PATTERNS IN NATURE I: VISUAL GEOMETRY

Faculty:Dr.Janet Caldwell Semester:Fall 2002

Office Hours: Tuesdays and Thursdays, Math Department, Robinson (3rd floor) from 9:30 –11:00.
                       I will generally be at Triad, Wing C (McSiip Office) after that. 


Phone: 256-4500, ext. 3871 (Math Dept.), ext. 3924 (Triad) or 610-565-1391 (home).


E-mail: caldwell@rowan.edu-- I generally check my e-mail on Tuesdays and Thursdays throughout the day.


Texts: Investigations in Geometry by Caldwell(2002)
 
 

Supplement:Geometry to Go
 

Prerequisites: Introduction to Programming, Statistics, Essentials of Biology, Chemistry of Everyday Life, Physics of Everyday Life - Please note that you should also have had Precalculus!
 

Course Description :

This course provides a thorough understanding of geometry and its connections to the natural sciences by using a variety of experiential teaching methods.Students in this course will draw upon their backgrounds in the sciences and in mathematics as they investigate the geometric concepts inherent in the world around them.This course is a much more advanced course than Introduction to Geometry, employing many of the concepts and techniques of precalculus and building upon the geometry learned in high school.The course is not as theoretical, however, as the Geometry I course which is required of preservice secondary mathematics teachers.This course is also different from the other geometry courses in that it will involve an explicit emphasis on the connections between geometry and science, requiring that students have sufficient backgrounds to recognize and understand these connections.This course will provide sufficient background in geometry for students to be able to read and understand journal articles as well as to teach the content in grades K-8.
 
 

This course will focus upon recent developments in geometry as well as fundamental concepts.Connections between geometry and the natural sciences will be investigated.Teaching methods will stress a visual approach to understanding concepts, making conjectures, and justifying reasoning.Students will use a variety of materials, from construction paper and pipecleaners to videotapes and computer sketching programs.Some proof will be included but will not be emphasized.Students will also be expected to read and analyze journal articles (e.g., Journal of Recreational Mathematics, Scientific American, World Wide Web sites such as the University of Minnesota's Geometry Center) independently.
 
 

Objectives:

Students completing this course will be able to:


TENTATIVE COURSE OUTLINE

 
UNIT
DATE
TOPIC
CALDWELL

2D Geometric Figures
9/5
Triangles, Quadrilaterals, and Polygons
Parallel Lines and Transversals
iii-iv, 1-11
9/10
Polygons and Circles
Constructions
12-21
9/12
Perimeter and Area
Written Assignment #1 Due: 

 

p. 6 #6 and p. 9 #12
22-34
9/17
Congruence
35-41

Transformations


 
 

 
9/19
Reflections
Written Assignment #2 Due: 
p. 14 # 4 and #5
42-47
9/24
Translations
48-52
9/26
Transformations, Quadratic Functions,
and Conic Sections
Written Assignment #3 Due: 
p. 41 # 10 and #11
53-60
10/1
Rotations
61-70
10/3
Matrices and Transformations
71-73
10/8
EXAM # 1
.
10/10
Tessellations
QUILT DESIGNS DUE
74-79
10/15
Similarity
Gnomons, Spirals, & Helixes
80-92
10/17
Trigonometry
Written Assignment #4 Due:p. 21#1
93-100
3D Geometric Figures
10/22
Spatial Visualization & Polyhedra
101-112
10/24
.AMTNJ CONFERENCE
No class –10 points extra credit
.
10/29
Surface Area and Volume
Written Assignment #5 Due: p.100 #15 and #16
 
113-127
10/31
Moving Between Dimensions
128-134
11/5
Projections
135-141
11/7
EXAM #2
  
Dimension
11/12
Fractals
SCHOOL PROJECTS DUE
142-148
11/14
Fractal Dimension
149-152
11/19
Measuring Fractals
Higher Dimensions
Written Assignment #6 Due:p. 92 #4, #5, #6
153-166

Non-Euclidean Geometries
11/21
Finite Geometries
167-173
11/26
Taxicab Geometry
Written Assignment #7 Due:p. 158#4 or #5
180-185
12/3
Polar Coordinates
QUILT SQUARES DUE
186-192
12/5
Spherical Geometries
193-205
12/10
Hyperbolic Geometries
Written Assignment #8 Due: 
p. 202 Activity V-5-C 
206-212
12/12
Review
APPLICATION POWERPOINTS DUE
..

