This bit of research gave me an idea — sew the lines on plastic canvas with filet crochet thread. Why?
The young student I mentioned yesterday told his family about how Mrs. Tammy knows how to draw curves with straight lines. Now, his sister wants to learn how and his mother said her son was absolutely amazed this was possible.
I plan to be very careful about introducing this to my students. The emphasis will be on play, not work. Inviting, not forcing. Design and creativity, not checking off a mathematical standard. A sprinkling of terminology where it lives, in this context, not a memorized definitions.
I am going to be quite technical here. If you have never taken calculus, please do not feel defeated. I am explicit to illustrate how high level this mathematics is. The name of the curve is a parabola. We made it by sewing lines tangent to the parabola at a series of points. The slope of each line expresses the rate of change at the point on the curve. And, if I sewed an infinite number of lines, I would make a perfect parabola. I sewed less than thirty lines, far less than a hundred, much less infinity. So, this design approximates a curve.
How wonderful that the seed for ideas taught in calculus can be sewn in early childhood by making marvelous designs.