COLLEGE GEOMETRY

Fall 2006

Dr. Janet Caldwell                                                                                                        856-256-4827

Robinson 230E                                                                                     caldwell@rowan.edu

 

Office Hours:  MW  3:00 – 4:30                                               610-565-1391 (home)

 

Course Description:  This geometry course uses both synthetic and analytic approaches to study advanced concepts in Euclidean geometry, to introduce non-Euclidean geometries, to explore the basics of transformational geometry and higher-dimensional geometry, and to trace the historical development of geometry.  Computer use is emphasized throughout the course.

 

Objectives:  This course is designed primarily for prospective secondary school mathematics teachers.  Its purpose thus is to further the student’s understanding of axiomatic systems, to trace the historical development of geometry, to explore the basic concepts of transformational geometry, to familiarize the student with the use of computer and graphing technologies in the teaching and learning of geometry, and to introduce selected advanced topics in the study of geometry.

 

Text:  Kay, David C.  (2001).  College Geometry: A Discovery Approach.  Second Edition.  HarperCollins.  Including accompanying Geometer’s Sketchpad computer program.

 

Course Requirements:

 

Homework and Class Participation             

Students are expected to attend class regularly and on time and participate in discussions and class activities.  Homework will be assigned each class period to be discussed at the beginning of the next class.  Homework may require computer time outside of class.  Selected problems will be discussed in class, with students presenting each one.  Homework problems may be collected for review and comment.  60 points

 

Projects              Seven projects will be assigned; each is 20 points.  The first and last projects will be completed in class, in small groups.  A project will also be assigned to introduce and begin to develop concepts for each of chapters 3 – 7; these will be due at the first class in which the chapter is discussed, as shown in the table on page 3.

 

Exams    Three exams will be given, as shown on the attached schedule.  Any student missing an exam will receive a grade of zero unless a phone call has been made to the professor prior to the exam and an excused absence (medical emergency or illness) is given.   Each exam is 100 points.  Exams are cumulative.

 

Choice:              You must choose at least one of the following assignments in order to receive a B in the course and two to receive an A.       

 

Book Reflection  Read Flatterland by Ian Stewart and write a 3-5 page personal reflection.  Your reflection should include what new geometrical ideas you learned about, as well as how your understanding of concepts that you already thought you knew something about changed.  What did you find most interesting?  What would you like to learn more about?  Why? What was most confusing to you?  Why?

 

Independent Project  Select a topic from geometry that we will not be discussing in class and submit it for approval by the end of February.  Write a 5-10 page paper and prepare a trifold presentation board for display and discussion in class on December 4th.

 

Conference Volunteer  Attend the NCTM Regional Conference in Atlantic City October 19th, 20th, or 21st as a volunteer and complete a brief reflections describing your experiences.  Include summaries of sessions attended as well as a discussion of your assigned task as a volunteer and any informal interactions with teachers at the conference. 

 

Geometry Walk  Create at least eight problems (more if your problems are easy) about geometric situations on Rowan’s campus.  Think about this as a bit of a scavenger hunt or a geometry walk.  Take folks to eight locations on campus and ask them to solve a problem at each location (related to that location).  You may require them to measure something at some locations, if you wish.  The problems should be sufficiently challenging that other mathematics majors would find them interesting.  You should hand in the following:

1.  A handout for participants in the geometry walk that shows their route and/or gives clues about the route.  This handout must include all of your problem statements.

2.  Solutions to each of your problems.

3.  A description of the process you used to develop your problems, including any resources consulted (books, web sites, etc.).

 

 

Grading Scale:                       A:  94 – 100     B+:  88 – 89     C+:  78 – 79    D+:  68 – 69   

                                    A-:  90 – 93     B:    83-87       C:    73 – 77     D:    63 - 67

                                                                        B-:   80-82       C-:   70 – 72    D-:   60 – 62

 

 

 

Tentative Course Schedule and Assignments

 

Date

Topic/Chapter

Homework Assignment

GSP

Notes

9/6

Examples & Proof

2.2   # 6, 7, 10, 11, 12

X

 

9/11

2.3, 2.4

2.3    # 1, 3, 6

2.4    #1, 2, 3, 7, 8, 9, 11, 12, 13, 14

 

 

9/13

2.5, 2.6

2.5    #1, 2, 3, 4, 5, 7, 9

2.6    # 1, 2, 3, 5, 6, 9

X

 

9/18

3.1, 3.3

3.1    #1, 3, 6, 7, 8, 9, 11, 14

3.3  #3, 5, 6, 7, 9, 11 + handout

 

 

9/20

In-Class Project # 1

9/25

3.4, 3.5

3.4    # 1, 2, 4, 5, 6, 9, 10, 15

3.5    # 1, 2, 4, 5, 6, 11, 12

 

Project 2 Due

9/27

3.6, 3.7

3.6 # 2, 3, 5, 8

3.7 # 4, 6, 8, 14, 15

 

 

10/2

Review

10/4

EXAM #1

10/9

4.1, 4.2

4.1    # 1, 2, 3, 5, 13;

4.2    # 1, 2, 3, 8, 10, 16, 19

Moment for Discovery on p. 231

X

Project 3 Due

10/11

4.3

4.3  # 1, 2, 4, 7, 14, 22;

Pythagorean Proofs & Similarity  Problems

X

 

10/16

3.8, 4.5

3.8 # 2, 3, 6, 8;

4.5  #1, 2, 3, 4, 6, 14, 15, 17, 19, 20

 

 

10/18

4.6, 4.7

4.6  #1, 3, 7, 9, 11, 12, 13

4.7  # 1, 2, 7, 8, 9, 13, 14

 

 

10/23

5.1, 5.2

5.1  # 1, 3, 6, 12; 5.2  # 2, 3, 5, 6, 11

X

Project 4 Due

10/25

5.3, 5.4

5.3  # 1, 2, 3, 5, 6, 8, 15, 18, 21;  handout

X

 

10/30

5.4, 5.5, 4.4

5.4  # 2, 3, 6, 7, 8, 9; handout

4.4  # 1, 3, 5, 7, 16

 

In Rob 212

11/1

Review

11/6

EXAM #2

11/8

7.1, 7.2

7.1 # 7;  7.2  # 5, 6, 7, 8, 9, 10

 

In Rob 212

Project 5 Due

11/13

7.3, 7.4

7.3  # 4, 6, 8;  7.4  # 1, 2, 3, 7

 

In Rob 212

11/15

7.5

7.5  #1, 2, 6, 7, 8, 9

 

 

11/20

6.1, 6.2, 6.3

6.2 # 4; 6.3 # 7, 13, 14

 

Project 6 Due

11/22

6.4

6.4  # 2, 3, 4, 10, 11 - 15

 

 

11/27

Spherical Geometry

Handout

 

In Rob 212

11/29

Spherical Geometry Project 7

 

 

12/4

Spherical Geometry Project 7

 

Choice Assg.

12/6

Spherical Geometry Project 7

 

Project 7 Due

12/11

Fractals

Sec. 4.6, # 20, 21

 

 

12/13

Review – In Rob 212

FINAL – Weds, 12/20 at 2:45?