Teaching Philosophy
I believe that all students are capable of learning mathematics and should be challenged to do so. Exemplary math teachers are those set high standards for all students, and then provide them the necessary scaffolding and support to reach those standards.
Students will be motivated if they are actively engaged in the learning process. It is important for teachers to incorporate many discovery and exploration activities into their lessons. These investigations allow students to come to a deeper understanding of the material, make connections between concepts, discover new related ideas, and recognize the need for further knowledge. In addition, teachers should provide justification for the topics that students are learning. A concept is taught not simply because it is in the standards, but because it addresses gaps in prior concepts and has implications in and beyond the subject.
I also feel it is important to address multiple learning styles by using a variety of instructional techniques, including group work. This allows the classroom to truly become a collaborative learning environment. Students should eventually recognize each other as both teachers and learners, instead of just classmates.
Here is a critical anaylsis on an article supporting this view.