Today I attended an ok session, a good session and a great session. The great session was in a room with about 12-14 teachers. We had various prompts we discussed around teaching, resources, technology, etc. I wish I could remember the prompts, because they were thought provoking and everyone could contribute based on their own experiences. What I found most fascinating in the end was that whatever type of school or level of teaching (elementary, middle, high school) we all had the common goal of doing what was best for our students. We recognized that teaching has changed both in terms of content and pedagogy over the past 10-20 years. But it ultimately comes down to building relationships and trust with the students in front of us. Without that foundation, it is challenging to have students learn anything, let alone math specifically.
Another topic that cropped up in our conversations was that students constantly ask "When am I going to use this?" The truth for many students is "After high school, you will never use this." For example, imaginary numbers or the quadratic formula are probably not useful to 90% (just my estimate) of college graduates after college. (My husband is a Ph.D. chemist and does not use the quadratic formula on a daily basis.) Does lack of utility for topic X mean we don't teach topic X? If the only reason for learning something was because it was useful, we never would have fractal based antennas in our cell phones. It was at this moment in the discussion that I said the following:
I truly believe this. Sure there is math content that needs to be taught, but most students won't remember it unless they go into a math or science field. What will carry students through their high school years and beyond in mathematics is the willingness to discover, try, fail, try again, fail once more, make connections and finally generalize. The generalization will not be a fill-in-the blank scaffolded note, but it will be the result of the understanding that they have discovered and constructed for themselves. Teaching in this way takes courage. A willingness to let go and trust your students and yourself. It is not easy and after 25 years of teaching, it is still a conscious decision that I have to make daily. I don't consider myself to be an "expert" or "master" teacher. I am like my students - a learner and I am trying to improve and become better at my craft on a daily basis.