
Intermath  CPTM
Summer Institute, Geometry Syllabus, Summer 2003 




Instructor: 105 Aderhold Hall Telephone: (706) 5424552 Fax: (706) 5424551 email: jwilson@coe.uga.edu Office Hours: Upon request. Important
Information: InterMath Website http://www.intermathuga.gatech.edu How to get into your folder by Fetch? Host: www.intermathuga.gatech.edu User ID: ceismctech\imCPTM1 Password: (given by the instructor) Directory: CPTM1 Select folder 'CPTM1' your folder name How to get into your folder by InterMath Webbased FTP? URL: http://www.intermathuga.gatech.edu/ftp User Name:imCPTM1 Password: (given by the instructor) Select folder 'CPTM1' your folder name How to get into your folder by WS_FTP? ProfileName: intermathtweb Hostname/Address: www.intermathuga.gatech.edu Host Type: Automatic Detect User ID: ceismctech\imCPTM1 Password: (given by the instructor) Select folder 'CPTM1' your folder name Click Here
to go to participants list Course Policies: This course will
concentrate on using various software applications to solve mathematics
problems, to organize pedagogical demonstrations, and to set up problem
explorations. All materials for the course are maintained by an Internet Web
page site and students will create and use web documents in the course. The emphasis is on
exploration of various mathematics contexts to learn mathematics, to pose
problems and problem extensions, to solve problems, and to communicate
mathematical demonstrations. The following
technologies will be used: Graphing
Calculator 3.2 (from http://www.pacifict.com)
Web
Page Browser (recommend Netscape 7.0
or Internet
Explorer) 2. GOALS ADDRESSED Participants will: ·
Expand and strengthen their mathematical knowledge and capabilities,
specifically in the domain of geometry by investigating challenging geometry
problems ·
Engage in problem solving by identifying patterns, forming
conjectures, and developing proofs through the use of technology ·
Use mathematicsspecific technologies such as dynamic geometry
software, graphing programs, spreadsheets, and the Internet to explore
geometry investigations ·
Write and post online solution processes to the investigations using
web page development software ·
Develop middle school mathematics instructional activities and
strategies that incorporate technologyenhanced mathematical investigations ·
Develop a network of peer educators available for continued support
during and following the workshop 3. IMPROVEMENT PRACTICES Participants will gain
knowledge and practice in developing instructional activities and strategies
for teaching geometry in the middle school classroom in order to positively
affect student achievement. Participants will also improve their own
mathematical competencies in the area of geometry. 4. COMPETENCIES Participants will be
able to: ·
Select and use appropriate technological software to explore, analyze,
and represent geometry problems ·
Communicate their mathematical thinking by expressing their reasoning,
analysis, and extensions of the mathematical concepts associated with an
investigation in written, verbal, and visual forms ·
Modify geometry investigations for appropriate use in the middle
school classroom ·
Make connections between InterMath/CPTM Institute experiences and
standardsbased reform documents, such as the NCTM standards 5. PERFORMANCE INDICATORS
As a result of this
course, participants will demonstrate their ability to: ·
Incorporate technology into the learning and teaching of geometry
concepts ·
Communicate mathematical understanding of a variety of geometry
concepts in the form of an online portfolio of investigation solutions ·
Plan middle school instructional activities based on InterMath
experiences 6. COURSE REQUIREMENTS
& ASSESSMENT Participants will be
assessed on the content and quality of their online portfolios. Feedback and
suggested modifications for a select number of writeups will be provided
throughout the workshop. Assessment will be based on use of representation,
analysis, appropriate selection and use of technological tools, creation of
extensions, and accuracy of mathematics. In addition to the investigation
writeups, the participants will also create two mathematics lessons that
integrate technology and geometry for use in their own classroom. Students
will also maintain a reflective journal starting with the initial class
meeting. Electronic Journal: As a part of this course, you are
expected to maintain a reflective journal (preferably online). This journal
is a log of your experiences within the course. It should include thoughts
about new skills and accomplishments that you acquire; critical incidents
that occur; and your thoughts and feelings about content (mathematics/geometry
investigations) and technology. If you are experiencing difficulty keeping a
journal, discuss it with your instructor who can provide you with additional
suggestions and assistance. Electronic Portfolio of Writeups: Each person will develop a
personal Web Page for the course. There will be a set of "Writeup"
projects. These are the "homework" for the course. Each Writeup
will be prepared as an HTML document (i.e. a Web Page document) and linked to
your personal web page. What is a writeup? The
"writeups" represent your synthesis and presentation of a
mathematics investigation you have done usually under the direction of one
of the assignments. The major point is that it convincingly communicates what
you have found to be important from the investigation. A writeup should
communicate the essential material you have synthesized from your
investigation. The format could be entirely in a wordprocessing document.
