I-MATH PROJECTS
These pages are dedicated to the teachers in I-MATH. In this course, the teachers each create a project for their students. The following is a project completed by one of our I-MATH teachers.
Campbell High School
Calculus and Plane Geometry.
My Classroom
I am a teacher at James Campbell High School. I have taught here for three years. In the past I have been the teacher for Pre-Algebra and College Prep Geometry. This year I was the Calculus and Plane Geometry teacher. Plane Geometry is a lower level Math class for the non-college bound student. For many it is the third and final math credit.
I was introduced to the Geometer's SketchPad (GSP) computer software in my second year of teaching. That year I worked the SketchPad in by photocopying lessons from a SketchPad book. We worked with the sketchpad only a hand full of times. I chose to take I-Math so that I could incorporate the sketchpad into my Geometry classes more.
My classroom is set up for my Geometry students. My boards are decorated with posters about shapes, area formulas, types of angles, and common geometry vocabulary. My students always sit in groups of four to work cooperatively. I find that when students can explain things to each other then they form a deeper understanding of geometry. I also post student work on the back wall for all to enjoy.
GeoSketchPad Lessons and My Project
I introduced my students to GSP by simply turning my computer's monitor and showing them the initial basics. After Chapter 2, the chapter on points, lines, etc. I showed my students that GSP can draw, manipulate, and measure these geometry basics. Their first taste with using the software themselves was when I brought them to the computer lab so that they could draw pictures and use their new vocabulary. I spend a lot of time in my classes stressing vocabulary.
One of the lab sessions was on the Pythagorean Theorem. You will find an outline of this lab at the link below:
Ben created these notes on The Pythagorean Theorem to practice creating geometric figures. He also reinforced the geometry concepts involved!
My next unit was on construction. I taught my students paper and pencil constructions and even used Patty Paper construction methods for such things as Perpendicular Bisectors and Angle Bisectors. After all of this I had my students working on the GSP doing the same constructions. They even did Incenters and Circumcenters.
I often used sketchpad in my class to do presentations. I would turn my computer and show them concepts such as two parallel lines cut by a transversal, and the sum of the exterior angles of a polygon (a presentation that I personally think is the greatest thing in the world). The sketchpad makes it easy to draw a perfect shape like the circle and then to show properties of that shape such as the radii and tangent line meet at a 90 degree or right angle.
When I first started to look at the Lab Files my first idea was to create my own lab files. First of all I wanted to gear my labs towards my students; secondly I wanted to align them to the book I was using. This way if a student missed a lesson then that student could open the lab for that section to catch up. I ended up creating these labs and used them as a review for the year's work. You will find an outline of the labs at the link below:
My students spent three days in the computer lab working on the files. For many this was a refresher for the year. They worked at their own pace and could spend more time on files for sections they had trouble with. Many spent time jotting down notes. I wanted the files to be a review, not an introduction to the geometry concepts.
The students created GSP files as part of their work. Creating files of their own gave them hands-on experience in using the software, as well as reinforcing concepts of the geometry course. The example below is Cheri's file illustrating the definition of a chord of a circle:
The big question is; do I think that this had an impact on my students? And the answer is yes. I feel the students learned more from the computer then they would if I reviewed the concept on the chalkboard or overhead. It was definitely more beneficial than any worksheet could ever be. Did it impact me as a teacher? And again the answer is yes. I know that it was a difficult transition to change from lecture to student-centered lessons, but I did it and it worked!
What would I do to improve it? I think if I am teaching geometry again next year, I would spend time having students do presentations with sketchpad. I would also hope to get more computers in my classroom so that students can work on GSP anytime that they wanted. I also think that I can change some labs and maybe even create more.
Other Lessons From This Year
Three-Dimensional Drawings, Polyhedrons, and Volume: I spent a unit on three-dimensional geometry. During the first semester I had my student create drawings using two-point perspective. They really enjoyed this creative outlet. After I had covered the syllabus for my school year I had time to cover another topic. I choose Polyhedrons. I started with hands on models made of paper to teach the students the names of polyhedrons including Pyramids, Prisms, Cylinders, Cones, and Spheres. From here I used plastic models to study volume. I really liked this lesson. I filled a cone with water and used that water to see how much of the cylinder it will fill. I also did this with pyramids and prisms; and hemispheres and cylinders.
At first, the students were unsure about their ability to draw 3-dimensional objects. But with practice, they took great pride in their drawings, which were very good. The illustration below shows Gary's constructions, using Geometer's Sketchpad , of a cube and a prism:
Patty Paper: This year I did two lessons with Patty Paper. Both took about two days for the students to work through. The first was a lesson on constructing Perpendicular Bisectors and Angle Bisectors. The students used the waxy paper that they can write on and fold-crease to find out that the bisectors are equidistant from the sides of the angle or the endpoints of the segments. The second lesson was on the properties of polygons including trapezoids and kites. I admit that both of these lessons came from my Geometry Book, but since then I researched Patty Paper on the web and even ordered a book on using it in your classroom that I will use next school year.
