Workshop on Geometry Software
Math 241
Fall 2015
Course number: 22128
Meeting Tu Th 2:00- 3:15
GMCS 421
San Diego State University
Professor: Mike O'Sullivan
Web page: http://www.rohan.sdsu.edu/~mosulliv/Courses/geometrysoft15f.html
Email: mosullivan@mail.sdsu.edu
Office: GMCS #413, ext. 594-0175
Office Hours: Tu Th 3:15 - 4:00.
and other times by appointment.
Detailed Information
Course Description
This one-credit software workshop provides prospective
secondary mathematics teachers an opportunity to explore a geometry
software program (GS).
Required Materials
We will use GeoGebra, which is an open-source product similar to
The
Geometer's Sketchpad. GeoGebra is available free on the web. It is
installed in the computer lab GMCS 421. Each student will create an
account on the web with GeoGebra and save their work to this account.
The instructor will access it and grade it via the web.
Schedule
| Week | Tu. date | Th. date | Topic |
| Week 1 | Tu Sept. 1 | Th Sept. 3 | Euclidean Geometry |
Week 2 | Tu Sept. 8 | Th Sept. 10 | Beyond Euclid |
Week 3 | Tu Sept. 22 | Th Sept. 24 | Algebra and Geometry |
Week 4 | Tu Sept. 29 | Th Oct. 1 | Trigonmetric Functions |
Week 5 | no meeting | Th Oct. 8 | Exponential Functions |
Week 6 | Tu Oct. 13 | no meeting | Explorations and Final Project |
Student Learning Outcomes
- Geometric constructions: Students will use the GS to do key
constructions from Euclidean geometry and explain the properties of
these constructions. Examples include the circumcircle of a triangle
and quadrilaterals with special
properties (rhombus, kite, parallelogram) and the midpoint
quadrilateral.
Students will also construct parabolas, ellipses and hyperbolas using
their foci (or directrix).
-
Graphs of polynomial equations and intersections of curves:
Students will use the GS to graph lines, parabolas and other
polynomial equations and explain how varying parameters affects the
graphs.
They will explore and explain how the intersection points of curves
vary as the parameters vary.
-
Graphs of trigonometric, exponential and logarithmic functions:
Students will use the GS to graph trigonometric, exponential and
logarithmic functions and explain how varying parameters affects the
graphs.
- Transformations and creative geometry: Students will use rotations, reflections,
dilations, and other transformations to produce complex and aesthetically appealing
geometric objects.
- Functionality of Geogebra: Students will become adept with key
capabilities of Geogebra that make it useful for teaching: creating
tools, exporting files, labeling figures, adding explanations, and
publishing their work.
Grading
-
Class Discussions: [5 points each week, 25 total]
Each week, we will discuss a few of the math topics that GSP enables
us to explore.
There will be a participation grade for each class meeting.
- Weekly Projects: [12 points each of 4 weeks, 48 total]
Each unit will involve submitting 1 GS file with several pages.
Although each student is required to submit his or her own file,
students are encouraged to collaborate when completing these projects.
All assignments will be graded on a scale from 12 points (3 points for
correct construction,
3 points for mathematical
explanation, 3 points for quantity, 3 points for quality of
presentation).
- Final Project: [30 points]
The final project is a cumulative portfolio of all the work you have
done for the course. You should update and revise your previous
work,
add additional content on a particular topic of interest.
The goal of this entire little course is to help you think about how a
GS might be useful in your future courses and future teaching.
Therefore, the final project should display your capability to use
this tool in a creative way.
(6 points for correct construction, 6 points for mathematical
explanation, 6 points for quantity, 6 points for quality of
presentation, 6 points for effective organization).
Grading scale:
94-103 A
90-93 A-
87-89 B+
83-87 B
80-82 B-
77-79 C+
73-77 C
70-72 C-
60-69 D