On Sep 1, 2013, at 5:03 PM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
>> 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.
Of course? Well I guess I will have to wait and see what you produce as your actual lesson leading up to and surrounding the "popcorn picker" activity. It is very difficult for me (or anyone) to imagine that you mean "of course" as I wrote it, because in all of the years of posting here, you never reference anything bearing even a semblance to structured mathematical reasoning. What you post here would lead any teacher to believe that you are having a great deal of difficulty getting the math across to your students. If your reply "of course" actually jives with what I just wrote then your students would answer the popcorn picker question before the video even starts.
Or is it just me that finds getting students to understand and own the structured reasoning the hard part of teaching mathematics?
> I do think that it works sometimes to give an activity and have the students try to figure out what is happening.
Yes, but it has to be placed at just the right time with respect to the epiphany. If the students are guessing then you know it isn't the right time and you need to back up some. For example, the epiphany in the popcorn picker activity is the realization that you can compare two expressions, algebraically, and determine when one is larger than the other. Why wouldn't a properly prepared student go right to that when you present the question?