Meets: 11:00 -11:50 MWF Room: Moreau 324
Instructor: Charles Peltier Office: Mad 214 Phone 4498(H:232-4951) email cpeltier
Office Hours: M 1-2 T10 - 11 W10 - 11 TH 2:30 - 3:30 F 10-11 or see/call me to make an appointment
Text: .Kay, College Geometry: a discovery approach, Addison Wesley Longman, 2001.
We will also be making extensive use of The Geometer's Sketchpad ®[a software tool for construction and exploration in the Euclidean plane - available on the networked MacIntosh computers] in class and for exercises.
Course objectives:
This course is intended primarily for mathematics majors who are pursuing the teaching option or who have an interest in plane geometry. It will provide a more advanced look Euclidean and non-Euclidean geometry, including development of a full axiom system for Euclidean geometry, an introduction to transformations, use of the Geometer's Sketchpad program for geometric exploration and construction (and teaching), and introductions to taxicab geometry and hyperbolic geometry. Besides the explicit content (theorems, specific results) we will focus on developing experience and intuition for geometry and skill in developing and writing proofs.
Significant non-mathematical contents of the course include explicit awareness of learning and problem-solving skills, the development of independent learning skills, and working in project groups. By the end of the course, you should be able to learn faster than you do now. You will be conscious of and able to assess your level of earning skills . We will use cooperative group learning, discovery learning, applied critical thinking, problem solving, and self assessment regularly. You will be expected to keep a learning journal to help you assess your progress.
Procedures:
Daily Schedule
On Monday and Wednesday, we will discuss the content of the asigned text sections, with interruptions for work on examples and diagrams using Sketchpad. We will follow the structure and outline of the text, but will not cover all details - particularly those that can be read in the text. You are responsible for reading the material before each meeting. There will be regular written assignments, collected weekly, graded and returned.
On Friday there will be a team learning exercise in class. You will be expected to complete the exercise in class and hand in the results at the end of class [See "In-class activities" below]
In-Class Activities
The activities in class will be planned to aid you in learning new material independently and in more depth than the text material. For each, there will be an activity sheet indicating the goals, the activities to be carried out, results to be handed in. One member of the team will have the responsibility for writing up the mathematical results["Recorder's Report"]; another will be responsible for an analysis of the team process used in achieving and turn in the results [Reflector's Report"]. You will also grade your work (according to the "Criteria" on the Activity sheet) on a scale of 0.0 (no accomplishment) to 5.0 (all criteria met perfectly). If I concur in the grade, I will double it, otherwise it will stand as your grade.
The report to be handed in will include:
A table of contents
Names and roles of team members
Recorder's Report
Reflector's Report
Team Grade for the activityLearning Journal
You are required to make weekly (at least) entries in your learning journal. At the minimum, these must include: 1. Strengths (as a learner - not "things accomplished") 2. Areas for improvement 3. A plan for addressing the areas for improvement 4. Most valuable thing learned this week (need not be mathematical content) 5. Answers to the "Critical thinking Questions" from the week's activity. In the week in which you are captain, you are to fill out an Activity Assessment (this may substitute for the regular weekly entry) There are forms for these entries in html (easier to read online) and MS Word (print more nicely - or you can type your entires in Word) format available through the Course Documents area in the Blackboard site. I will collect these approximately every three weeks, read them and respond. They will be graded on the basis of the thoughtfulness of your entries.
There will be three writing assignments on topics related to the material developed in the course. These will be graded based on the criteria in the "Guidelines for advanced writing proficiency in mathematics". At least one of the papers will be revised by the end of the semester. These papers will be used in developing your portfolio for the Junior level of the Advanced W requirement.
Tests
There will be two written tests during the semester [dates: 9/26 and 11/7] and a cumulative final examination. [12/15 8am]
Total points on:
1.) Two tests during the semester - 25-35% 2.) Final examination 15-25% 3.) In-class (group) exercises 10-20% 4.) Discussion and exercises 10-20% 5.) Writing assignments 15-25% 6.) Learning Journal 5-10%
Actual point distribution (within these ranges) will be determined by the class.
The grading scale is based on: 60% < D < 70% < C < 80% < B < 90% < A, with + and - grades occupying the top and bottom 2% of the range
Weekly schedule
week dates text sections topics 1 8/24-8/26 1.2,1.4 Course Introduction, Discovery in Geometry, Sketchpad 2 8/29-9/2 2.3-2.4 Incidence Postulates, Ruler Postulate, Models 3 9/5-9/9 2.4-2.5 Angle measure (Protractor Axiom) 4 9/12-9/16 2.6, 3.1 Plane separation, Triangles and congruence relations 5 9/19-9/23 3.2-3.3 Other criteria for congruence , Perpendicular bisectors 6 9/26-9/30 3.4 TEST 1 9/26 Exterior angle inequality 7 10/3-10/7 3.5-3.6 Geometric inequalities,more congruence, 8 10/10-10/14 3.7-3.8 Properties of quadrilaterals, circles 9 10/24-10/28 3.8, 4.1-4.2 Euclidean parallelism, parallelograms, parallel projection 10 10/31-11/11 4.2-4.3 Similar triangles, Pythagorean theorem, Trigonometry 11 11/7-11/11 4.5 TEST 2 11/7 Circle theorems (tangents, secants) 12 11/14-11/18 6.1-6.2 Hyperbolic geometry - history, parallel axiom 13 11/21 6.2 Hyperbolic triangles 14 1/28-12/2 6.2-6.4 Hyperbolic geometry - multiple parallels, angle sum 15 12/5-12/7 6.4 Models of hyperbolic geometry [short week]
Read the statement in Student Handbook on Academic Honesty (on-line here ).In this course academic dishonesty will result in a grade of 0 for the work involved, and notification of the Office of Academic Affairs. A second occurrence will result in failure for the course, with notice to Academic Affairs. On tests, no assistance (including other people, books, notes, etc.) is permitted. You should work together and/or seek help from the instructor on regular assignments, but each student must hand in her own work and is responsible for her own understanding. Team work requires participation by all members of the team. For more information, see the Math Department Honesty Policy
Maintained by cpeltier@saintmarys.edu
Last update 8/19/05