Text(s)/Materials:

Reference Text: Alfred S. Posamentier. (1979). Excursions in Advanced Euclidean Geometry. J. Weston Walch

Course Description:

Advanced Geometry includes exploration of advanced topics in geometry selected from such areas as: points of concurrence, cevians, the golden mean, fractals, matrix transformations, geometric averages, non-Euclidean geometries, geometric probability, modelling, spirals, the theorems of Ceva, Menelaus, Pascal, Desargues, and Pappus. The course exposes students to a variety of concepts, ideas and problem solving strategies which are developed and extended through class discussion and interactive exploration.

Teaching and Learning Methodology and Philosophy:

The role of the teacher is that of facilitator so students can have the opportunity to enhance their own mathematical maturity through individual inquiry. The course emphasizes individual and group explorations, discussions, conjecture, validation, and problem solving. Verbal and written communication are stressed. There is an emphasis on making connections between and among topics in geometry and other topics within and outside of mathematics. Ideas and concepts are introduced in class and exploration proceeds as directed by class discussion. New ideas and successful mathematical inquiry takes place through catalytic interaction. Much of the learning is expected to take place through problems designed as stepping stones to concept development. The success of the course is dependent upon the contributions of each member of the class.

Student Expectations:

Students are expected to be involved in class discussions and explorations. Substantial time is expected to be spent in preparation, reading and individual exploration outside of class. Students should be able to explore independently and in small groups and to contribute to class exploration through extensions, conjectures and connections. Every student has the opportunity to express creativity and be a part of new discoveries. Involvement, risk taking and sharing ideas is what this class is all about. Many students get so involved in an idea that it becomes an area of independent inquiry with me outside of class.

Assessment Practices, Procedures, and Processes:

Students are evaluated through varied assessments, both group and individual. Grades may be determined by taking into account some of the following:
• Classroom participation, involvement, and contributions to exploration.
• "Take Home" problem sets which include both the use of concepts generated in class and independent, open ended investigation.
• In class, group or individual quizzes and exams.
• Attendance [This is essential, since it is not possible to recreate the spontaneous class discoveries and catalytic involvement.]
• Individual (and group) research projects, reports, and portfolios
• Self evaluation by the student with reflection on: contributions made to the success of the class, sharing of ideas both outside of class and within, and level of involvement.

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