DISCOVERING GEOMETRY
with FRANK CASDEN
The subject area of this course is mathematics.
The topics to be included are:
Geometrical Drawing:
Line designs
Daisy designs
Mandalas
Islamic Art
Reflectional and rotational symmetry
Inductive reasoning and picture and number patterns
The building blocks of geometry: point, line plane
Definitions and usages of ray, line segment, and angles
Angle measurement
Line and angle relationships
Geometric constructions
Polygons: definitions and angle relationships
Tessellations:
regular and semi regular 
The course emphasizes hands on skills which included mastering
usage of the straightedge, compass, ruler, and protractor. Students produce
a wide variety of geometric designs using these tools. Writing skills
are also emphasized as students are required to write reports on two projects:
an Islamic art poster and a poster of semi regular tessellations. These
two projects, which undergo several stages of revision, are suitable for
their Learning to Learn portfolios.
The students work is assessed daily for the quality of each assignment.
The projects are assessed for completeness, mastery of the geometric relationships
involved, and thoroughness of the written explanation. The material on
inductive reasoning, geometric definitions, and line and angle relationships
is assessed by written quizzes.
Instructional material includes:
Discovering Geometry  An Inductive Approach, Michael Serra, Key
Curriculum Press
"Mathematics and Islamic Art" , instructional material from
the Metropolitan Museum of Art.
Geometric Concepts in Islamic Art, Dale Seymour Publications
Tessellations, Dale Seymour publications
The Instructional strategies used are a combination of teacher centered
instruction and demonstration, and cooperative group work. The majority
of the time students will be working in small cooperative groups to explore
and discuss the requirements for a particular geometric design or the
essential geometric relationships involved in the activity.
This course correlates with the New York State "Standards"
as follows:
Standard 1: Students use mathematical reasoning to analyze mathematical
situations, make conjectures, gather evidence, and construct an argument.
All parts of this standard are addressed.
Standard 2:Students use number sense and numeration to develop
an understanding of the multiple uses of numbers in the real world, the
use of numbers to communicate mathematically, and the use of numbers in
the development of mathematical ideas. Some parts of this standard are
addressed. Standard 3: Students use mathematical operations and relationships
among them to understand mathematics. All parts of this standard are addresses.
Standard 4: Students use mathematical modeling/multiple representation
to provide a means of presenting, interpreting, communicating, and connecting
mathematical information and relationships. Some parts of this standard
are addressed.
Standard 5: Students use measurement in both metric and English
measure to provide a major link between the abstractions of mathematics
and the real world in order to describe and compare objects and data.
Most parts of this standard are addressed.
Standard 6: Students use ideas of uncertainty to illustrate that
mathematics involves more than exactness when dealing with everyday situations.
Most parts of this standard are addressed.
