when making a circle, it's just a line going forward+turning. it slowly turns while it goes forward, making a circle. when making any polygon, you must find the angle of the shape first. then command Mr. Turtle to draw the amount of sides it has.
Camilla told me in her reflective comment on my class web site. She was trying to explain what she had discovered about how to build a circle and then convert what she "knew" about a circle and turn that knowledge into a polygon.
They strained and experimented. It worked and their discoveries thrilled them. Molly went on to say
I learned that if you want t make a shape, sya a pentagon, then you will take the amount of angles, 5, and divide that into 360 and you will get the degree. With circles it's a continous line kind of wrapped around an invisible sphere in a way. Once you figure that out it's, really easy.
. Now her math teacher might do handsprings if she could only overhear this reflection.
My students couldn't be torn away from their computers. The learning and their metacognition of how they learned it is fantastic.
Here's my only regret. My colleagues don't have time to incorporate this learning into their math lessons. I totally understand why they feel that way. The pressure seems insurmountable. It's just one more thing to do. But somehow...either through co-teaching or swapping classes or something I think it is imperative for this kind of teaching to find it's way into the mainsteam core curriculum.
It is criminal for it to remain in computer class. I really believe with my whole heart that if I were to co-teach this for a year or two with the math teacher as they normally crossed their geometry lesson that addressed the properties of circles and polygons, they would easily meet all their teaching objectives and more. I believe that within those 2 teaching cycles they would see that this material teaches itself and that the programming hurdle they are so uncomfortable with IS amyth and that the kids can lead them. All the math teachers have to do is stand back and guide with the math questioning they already so capably do everyday in their classrooms.
Argh when will this ever become apparent. In this insane world of NCBL this kind of teaching is THE only answer because without this deep understanding our kids have no chance of achieving the test scores that some legislator who has never been near a math classroom set. Drill and kill won't get us there. But this kind of experimental, conceptual teaching will because it makes our students in real young mathematicans.