**Major Project**

The major project is intended to allow you, individually or in
pairs, to explore a specific topic in depth. Projects can
be either a report of your joint mathematical investigations within
your chosen topic or a complete teaching resource package for
a unit on your chosen topic. The following descriptions
are adapted from Dr. Hatfield's EMAT 4500/6500 course:

**A:** **Report
of your mathematical investigations**

These papers will deal with your (or your pair's)
own exploration of an approved mathematical problematic situation,
chosen because it could potentially be developed with middle or
secondary school students. It must be approached as an authentic
investigation in which you search for patterns and relationships,
formulate your own search path, make speculations and conjectures,
develop possible generalizations, and seek justification and
proof.
The report should include reflections from each member of the
group and a summary that discusses applications, connections within
and outside of mathematics, and impacts of your experiences into
your future teaching practices.

**
B:**

These reports will provide a comprehensive set of originally developed instructional materials that a middle or secondary teacher could use to teach an approved enrichment topic. The package should provide student materials, didactical rationales, and detailed guidelines related to all activities of student and teacher, including assessment and evaluation. Reflections from each member of the group should discuss connections, applications and impacts of your development experiences into future teaching practices.

Both types of projects must make effective use of appropriate technologies. The rationale for the choice of technologies must be clearly stated in the report.

Your report should also highlight the NCTM Principles and Standards AND the Georgia Performance Standards (GPS) that are addressed through the activities in your investigation or resource package.

A major change in the new GPS
is the nature of the courses in the secondary school curriculum.
All courses at the secondary level will be INTEGRATED mathematics
courses (Math 1, 2, 3 & 4). Thus, I encourage you to develop
a teaching resource package that integrates several mathematical
topics.

Some possible broad topics

· Conic sections

· Physics/motion/vectors

· Optics

· Non-Euclidean geometry

· Analytic/synthetic geometry

· Complex numbers

· Number theory

· Functions (inverse, identity)

· Social choice/voting systems

· Game theory

· Trigonometry

· Mathematical systems

· Matrices

· Sequences and Series

· Probability

· Data and statistics

__Some possible starting points__

· Non-decimal bases and ancient numerical systems

· The algebra of modula arithmetic

· Patterns in repeating decimals

· Fibonacci sequences

· Golden ratio and the divine proportion (geometric, algebraic, applications)

· Pascal's triangle

· Geometric and numerical relationships using areas and perimeters- · The mathematics of Geographical
Positioning Systems (GPS)

· Exponential and logarithmic functions

· The probabilities of winning the various Georgia Lotto games

· SAT statistics by state - · The Central Limit Theorem
- · A Fathom Survey

Only one final project report is required from
each pair but individual reflections and summaries will be required
from each member of the pair.

For type A reports, individual members should include their own
particular conjectures, discoveries etc. A group summary
should synthesize these various aspects of the mathematical
investigation.

For type B reports I suggest that the various components of the
course package be divided between the pair. It is very critical,
however, that the pair develops an overall plan for the package
before individuals start working on their respective parts.
This overall plan needs to be included in the report. It
will be necessary for each member of the pair to be aware of what
the other member is developing throughout the process.

Reports must be mounted on
each member's web page with links to appropriate files and resources.

Each pair or individual will present their report during the final
class period on Tuesday, June 6 from 8:00 a.m.-10:45 a.m.

Grading will be based on a total of 100 points.

Overall quality of the report--- 50 points (assigned to both members of the pair)

· Does it include all relevant aspects as listed above?

· Is it well written?

· Is it well organized?

· Is it mathematically sound?- · Does it make appropriate use of the technologies?
- · Does it demonstrate originality or creativity?

· Did all members of the group contribute to the report?

Individual contributions to the report--- 20 points to each member

Individual reflections and summaries---10 points to each member

Presentation of the report--- 20 points to each member

· The presentation should be planned to last approximately 20 minutes

· Each member needs to take an active role in the presentation

· It should begin with a brief overview of the project

· It should include a sample activity that involves the rest of the class in the use of technology

· A summary of findings (for type A projects) should be presented

· Implications for teaching the unit should be shared (for type B projects)

· Each member of the group should share brief reflections on their experiences

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