> > 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? Of course. > > 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. What you describe in the paragraph above isn't the norm in my room or in classrooms I visit. I do think that it works sometimes to give an activity and have the students try to figure out what is happening.
I haven't seen Dan teach so I can't comment on your description of his classroom.
Richard > > Bob Hansen > >  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.