I was recently reminded of how important it is to evaluate student interaction when determining the professional development needs of a school or teacher.
I was in a classroom, trying to be invisible, observing a strong teacher and her students. Three very engaged students were debating the appropriate approach to solving an algebra problem; they were making good progress by eliminating various approaches through identifying faulty reasoning and recognizing the unreasonableness of their answers. They had narrowed in on two solution paths and were debating the merits of each when one student said, “Let’s wait for the teacher, she’ll tell us the right way.”
At that point they raised their hands and waited patiently for the teacher to approach their tables. The mathematical thinking that had been so lively was now dead. Once the students were given a nudge in one direction they re-engaged, but not in the same way. What I observed afterwards was a mechanical exercise in arriving upon a correct answer and much less rigorous than problem solving I observed prior to their asking for help. The habits of mind they were initially engaged in are sophisticated and useful well beyond the classroom (for instance, as vice president at a publishing company).
A number of us on Sine of the Times have cited CCSS Mathematical Practice Standard #1: “Make sense of problems and persevere in solving them.” The power of this standard and how it can be cut short by a well-intentioned teacher has never been more clearly demonstrated to me than in this classroom. This classroom reinforced my belief that we will only address the CCSS Math Practice Standards if we embed the practice of reflection through peer observation and regular video analysis into our day-to-day routines. What are the teaching practices that will engender these same students with the perseverance to struggle without asking for help from an authority? What are teaching practices that force students to ask themselves harder questions rather than ask the teacher?
I look forward to hearing your ideas.