After all, an HTML document is basically a word processing document with links.
The HTML format, however, can combine narrative, pictures, and program
applications in a dynamic document. Writeups should be posted to your
personal Web Page. If you work as a team on a writeup, post the writeup
into each team member's Web Page but label collaborative effort. Criteria
should include correct mathematics, use of technology, and how well you
communicate. "Solution" might be another word for
"Writeup." Click here to see a template for
writeups. Electronic Portfolio of Lesson Plans: Participants are required to
create two mathematics lessons that integrate technology and geometry for use
in their own classroom. The "lessons" are to be your creations of
material to incorporate technology into classroom lessons. The material can
be individual lessons or a unit of material. Your criteria should be on its
usability in your classroom or in other peoples classroom and something you
feel good enough about to share with colleagues over the web. Click here to
see a template for lesson plans. A.
Introduction to InterMath E.
Participants engage in investigations in Points, Lines and Planes F.
Journal A.
Participants begin their first web page writeups to include in their online
portfolios D.
Journal Day II. Tuesday ( A.
Participants engage in the Circles investigations D.
Journal A.
Participants add writeups to include in their online portfolios D.
Journal Day III. Wednesday ( A.
Participants engage in Triangle Investigations B.
Participants explore investigations focused on area, perimeter, and
trigonometry with triangles C.
Journal A.
Participants add writeups to their online portfolios Day IV. Thursday ( A.
Participants engage in the Quadrilateral Investigations B.
Participants engage in the Polygon Investigations C.
Journal A.
Participants add writeups to their online portfolios D.
Journal Day V. Friday ( A.
Participants engage in the 3D Object Investigations B.
Participants engage in Coordinate Geometry Investigations C.
Participants engage in Transformational Geometry Investigations D.
Journal A.
Participants add writeups to their online portfolios D.
Journal 9. MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS Points, Lines and
Planes ·
Solve problems involving properties and concepts of points, lines and
planes in a twodimensional setting ·
Classify lines as parallel, perpendicular, intersecting and skewed Circles ·
Solve problems involving properties and concepts of circles such as
area, circumference, diameter, sector, angles, arcs, radius, equation of a
circle and Pi Quadrilaterals ·
Classify quadrilaterals as squares, rectangles, parallelograms,
trapezoids, or rhombi ·
Solve problems involving properties of quadrilaterals such as parallel
lines, diagonals, midpoints, length, width, area, perimeter ·
Explore what happens to the area and perimeter of a quadrilateral as
the dimensions are modified Triangles ·
Classify triangles as acute, obtuse, right, equilateral, equiangular,
isosceles, and scalene ·
Explore triangle properties and triangle centers such as medians,
altitudes, angle bisectors, centroid, orthocenter, circumcenter, incenter,
etc. ·
Solve triangle problems involving change of dimensions, perimeter,
area, and the Pythagorean Theorem Polygons ·
Classify polygons as regular, convex, and congruent ·
Construct polygons in GSP; determine which can create tessellations ·
Explore problems involving properties of polygons such as vertex
angles, interior angles, exterior angles, area, perimeter, apothem, lines of
symmetry, diagonals 3D Objects ·
Solve problems involving volume and surface area of cubes, cylinders,
rectangular solids, spheres, cones, and pyramids ·
Explore the properties of vertices, edges, faces, and dimensions of
solids Center
for Proficiency in Teaching Mathematics (CPTM) 2003 Summer Institute Participants 