On Sep 1, 2013, at 8:34 AM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> Bob, are you familiar with the computer language LOGO?
Yes, of course.
> I'm interested in its use in geometry teaching not so much for sophisticated programming but in giving students another vehicle for applying their geometry learning. For instance, if I have the 'turtle' travel 100 pixels, make a 90 degree turn to the right and then travel 50 pixels, how many degrees does it then have to turn and how many pixels will it need to travel to get back to the starting point?
And if we nailed 2x4s together in the same proportions, would you call it "using carpentry to teach geometry"?
I think what you are talking about is applying geometry to something hands on. But you still have to teach it (geometry) first. You have to go to the board and teach the pythagorean theorem or law of sines and make a reasonable effort to justify its validity. And then use it in several imagined cases first so that it has mathematical roots (in the students' heads). And then do the hands on activity and apply it. You will find, if you do it like this, that the application of it (geometry) comes easily.
Is that what you mean?
What many teachers do though is put the cart before the horse. They start with the activity and talk to the math behind it. I am not talking about Dan of course. He realized that doing an activity and just talking to the math behind it is stupid. So he just does the activity.
 justify - show through reason that something is true. This does not have to be axiomatic. Except for the pure mathematician, most truth in mathematics is based on consistency and statements that do not lead to contradictions. Much of the justification is circular. For example, showing that the pythagorean theorem is a special case of the law of sines.