My philosophy of teaching can be summarized as a desire to create a problem solving atmosphere.  I believe that this involves many aspects of teaching and instructional design as well as personal attitudes and relationships with students.  In order to create a true problem solving atmosphere within a classroom, several things must be done by the teacher.  First, a classroom of non-judgment is necessary, where students can feel confident and free to share their ideas and insights, even if not fully formed or sure of accuracy.  Second, it requires a teacher who will listen to the ideas and suggestions of the students fully without interruption or correction.  This requires some patience on the part of the teacher, but is well worth the time as students develop their own mathematical thinking processes.  Third, a problem solving atmosphere is one where different methods of thinking and developing the mathematical mind is not only allowed, but greatly encouraged.  Asking students for their own mathematical strategies and justifications and engaging them in advancing their own understanding in ways that work for them can greatly increase the intrinsic motivation of students to learn and study mathematics.

I believe that this philosophy of teaching can greatly increase student engagement and enthusiasm as well as the level of student understanding.  An atmosphere where personal thought and mathematical growth is greatly encouraged can make great strides in student success and zeal for future mathematical studies.