 
 

Evaluation:

The grading scale used is 90%=A-, 80%= B-, 70% = C-, 60%=D-.


 
Projects- 35 points each
105 points
B+: 435-449
C+: 385-399
D+: 335-349 
Exams - 100 points each
300 points
A: 465-500
B: 415-434
C: 365-384
D: 315-334
Written Assignments
80 points
A-: 450-464
B-: 400-414
C-: 350-364
D-:300-314
Class Participation
15 points
 
"
'
'
TOTAL 
500 points 
'
"
"
'

 
 

Projects:
 
 

QUILT This project involves designing and actually creating a quilt square that illustrates a geometric concept.  You will work with a partner and will be assigned a topic.  Squares may be pieced or appliquéd (using iron-on fusible fabric).  If appliquéd, then all edges of all pieces MUST BE stitched down by machine (preferably with a zigzag stitch) or by hand.
 
 

Please note that your design area is 12 inches x 12 inches, but your completed square should be 13 inches on a side (to allow for sewing squares together).   In other words, there should be a ½ inch border around the square.  This border should NOT be of a contrasting fabric, however.

 
            Your quilt design is due October 12 th.  This must include a scale drawing of your square, actual size patterns for the various pieces to be used (be sure to include seam allowances, if needed), a list of needed fabrics (with the dimensions of rectangular pieces for each), and a cutting layout (clearly showing how each rectangular piece of fabric will be used).  You must also include a brief paragraph describing your square and how it shows the geometric concept assigned.  This part of the project is worth 18 points and will be graded on completeness, accuracy, quality of the description and the design, creativity, and practicality.
 
            Your completed square is due December 3rd.  The completed square will be graded on accuracy of measurements, execution of design, and quality.  This part of the project is worth 17 points.

 
 

SCHOOL PROJECT
 
 

This project involves working with elementary students in Harrison Township on geometry (class observation, instruction, and reflective journal).  You will be assigned in pairs to a specific classroom to visit on specific days at specific times.  You are expected to arrange for any absences or deviations directly with the classroom teacher in such a way as to be able to complete three visits prior to the project’s due date of November 12th.  During your first visit, you will simply observe the mathematics class, paying particular attention to the tasks students are doing and what these tasks show about students’ learning.  At this time, you should discuss what you will be doing in subsequent visits (working with small groups of students) with the teacher.  You will turn in a journal which describes each visit in detail, including what happened in the classroom (what the teacher did, what you did, what students did), the instructional activities, specific descriptions of students’ thinking that you observed, analysis of NJ Math Standards addressed in the lesson, links to content you have studied so far at Rowan, and any additional comments or personal reactions.  This project will be graded based on the quality and completeness of your journal and on the extent to which project requirements were fulfilled.
 
 

APPLICATION POWERPOINT
 

You will be expected to select an application of geometry to the sciences and read three articles on this topic from current journals and/or the Internet.  At least one article must be from the WWW and at least one article must be from a journal.  You will prepare a brief Powerpoint presentation (with notes explaining the slides and including sources for information and images) that introduces this application to other members of the class.  The Powerpoint should be approximately 10-20 slides and will be posted on WebCT for other members of the class to review.  Some Powerpoints will also be viewed in class.
 
 

Written Assignments
 
 

Periodically, specific written assignments will be collected for grading.  These will frequently include problems to be done on Geometer’s Sketchpad.   They may also include constructions with compass and straightedge or paragraph proofs.  Such assignments will be given eight times during the semester and are noted on the syllabus.
 
 

Policies 

Attendance/Class Participation : You are expected to attend each class; it is impossible to participate in the problem solving activities unless you are present.  Since the activities are designed to help you build upon your own understanding of mathematics.  And getting the notes @ from someone else will simply not work!  Attendance will be taken at the beginning of each class session.

 
 

Makeup Exams: Makeup exams will be given only if you have called and left a message prior to the start of the exam indicating the reason for your missing the scheduled exam.  Valid reasons should be beyond your control (e.g., illness, accidents, hospitalization); oversleeping is not a valid reason to miss an exam.  Makeup exams will generally be scheduled as soon as possible.