The school year is upon us and it is with great excitement that I look toward this new school year. I just sent off the first draft of my dissertation proposal, we just got our edited version of geometry text back from the printers, and our newly edited trigonometry text is hot off the presses as well. It always seems like there is a fresh energy surrounding the beginning of the school year that emanates from the students and is just contagious – even after twenty years of teaching.

I recently read a great essay entitled “Questioning Authority” by Charles Bingham in his book about relational authority (SUNY Press). In it, he discusses Gadamer’s view on questioning as an act that “breaks open the being of the object” and “revealing the questionability of what is questioned.” Basically, Gadamer believes that a true question is one that is asked only when the answer is not already determined – it may “sow the seeds of its own answer” but the questioner is really asking about something she truly doesn’t understand. So the philiosophical question that Bingham poses is just this – can a teacher ask a “true” question? It seems that for the most part, in a mathematics class teachers, including myself, generally ask questions that they previously know the answer to and have an expectation of a response. This is really how we teach and make sure that we are fulfilling our curriculum and students are “learning” what we need them to learn.

However, Bingham posits that we can ask “true” questions if the experience of the students is that they are “true.” In other words, one must look at the intention of the question posed by the teacher – if the teacher hopes to “break open” the subject matter as can happen with a true question, and if it experienced that way by the students in the classroom, then in the students’ expeirence it is a true question. Math teachers can ask questions in a true way, questions like why did you choose that method to use? what other problems does this remind you of? Do you prefer this method or that solution? Describe your reasoning process for the rest of us here. Why does that prove your statement? What’s the contradiction in what you just said? and many others.

Think how differently the teacher-student dialogue would be if math teachers posed true questions throughout the class period. Today in a faculty meeting, an English teacher colleague of mine had us all read an Emily Dickinson poem (much to my dismay) and then everyone was able to raise their hand and say one part of the poem that was confusing to them. This was totally acceptable that without any explanation of poetry or review of Dickinson’s works, we were able to creatively and openly express our confusion and process of “not-knowing.” I wondered how acceptable this would be to my colleagues in a mathematics lesson. How many of them would’ve expected a review of some algebra and then an explanation of the problem before questions were allowed. I then wondered how different our education system would be if the questioning process in mathematics classes was more like that in the English class.