Throughout my Teach For America training, we were continually reminded of the importance of having a sense of urgency. The intention of this is to focus on maximize learning within classtime, but as I was thinking about the implications of this being too urgent can be a bad thing in the math classroom because it promotes the memorization of math rather than the discovery of the intrinsic logic of math to solve the problems of the world. This process of discovery must be methodical and enable every student to approach problems in ways that make sense to them. Consequently, whole class lectures can inhibit individual thought and leave concepts shrouded in mystery to those student's brains that don't work in sync with the teachers'.
To solve this, math teachers must promote individual thought on a daily basis and in a variety of contexts as every student will excel in different situations and success in one area can be used to promote successes in others. The discovery of concepts should not be limited to formal mathematics, but should also include logic philosophy, and generic problem-solving questions. These various disciplines demand similar thought processing skills and moving between them all can increase student investment and promote cognitive flexibility. Finally, writing must be the act that permanently cements these concepts in students' minds. Taking time for students to write what they notice, what the next step should be, other ways to solve similar problems, and what they learned can highlight individual learning at critical points in the lesson and promote higher order thinking skills.
While the idea of a timer is a good one (and is a good idea for the teacher to have timed out each portion of the lesson for themselves to have in the back of their head), a noisy timer can disrupt student thought and increase anxiety to finish before the bell instead of being completely devoted to the problem at hand. Math takes time to digest and so our sense of urgency needs to be translated into a steady, disciplined, and directed thought process that focuses on depth and not so much breadth.