Over the course of the semester, we have looked at many connections to the past, including history and concept development. In this project we will look at connections relevant to the future - the purpose of this final project is to reflect on connections of a geometric topic to active research [ie the future of a field] and/or to your intended career [ie your future].
Career Focused Connections Research and discuss the connections of your topic to your intended career path by giving some specific examples.
For example, if you are planning on teaching middle grades or high school, you could choose any geometry topic related to the NCTM Standards for Geometry, Measurement, Reasoning and Proof, or Connections. Then, you might design a lesson plan, summarize some related classroom activities, worksheet ideas, and/or connections to program or testing requirements. [You can use books, articles and the web to help you]. In addition, you should reflect on the relationship of your topic to the NCTM Standards for Geometry, Measurement, Reasoning and Proof, or Connections, and the NC Standard Course of Study. Finally, find at least one recent application or unsolved problem related to your topic (so that you can answer the question - why is this important today).
Or you might choose a topic like regular polyhedra or symmetry and look at connections to topics in courses in your major [symmetries of regular polyhedra as groups in modern algebra] or in your field [efficiency and strength of regular polyhedra applications to architecture, chemistry, or biology, or symmetry in physics...]
or Active Research Focused Connections Discuss the role of your topic in current research and summarize a related problem that is unsolved. Find at least two related scientific or mathematics research journal articles [ie technical articles that went through a rigorous academic peer review process before being published - if you are unsure about whether something is a technical scientific or mathematics research journal versus a media source, ask Dr. Sarah and also check for information about the editorial board and publishing process and intended audience].
Here are some samples of previous final project topics, but you are
not limited to this list:
Archimedes: The Man who Made Math Solid
Can You Hear the Shape of a Drum?
Decline and Rise of Geometry in 20th Century North America
Double Bubble Problem
Geometry and the Art of M.C. Escher
Geometry and DNA
Geometry and Medical Imaging: Humpty Dumpty - Putting the Pieces Back Together Again
Geometry of Music
Geometry, space and technology: Challenges for teachers and students
Geometry of the Universe
Mapping the Brain
Number Patterns in Geometry
Origami Folding Axioms: Planes, Cranes and Math
Packing Problems (Packing Geometric Shapes Into Other Geometric Shapes)
Visualization in the teaching and learning of mathematics