments will involve analysis
or elaboration of the draft Georgia Performance Standards. The
intent of the final project is a similar exploration of a topic
of your choosing.

**Proposed Topics**

- Calculus and the mathematics of change
- Number systems and their extensions
- Combinatorics and discrete mathematics
- Exponents and logarithms
- Probability, statistics, and data analysis

**Themes**

· Reasoning. Mathematics involves understanding why statements are true and why procedures produce correct answers. You should have two explanations whenever possible.

· Problem solving. Mathematics involves solving problems you haven't seen before. (How might you distinguish between problems and exercises?)

· Connections. The power of mathematics arises from the fact that apparently different problems can have the same solution. (How is a solution different from an answer?)

· Representations. Mathematical thinking and communication involves representations of mathematical ideas. You will explore ideas graphically, numerically, symbolically, and in contexts, and you will make explicit connections between and among the representations. (Why are two representations better than one?)

· Definitions and conventions. Mathematical thinking and communication is facilitated by agreeing upon definitions and conventions. (How should definitions be used? Can definitions or conventions be proven?)

**Assignments**.
Some assignments will be graded. We ask that you keep all of your
assignments in a portfolio stored and organized electronically
and in a 3-ring binder. The portfolios will be examined at the
end of the semester.

Effective teachers make liberal use of materials and resources provided in textbooks, on the Web, by colleagues, or via handouts from presentations. Such materials are not used directly but rather are modified to fit the particular circumstances for which the teacher intends to use them. We expect that you will do the same in this course and, in addition, that you will cite your sources.

**Textbooks and materials**.
There is no official textbook for the class, though we suggest
that you own a copy of the *Principles and Standards for School
Mathematics* (NCTM, 2000). We also reserve the right
to require or recommend books as the term progresses. Additional
resources are available in 111/113 and in the curriculum library
on the second floor of Aderhold. We also ask that you have a graphing
calculator and bring it to class. We recommend a TI-83 or better.

**Grading**

Graded assignments: 20%

Midterm exams: 40%

Participation: 10%

Final project: 20%

Portfolio: 10%

**Final project**.
The project is intended to allow you, in groups of 3-4 people,
to explore a specific topic in depth. The project will include
both individual and group components. More detail is forthcoming.
Possible topics may include the following:

- Conic sections
- Physics/motion/vectors
- Optics
- Non-Euclidean geometry
- Analytic/synthetic geometry
- Solid geometry
- Complex numbers
- Number theory
- Functions (inverse, identity)
- Social choice/voting systems
- Game theory
- Trigonometry
- Mathematical systems
- Matrices

**Memberships**.
We suggest that you join the National Council of Teachers of Mathematics
(NCTM) and subscribe to the *Mathematics Teacher*.
Student membership is $36, and you may join online at http://www.nctm.org.
It is also a good idea to join the Georgia Council of Teachers
of Mathematics (GCTM). See http://www.gctm.org. Student membership
is free for juniors and seniors, and you may join NCTM and GCTM
by filling out a single form. We expect that you are already a
member of UGA's Mathematics Education Student Association (MESA).
See http://www.ugamesa.org.