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Geometry
Institute for
June 12-16, 2006
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 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
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.
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 classroom
· Make connections between the experiences in the Geometry Institute and the Georgia Performance Standards
Performance Indicators
As a result of this
course, participants will demonstrate their ability to:
· Communicate mathematical understanding of a variety of geometry concepts in the form of an online portfolio of investigation solutions
· Plan instructional activities based on the experiences in the Geometry Institute
· Incorporate technology into the learning and teaching of geometry concepts
Course Requirements and
Assessment
Participants will be
assessed on the content and quality of their 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 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 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. Participants are required to create at least five write-ups. Each Write-up will be prepared as a Microsoft Word document with links to the appropriate technology files.
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 should be entirely in a word-processing document with
references to appropriate technology files.
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 focused on teaching geometry concepts in your classroom. The "lessons" are to be your creations of material to incorporate technology into classroom lessons. The lessons should be appropriate for 1-2 days of classroom instruction. Your criteria should be on its usability in your classroom or in other peoples’ classrooms and something you feel good enough about to share with colleagues.
Click here to see a template for lesson plans.
Electronic Journal: As a part of this course, you are expected to maintain a reflective journal. You will write in the journal at the end of each morning and afternoon sessions. 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.
Follow-up Sessions: Several follow-up sessions will be scheduled during the school year.
Information
about Geometer’s Sketchpad can be found at http://www.keypress.com
Paul Kunkel’s website for Geometry Constructions http://whistleralley.com/construction/reference.htm
Practice the first 7 constructions for homework.
National Library of Virtual Manipulatives--You will need the software Java to run these applets—Java can be downloaded free from
http://www.java.com/en/download/manual.jsp
An interactive geometry investigation, Exploring
Geometric Solids and their
Properties at the NCTM website.
Some tutorials for Geometer’s Sketchpad:
Introduction
to Geometer's Sketchpad
Tutorial on Geometer's Sketchpad from Annenberg/CPB Learner.org. This web site
gives instruction on creating constructions for various objects.
Basic Skills with GSP
Downloadable GSP-based tutorials that introduces the user to basic and common
features of GSP. This is an interactive tutorial.
Math Teacher Link is a
web-based professional development program for mathematics teachers at the 9 -
14 grade levels. It provides short courses on the use of technology in teaching
mathematics. One of the courses is a GSP tutorial called
Using the Geometer’s SketchPad. The
courses may be taken for credit but are available for guest participation. Just select the course and then click on Step
By Step Instructions on the left. You
can then download the modules.
The Virtual Institute
Two page tutorials on GSP basics.
Helpful Information
1. Accessing Geometer’s Sketchpad in University
Hall 162
Start
Programs
Departmental Programs
Teacher Education
Geometer’s Sketchpad
2. Adding a button to Word’s toolbar
It is helpful to add a button to the toolbar for commands such as superscript, subscript, symbols, and Equation Editor.
1. Make sure the toolbar you want to change is visible in your document window.
2. On the Tools menu, click Customize.
3. Click the Commands tab.
4. In the Categories box, click a category for the command you want the button to perform. For example, to add a button for symbols, select the Insert command; to add a button for superscript, select the Format command.
5. Drag the command you want from the Commands box to the displayed toolbar.
6. Additional information to Create a Custom Toolbar can be found through Microsoft Office Word Help.
3. Generating a random integer on the TI-84
Use the random number generator on TI-84 to generate an integer between -5 and 10:
Math PRB randInt(
Then enter the arguments of -5 and 10 by typing -5,10) A comma separates the beginning and ending values and the right parenthesis closes the list of arguments. Then press ENTER. If you continue to press ENTER, additional random integers beween -5 and 10 are generated.
The compasses, rulers, protractors, and AngLegs used in the workshop can be ordered from Safe-T Products at http://www.classroomprdcts.com/