Another posting of a reflection I wrote at the outset of my teacher education program three months ago.
Reflection about where I am in learning about teaching math
“A teacher makes over 3,000 nontrivial decisions daily.” Enhancing Professional Practice: A Framework for Teaching, Danielson (1996)
To date, my two weeks at my placement, and in the C&I course, provide me with a rich set of experiences to reflect upon and learn from within [our teaching program]. It is clear that teaching math involves so much more than the mathematics, itself. Teaching math well spans multiple dimensions to include pedagogy, curricula, environment, adolescent behavior and psychology, interpersonal skills and teamwork, to name a few. Much of what Iʼve seen and learned so far in [our teaching program] is that teaching parallels what Iʼve learned in life, but took 30 years to learn: that there is no one set way to address the multitude of situations one encounters in the course of the day, and teachers, with 150+ students a day, must contend with this dynamic every day of the school year.
The C&I readings, videos, group work and discussions helped elevate my level of thinking about teaching math to a more abstract, almost philosophical level. Specifically, our discussion today about assessments, both course related and standards related, as they relate to mathematical understanding versus proficiency, makes me question the definition of proficiency. Is instrumental understanding, of mathematical procedures and formulas, that emphasizes memorization the best measure of proficiency? Or is demonstration of contextual learning more important? Or perhaps some mixture of the two? And is the mixture the same for those students that wish to pursue a non-technical career versus those that wish to pursue a technical career?
In speaking to the latter question, when I attended the US Military Academy at West Point, cadets essentially took the same curriculum regardless of whether one intended to pursue a degree in history or engineering. However, there was a subtle distinction in the level of rigor, depth and breadth of certain content depending upon the intended major. Hence, we were divided into two educational tracks called HPA (Humanities & Public Affairs) and MSE (Math, Science, Engineering) with HPA for the non-techies and MSE for the techies. While everyone took calculus, chemistry, physics, history, english, foreign languages, law, political science, etc, the intensity and emphasis for each of these varied depending upon your track, which helped immensely.
Iʼve recently learned, thanks to [our teaching program], about the potential, even today, for tracking to be used in subtle, and not so subtle ways, to do great harm to minority students, as well as how it has been used historically to perpetuate inequities in education. And that heterogeneous classrooms are an excellent way to provide equitable learning opportunities to all. Having said that, I wonder if some aspect of the “tracking” I experienced at West Point, if applied at the secondary level, could help address the challenges experienced by students who do not wish to pursue a rigorous approach to math, science or even history or english, for that matter, depending upon their intended career path.
I hope to be able to vary pedagogical approaches with my cooperating teacher at my fall placement in order to see what works best, when and with whom. I see myself as a hybrid of some of the teachers weʼve seen in videos where I mix some direct instruction with group work and whole class discussion, sometimes for no specific purpose other than stretching studentsʼ thinking, but more often for ensuring a deeper, contextual understanding exists. Ideally, my students will feel as comfortable with, and master, standardized tests such as the CSTs, CAHSEE, ELM, etc as with more open-ended problems requiring higher level thinking and understanding.