Math Entry

What did I learn?
There was strong evidence to support our varied learning styles and the approaches we take, as thinkers, in order to solve problems.  Some of us are "big-picture" thinkers.  Some of us are visual learners and like to demonstrate our thinking and understanding through the use of pictures and drawings.  Others of us tend to be procedural and first run the numbers--the use of pictures is an afterthought or a means to support mathematical computations (do the numbers lie?).  Some of us are spatial and can represent our undersatnding in more than one spatial arrangement.  I also learned that an awesome responsibility of the teacher is to monitor and probe for explanations and listen to students' justifications.  In really hearing their thought processes, a teacher can organize the order of presentations in a way that can be meaningful and in a way that can support fluid learning.  All of the presentations are related sequentially and conceptually.

What do I have questions about?
I am most curious about the appropriate timing of classroom congresses.  Is it advisable for them to come at a particular time in the unit?  Before, during, after?  I would imagine before or during, as the element of inquiry seems key.  At the time, I was very curious as to how this type of model could be introduced/utilized in a higher mathematics classroom--i.e. calculus.  I wondered if I had been exposed to this type of learning experience would I have understood calculus, or thought about the subject, differently than I otherwise do currently?

What are the implications for classroom use?
Here is a model that if used effectively could open our eyes as educators to the thinking patterns of our students.  And in tandem with this, our students become the teachers as they devise ways of thinking and explaining so that their peers have a deep understanding of the subject matter.