## Suggestions for Presentations and Papers in Math 3050

### Class Presentation

1. Consider starting with a question.
It may be the question you started with (or that you evolved while working on the project. It may be a question you now know how to answer - or it may be a question that still intrigues you.
2. Be conscious of 'Which geometry' you are using, in the sense of Klein's hierarchy of geometries. Near the end of your presentation, you may want consider the following type of question: What if ... (another geometry) ... ?
3. Where possible, include some specific activity for the other students, so they can play with some of the concepts. Something visual to keep in mind, some concrete situation they can tie the concepts to, etc. will have additional impact.
4. Make connections: - connections with other subjects, with other parts of math, with other applications etc. That can also assist the impact of a presentation.
On the final assignment in the course, I will ask everyone to include a paragraph on each of the presentations given, including:
• their statement of what was the key question being considered in the presentation;
• whether this question was answered - and what the answer was;
• what kind of geometry was actually being used.
Note: I need at least one weeks warning to arrangeclassroom computers, videos, etc. (An overhead can be arranged at short notice).

### Written Report

This will be completed after your class presentation. The feedback you receive in class may give you some additional insights on the communication of the material. After your class presentation and before your written presentation, I will probably offer some specific questions or issues that could be addressed in your written report. Here are some general suggestions:
1. Begin and end with questions. Why did you start this theme? Did you get an answer to your question? Did you discover new questions? The evolution between these makes one interesting theme for a paper.
2. Consider which geometry you (and your sources) used. Is it clear why other geometries were not used? (E.g. the critical properties do not belong to a higher or alternate geometry; the motivation is restricted to a specific situation ... .)
3. If possible, include at least one 'Theorem' and its proof in the write up. Proofs are an important aspect of mathematics - not the whole story but a basic ingredient. If this is not possible, consider stating some 'Theorems' that do apply, and the kinds of mathematics they use for their proofs (even if these are beyond your current knowledge or the time available).
4. Connections to other branches of math are always good. Connections to other disciplines are also important. If these do not appear integrated into the core written presentation, consider a section on these connections.
5. If you are considering math teaching as a career, you might include some comments on whether this topic is suitable for high school in terms of:
• intellectual content;
• motivation and interest for students.
6. Diagrams or visual (or 3-D) components are desirable: this is 'geometry' and that aspect has been imporant to the course.
7. Of course cite sources: including URL's for Web sources, private communications for sources from individuals, etc.
8. Some report on how your own ideas changed while doing this project would be an interesting 'dialogue' at the end of the report.