Intermath | CPTM Summer Institute, Geometry Syllabus, Summer 2003

InterMath- Geometry

 

Instructor:
James W. Wilson

Office Address:

105 Aderhold Hall

University of Georgia

Athens, GA 30602-7124

Telephone: (706) 542-4552

Fax: (706) 542-4551

e-mail: jwilson@coe.uga.edu

 

Office Hours: Upon request.

 

Important Information:

InterMath Website

http://www.intermath-uga.gatech.edu

How to get into your folder by Fetch?

 

Host: www.intermath-uga.gatech.edu

User ID: ceismctech\im-CPTM1

Password: (given by the instructor)

Directory: CPTM1

Select folder 'CPTM1' your folder name

 

How to get into your folder by InterMath Web-based FTP?

URL: http://www.intermath-uga.gatech.edu/ftp

User Name:im-CPTM1

Password: (given by the instructor)

Select folder 'CPTM1' your folder name

How to get into your folder by WS_FTP?

 

ProfileName: intermath-tweb

Hostname/Address: www.intermath-uga.gatech.edu

Host Type: Automatic Detect

User ID: ceismctech\im-CPTM1

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)
Geometers Sketchpad 4.04 (from http://www.keypress.com)
Spreadsheets (recommend Microsoft Excel)
Hand Held Calculators such as TI-81, TI-82, or TI-83 (TI: Texas Instruments)

Web Page Browser (recommend Netscape 7.0 or Internet Explorer)
Web Page Authoring Tool (recommend Microsoft Word or Netscape 7.0 Composer)

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 mathematics-specific 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 technology-enhanced 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 standards-based 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 write-ups 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 write-ups, 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 Write-ups: Each person will develop a personal Web Page for the course. There will be a set of "Write-up" projects. These are the "homework" for the course. Each Write-up will be prepared as an HTML document (i.e. a Web Page document) and linked to your personal web page.

What is a write-up?

The "write-ups" 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 write-up should communicate the essential material you have synthesized from your investigation. The format could be entirely in a word-processing 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. Write-ups should be posted to your personal Web Page. If you work as a team on a write-up, post the write-up 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 "Write-up."

 

Click here to see a template for write-ups.

 

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.

7. COURSE OUTLINE

Day I. Monday (June 2, 2003)

Morning Session

A. Introduction to InterMath
B. Introduction to Technology
C. Work through a geometry investigation as a whole class using technology
D. Discuss the components and structure of a write-up (including extensions)

E. Participants engage in investigations in Points, Lines and Planes

F. Journal

 

Afternoon Session

A. Participants begin their first web page write-ups to include in their online portfolios
B. Continued technological teaching and support (especially with GSP and the structure of a write-up)
C. Discuss the components and structure of a write-up (including extensions)

D. Journal

Day II. Tuesday (June 3, 2003)

Morning Session

A. Participants engage in the Circles investigations
B. Continued technological teaching and support (especially with GSP and the structure of a write-up)
C. Participants explore systems of measurement and Logic investigations

D. Journal

 

Afternoon Session

A. Participants add write-ups to include in their online portfolios
B. Continued technological teaching and support (especially with GSP and the structure of a write-up)
C. Participants add middle school lesson plan to their online portfolios

D. Journal

 

Day III. Wednesday (June 4, 2003)

Morning Session

A. Participants engage in Triangle Investigations

B. Participants explore investigations focused on area, perimeter, and trigonometry with triangles

C. Journal

 

Afternoon Session

A. Participants add write-ups to their online portfolios
B. Introduction of spreadsheet program
C. Journal

Day IV. Thursday (June 5, 2003)

 

Morning Session

A. Participants engage in the Quadrilateral Investigations

B. Participants engage in the Polygon Investigations

C. Journal

 

Afternoon Session

A. Participants add write-ups to their online portfolios
B. Introduction of graphing program
C. Discuss and brainstorm ideas about modifying the InterMath experience for a middle school mathematics classroom

D. Journal

Day V. Friday (June 6, 2003)

 

Morning Session

A. Participants engage in the 3-D Object Investigations

B. Participants engage in Coordinate Geometry Investigations

C. Participants engage in Transformational Geometry Investigations

D. Journal

 

Afternoon Session

A. Participants add write-ups to their online portfolios
B. Each participant creates a technology-enhanced mathematical investigation for their own classroom
C. Participants add middle school lesson plan to their online portfolios

D. Journal

 

9. MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS
(Click Here to see a list of selected InterMath investigations clustered for Geometry )

Points, Lines and Planes

         Solve problems involving properties and concepts of points, lines and planes in a two-dimensional 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

3-D 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

(Click Here to see a list of selected InterMath investigations clustered for Geometry)

Center for Proficiency in Teaching Mathematics (CPTM) 2003 Summer Institute Participants