COURSE DESCRIPTION
Goals Addressed:

• 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 Course
• Develop a framework for thinking about the learning of geometry.

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:

• 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 geometric investigations for appropriate use in the middle school classroom
• Make connections between InterMath experiences and standards-based reform documents, such as the NCTM standards

• Textbook: Van de Walle, J. A. (2004). Elementary and Middle School Mathematics: Teaching Developmentally (fifth ed.). Boston, Ma: Pearson Education, Inc.
• Geometer’s Sketch Pad (GSP) is an interactive geometry program used for exploring, constructing, measuring, etc. This program will be used for demonstration purposes as well as a way for you to deepen your understanding of geometrical concepts. This program will be necessary for you to install on your personal computer.
• Excel or some other spreadsheet application will be necessary for exploration activities.
• Graphing calculator (TI-83 or 84) and/or a Graphing Program

I. Week 1

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)

II. Week 2

A. Participants engage in investigations in Points, Lines and Planes
B. Participants begin their first web page write-ups to include in their online portfolios
C. Continued technological teaching and support (especially with GSP and the structure of a write-up)

III. Week 3

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

IV. Weeks 4-5

A. Participants engage in the Triangle Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of spreadsheet program

V. Weeks 6-7

A. Participants engage in the Quadrilateral Investigations
B. Participants add write-ups to their online portfolios
C. Introduction of graphing program

VI. Week 8

A. Participants engage in the Polygon Investigations
B. Participants add write-ups to their online portfolios

C. Discuss and brainstorm ideas about modifying the InterMath experience for a middle school mathematics classroom

VII. Weeks 9-10

A. Participants engage in the 3-D Object Investigations
B. Participants add write-ups to their online portfolios

VIII. Week 11

A. Participants explore systems of measurement and Logic investigations
B. Participants add middle school lesson plan to their online portfolios

IX. Week 12

A. Participants engage in Coordinate Geometry Investigations
B. Each participant creates a technology-enhanced mathematical investigation for their own classroom
C. Participants add middle school lesson plan to their online portfolios

X. Week 13

A. Participants engage in Transformational Geometry Investigations
B. . Participants add write-ups to their online portfolios
C. Participants should work on a lesson plan consistent with InterMath for their students

XI. Week 14

A. Each participant will take a Geometry exam

B. presents their entire instructional activity to the entire class
C. Class will provide feedback on the lesson plan

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

Lindell Dillion	Tabitha Davis
Jennifer Woods	Jana Bowling
Laura Sims	Lauren Mofield
Carla McNeely	Lauren Johnson
Andrea Heath	Erin Grotel-Bundrige
Tiffany Graham	Amanda Pulley
Chantel Lewis	Norma Smith
Erin Hutto

• Absence/Tardy/Make-up Policy:
  Regular attendance is essential for successful completion of this course. Attendance will be taken daily. More than 3 absences from this class may result in a breach of contract. Your grade may be lowered and your stipend may be revoked as a result of excessive absences. Students entering late or leaving prior to the end of the class period will be counted absent for the day.
  
• Academic Honesty:
  The integrity of students and their oral and written work is a critical component of the academic process. All written work submitted in this course will be individual work unless otherwise directed by the instructor. Students must properly document all outside sources used for outside of class assignments. The submission of another’s work as one’s own is plagiarism, and will be dealt with using the procedures outlined on pp. 69-72 of the 2004-2006 GC&SU Undergraduate Catalog
  
• Request for Disability Modifications:
  Georgia College & State University complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act. Any student who may require an accommodation under such provisions should contact the instructor privately as soon as possible and no later than the end of the first week of classes or as soon as you become aware. No retroactive accommodations will be provided in this class. Please contact Dr. Craig Smith, Chair, Georgia College & State University Committee on Learning Accommodations, Kilpatrick Education Center, Room 103 or (478) 445-4577 to submit your documentation and coordinate necessary and reasonable accommodations. All discussions will remain confidential.
  
• Safety/Common Courtesy:
  Fire drills may be conducted during the semester. In the event of a fire alarm signal, students will exit the building in a quick and orderly manner through the nearest hallway exit. Learn the floor plan and exits of this building. Do not use elevators. Crawl on the floor if you encounter heavy smoke. Assist disabled persons and others if possible without endangering your own life. Assemble for a head count on the front lawn of the main campus.

COURSE ASSESSMENT

Undergraduate:

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 a mathematics lesson that integrates technology and geometry for use in their own classroom. Points will be assigned on a rubric, to be given later, addressing the above criteria. The grade will be determined by a ratio of points earned divided by total possible points multiplied by 100.

60% Write-ups
20% Lesson Plans
20% Final Exam

For final percentages falling in the following intervals, a student will earn at least the corresponding letter grade: [90,100] A; [80, 89.99] B; [70, 79.99] C, [60, 69.99] D; [0, 59.99] F

Graduate:

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 a mathematics lesson that integrates technology and geometry for use in their own classroom. Graduate students will be asked to align their write-ups and lesson plans with the Georgia Performance Standards (GPS). http://www.georgiastandards.org
Points will be assigned on a rubric, to be given later, addressing the above criteria. The grade will be determined by dividing the number of points earned by total possible points and multiplying by 100 to obtain a percentage of points earned.

60% Write-ups
20% Lesson Plans
20% Final Exam

For final percentages falling in the following intervals, a student will earn at least the corresponding letter grade: [90,100] A; [80, 89.99] B; [70, 79.99] C, [60, 69.99] D; [0, 59.99] F