Last weeks class my eyes were wowed to the idea of creating figures using patty patter. You know, the paper between your frozen hamburgers. For 2 hours my classmates and I constructed basic quadrilaterals squares, rectangles, trapezoids, rhombus, parallelograms, and also basic bisecting properties. I have had zero past experience with patty paper and was very impressed with the ease of transformations.
My thoughts are with the patty paper, the students understand the ideas behind the constructions a lot better. For example. When creating an angle bisector, you take an angle and you fold the two sides of the angle on top of one another. When you create the crease were the fold line happens you then get the bisecting line of the angle. Or take for example the perpendicular bisector of a line. Fold the patty paper on itself so the line on the paper is exactly on top of itself including the two end point on one another. From here you really understand the idea that a perpendicular bisector is a perpendicular line in the middle of an original line. The thought of the topic becomes so clear on what this vocabulary is and the student is not lost in the process. Which happens when we construct objects with compass and straight edge.
Why would we use a compass and a straight edge then. One of my philosophies as a teacher is, "I teach students with math, I don't teach math" Compass and straight edge are a great tool for teaching fine motor skills. Using these items takes practice and more practice. Students can fine tune these skills and become very good at creating simple constructions. My fear is students become lost in the idea of creating the figure and don't focus on what they are trying to achieve. For example a simple reflection of a figure over a line with a compass and straight edge takes 4 or 5 different actions for each vertices of the figure. If you are reflecting any quadrilateral the student is constructing 20 different movements. They loose sight of the idea that the image is "flipped" over a line. With patty paper it is simple and obvious. The figure is drawn and you make a fold over the line and copy the figure to the other side of the figure.
What is the conclusion then? I believe there can be a balance of the two. The skills compass and straight edge provide working side by side with patty paper can be the best for student's learning. This way we are getting the best of both worlds. We can even can throw in technology constructions for a well for a rounded learning experience that differentiates to all students.
I agree that you can use both. Patty paper is easier to use in my opinion than compasses. The biggest problem I see is that most textbooks do not support patty paper. Every geometry book I have seen uses compasses and straight edges for constructions. I can not think of any geometry books that I have seen that use patty paper. You would need to do the research to find activities to include patty paper in the classroom. It would require some more work on your end to find the activities that work best for your classroom. In the end, using both would make student learning more interesting and be able to give chance to compare and contrast these two methods.
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