Geometry is a beautiful subject full of fascinating mathematics, history, and connections to other mathematics.
Since this course is intended for future math professionals, secondary math teachers, the course will aim for a high level of competence in the fundamentals, a broad appreciation of the structure of the subject, and a robust ability to solve problems, write proofs and explanations, and explain mathematics verbally and in writing.
Students will also make drawing and models that will develop geometrical visualization and insight.
This course will be devoted to the geometry of the Euclidean plane and 3-space. The first half of the course will be devoted to the basic topics of plane geometry: congruence, similarity, triangles, parallel lines, polygons, circles. The second half of the course will explore more about 3D geometry, some advanced Euclidean plane geometry topics and the transformational approach to geometry.
The topics are chosen because they relate to geometry in secondary schools (though of course teachers need to go beyond the math taught to secondary students!). While this course is not a methods course, there will be some reading about the teaching of geometry and the history of geometry as well as matheatical content of geometry.
A number of pedagogical approaches to learning geometry will be used, giving students a taste of several ways to teach and learn. These approaches include group investigations and hands-on experiments with paper folding and mirrors, computer investigations, and model building. Students will work on improving their skills in problem-solving, proving theorems and explaining mathematics to others throughout. Drawing and constructions with straightedge and compass and other tools will be emphasized throughout.
See the explanation on the textbook page.
Problem solving, proving and writing will be an important focus of the course. There will be regular problem sets, one or more per week, that will be turned in and graded. In addition, there will be work in class that will sometimes be turned in.
Students will present homework and other problems in class. In addition each student will prepare a short papaer and a class presentation on an assigned topic once during the quarter.
There will be a quiz about every two weeks, one midterm and a final exam. In addition, students will be evaluated informally during class by oral questions and informal interviews.
Grades will be based on the tests (about 50%) the homework (about 30%) and classroom participation and informal evaluation (about 20%).
Since a grade of 2.5 or above in this course, among other things, is supposed to certify that the student knows the Euclidean geometry required by the State of Washington to teach secondary mathematics, a strong and reliable ability to handle standard problems and explain basic concepts clearly and correctly will be very important to earning such a grade of 2.5 or above. An honor grade of 3.0 or above will reflect understanding of more challenging problems and more advanced concepts.