MATH 512: Professionalized Subject Matter in Geometry           Spring 2012

Reference Number: 2390 (graduate); 2825 (undergraduate)

Meeting Times and Room: W 7:05-9:35, K237

Instructor: Dr. Sandra Caravella                Office: K520 (in Math Dept, K506)

Email: scaravella@njcu.edu                        Phone: 201-200-3348

Website: http://faculty.njcu.edu/scaravella

Office Hours:  M 11-12; W 6-7; Th 11-12, 1-2, 4-5

Required Textbook: Leff, L.S. (2010). Let’s review: geometry. Barron’s Review Course Series. Barron’s Educational Series, Inc: Hauppauge, NY.

ISBN-13: 978-0-7641-4069-3; ISBN-10: 0-7641-4069-8

Course Description                                                              Credits: 3

This course provides a review of fundamental concepts of geometry and an investigation of their significance in teaching of secondary school mathematics. Concepts to be analyzed include: logic, proof, and axiomatic systems; physical and geometric models; sets, relations, and transformations; non-metric and metric concepts; and coordination of spaces. Attention is given to: historical considerations bearing on the teaching of geometry; integration of geometry with algebra and science; and significant literature on the subject. This course requires evidence that the student can make effective use of these concepts in the classroom.

Course Goals

· Use basic concepts of geometry to solve a variety of geometry problems.

· Examine the significance of fundamental concepts of geometry in the teaching of secondary school mathematics.

· Develop geometric proofs within the context of a specific axiomatic system.

· Examine the role of axiomatics in secondary school geometry.

· Identify geometrical and algebraic relationships.

· Examine the interaction of algebra and geometry in the curricula for secondary school geometry.

· Create and present a geometry lesson or lesson plan that effectively uses concepts learned in the course.

Your grade will be based on:

• 3 quizzes 
• A midterm
• A final exam
• Weekly assignments (computer labs and special assignments)
• A final project consisting of the preparation and presentation (written and oral) of a lesson plan or lesson in geometry

There will also be weekly ungraded homework assignments. Tests and quizzes will be based on these assignments, plus whatever is covered in class.

Determination of Grade

Your final average will be determined by the following point system.

3 quizzes                            100 pts (30-40 pts each quiz)

Midterm                              100 pts

Final exam                          100 pts

Weekly assignments              50 pts

Final lesson plan                   50 pts

Grade Scale (rounded percentage of total points): 93-100 (A); 90-92 (A-); 87-89 (B+); 83-86 (B); 80-82 (B-); 75-79 (C+); 70-74 (C); 65-69 (C-); 55-64 (D); below 55 (F).

If higher, your final exam score will replace the lowest of your midterm score, your cumulative quiz score, or your combined weekly assignment/final lesson plan score.

Make Up Policy

Late Work Policy

The instructor reserves the right to refuse any work that is submitted late. If late work is accepted, points may be deducted for lateness.

Important Dates

Midterm: March 7

Final: May 9

Other Resources

Bennett, D. Exploring geometry with the geometer’s sketchpad. Key Curriculum Press: Emeryville, CA.

Common core state standards for mathematics. (2011). Common Core State Standards Initiative, http://www.corestandards.org/.

Crane, T.V. & Rubenstein, R., eds. (2009). Understanding geometry for a changing world: Seventy-first yearbook. National Council for Teachers of Mathematics: Reston, VA.

DeVilliers, M.D. Rethinking proof with the geometer’s sketchpad, Key Curriculum Press: Emeryville, CA.

National library of virtual manipulatives in geometry. (2010). http://nlvm.usu.edu/en/nav/topic_t_3.html.

Principles and standards for school mathematics. (2000). National Council for Teachers of Mathematics: Reston, VA., http://www.nctm.org/.

The Geometer’s Sketchpad resource center. (2009). http://dynamicgeometry.com/.

Course Content

Topics include: the language of geometry; parallel lines and polygons; congruent triangles; special quadrilaterals; ratio, proportion, and similarity; circles and angle measurement; transformation geometry; and coordinate geometry.