I received an email from a former student (R.L.) who I taught a few years ago. She’s a senior now in college and is taking an education class. She wrote a paper that she wanted to share with me, because half of it centered on her time in our Advanced Precalculus class during her junior year. I know I’m a warm-demander teacher (or at least that’s what I strive for). I try to make my classes a little bit harder than kids think they can do (but exactly at the level I know they can do). Reading her essay made me feel a lot of things, but I love how in so many ways she captured some of the things I strive for and do in class. The fact that she noticed them and remembered them years later means a lot.
She said I could share that part of her essay here on my blog when I asked. I like to archive good things in teaching, and this is something I’d like to archive. So here it is.
I’ve been thinking about ways that coaching, questioning, and telling played out in my education at Packer. Packer was the ideal setting for these methods of learning, as we had small, seminar-style classes and teachers with the capacity to work with students one-on-one and develop individual relationships. Upon reflection, my eleventh grade math class, Advanced Pre-Calculus with Mr. Shah, exemplified coaching, student-telling, and questioning, and also included exhibition-style projects.
This was the hardest class I took in high school. The content was very challenging, and Mr. Shah’s approach to math drove me crazy. Mr. Shah sees math as a creative field, one that demands critical thinking and a deep conceptual understanding of topics that many see as surface-level and robotic. Mr. Shah’s packets used broad questions as the benchmarks of understanding, pushing students to explain concepts using their own words. His problems had a playful tone, and we spent most of our class time working through material in small groups while he played music in the background and buzzed around answering questions and challenging students to think more deeply. Why are conics important? What is the meaning behind this geometric sequence? Why did you choose to solve this combinatorics problem this way? At the time, these questions made the class a nightmare for me – the content was already challenging enough (it was in this class that I failed the only test I’ve ever failed), and the way he forced us to think about it made it even harder. But, after reading Sizer and thinking about coaching, telling, and questioning, I see what Mr. Shah was doing.
In addition to trying to make math more fun and meaningful, he was pushing us to develop mathematical skills that built upon each other. Sizer writes that the “subject matter chosen should lead somewhere, in the eyes and mind of the student” (Sizer, 111). The curriculum progressed when we made “mathematical discoveries,” and those discoveries led us to mastery of complicated skills and a deeper understanding of concepts. Mr. Shah never talked at us. Discoveries came through telling, but, it was table-mate to table-mate telling. As the teacher, Mr. Shah’s role was to encourage our discoveries and offer support as we worked through our own questions and explained concepts to one another.
Through his approach, we were also practicing broader skills like critical thinking, creativity, perseverance, and thoughtful reflection. He centered the class around group work and we spent a significant amount of time reflecting on our individual contributions to the group and the strengths and weaknesses of our team. I honed these skills in my other classes at Packer, and I am sure they are part of my academic success at Tufts. Mr. Shah’s class was enormously challenging for me, but in writing this paper I have found an appreciation for his approach, and I know I owe him a thank-you.
Lastly, Mr. Shah also incorporated exhibition-style projects into our curriculum. He called them “Math Explorations,” and we had to do four of them throughout the year. They were not as big as these example exhibitions and they did not center around a presentation [like someone mentioned earlier in the paper], but they provided an opportunity for individual exploration in a subject area of our choosing. Being the English-lover I am, for one of my Math Explorations I wrote a series of math poems – a sonnet, some haikus, an ode, and a free-form poem. I was proud of these poems. It was exciting to take ownership in a class in which I often felt overwhelmed, and pursue something that made the content relevant to my interests. These projects were empowering, and they helped me feel connected to the material and confident in the class. If this is the power of exhibition-style learning, then I’m in full support, because the takeaways made a difference in my learning. If only more schools had teachers like Mr. Shah and the resources and the capacity to make classes like his more widely available.