Geometry is a beautiful subject full of fascinating mathematics, history, and connections to other mathematics.
Since this course is intended for future math professionals, i.e., 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 drawings and models that will develop geometrical visualization and insight. Various geometrical manipulatives will be used for hands-on exploration.
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 and more 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!).
The mathematical approaches to these topics will include traditional synthetic reasoning from axioms, transformations, and coordinate geometry.
While this course is not a methods course, the methods of inquiry and instruction used in the course will provide examples for thinking about teaching.
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. Geometer's Sketchpad software will be used extensively in Math 487 and also in 444. 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. Making physical models will be an important part of the investigation of shapes in 3D space.
See the explanation on the textbook page.
Problem solving, proving and writing will be an important focus of the course. There will be regular larger problem sets about once a week and more frequent short sets. Assignments will be evaluated and graded in a variety of ways.
Students will discuss some key homework problems in groups during class. There will be some presentations at the board.
There will be two quizzes, one midterm and a final exam. In addition, students will be evaluated informally during class by short written questions, oral questions and informal interviews.
For more about Assignments, see the Introduction to Math 444 Assignments.
Grades will be based on the tests (about 50%) the homework (about 35%) and classroom participation and informal evaluation (about 15%).
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.
Grades in 487 will be based on active and thoughtful participation in the labs. Students in the labs will mostly be evaluated by instructors "walking around and talking." If a student misses a lab, then to get credit for the lab, written evidence (or Sketchpad files) showing that the lab was completed must be presented in a timely way. If more than two labs are missed and not made up, there will be no credit.
It should be noted that even though written assignments in 487 itself are not required, the learning from 487 will be used and called on in written assignments in 444.