One of the joys of my engagement in the interweb of math teacher bloggers (some of whom I stumbled across my self many of whom I have discovered through the MTBoS challenges) is that I feel my brain tickled and challenged. One of the most consistently challenging of the bloggers is Michael Pershan and he has recently been writing a series of posts about what he finds interesting. Kind of math-y in general, but also just musings. I used to think that success as a math teacher might be measured by running into a student after college and having him/her still be able to answer, say, a trig question about oblique triangles. Luckily, I grew out of that and have a different idea of what success might mean. I have a story from a former student (Chris S.) that I think is apropos here – and I apologize if it seems like I am patting myself on the back here, trust me when I say that there are many students who don’t see their experience with me the way that Chris did. For a few years, I was living in NJ a mere 35 minute express train ride into Penn Station. On days when I was off work but my wife was not, I would often head into Manhattan. Chris was working there at the time doing some high powered financial advising. He was one of the more brilliant kids I’ve ever taught and I have kept in touch with him since he graduate in 1994. So, one day we are having lunch and he is recalling a particularly thorny data analysis problem he had been wrestling with. Much of what he detailed was over my head, but it was great to sit and listen to him so passionately recalling a struggle. He said that his boss, let’s call him Ned (I don’t recall his actual name), helped him with a major breakthrough. He said that one morning – after wrestling with this problem for over a week on and off – he told Ned that he needed to take a long lunch and get out from under this problem. He came back a few hours later and Ned had made an important advance on the solving of this problem. Chris then said to me, “Jim, Ned kind of reminds me of you – he just asked some questions of the data that I did not think of asking and this allowed me to finally solve this problem.” I still get kind of chocked up thinking about this day. He did not say that he remembered a certain lesson or a success on his AP test. He did not say that he remembered having fun in my class, but I think he did. He did not say that he thought of me as a caring teacher, but I think our ongoing relationship says that he does think of me this way. No, what I took away from that conversation was that I challenged him by asking questions he did not think of. What I inferred (maybe this is just optimism on my part) is that he finds this to be a positive trait. He was speaking with admiration about his boss. Now, I know for sure that Chris is a smarter person than I ever have been and I know that many of my students fall under this category. But what I hope that I can convey is the value of questions. Many times in the classroom these are restricted to a mathematical context, but I want my students to develop an appreciation of a good question and develop the habit of asking good questions about the world around them. There is a quote I found in my reading years ago when I was a student and it is a quote I share with my students. I have not found the correct citation for it, so I apologize for not being able to give credit where it is due. Here is the quote:
Genuine enquiry is an important state for students to recognize and internalize as socially valid. Consequently it is an important state for teachers to enact. But it is difficult to enquire genuinely about the answer to problems or tasks which have well-known answers and have been used every year. However, it is possible to be genuinely interested in how students are thinking, in what they are attending to, in what they are stressing (and consequently ignoring). Thus it is almost always possible to ask genuine questions of students, to engage with them, and to display intelligent directed enquiry. For if students are never in the presence of genuine enquiry, but always in the presence of experts who know all the answers, then students are likely to form the impression that there is an enormous amount to know, and that experts already know it all, when what society wants (or claims to want) is that each individual learn to enquire, weigh up, to analyse, to conjecture, and to draw and justify conclusions.
One of the amazing librarians I work with found the citation for me. You find the whole text at http://www.math.jussieu.fr/~jarraud/colloque/mason.pdf
The author is John Mason