In Alan B. Schoenfeld's article, In Fostering Communities of Inquiry: Must it Matter that the Teacher Knows "The Answer"?, he discusses his personal experiences both as a professor of university courses on problem solving and as a participant in a research group comprised of many different levels of experience and education, from masters students to professors.
During the discussion he uses several examples of how, in the problem solving class, usually the students expect him to have "the answer" as he is the teacher. He admits that he knows exactly what will happen in the class; he can predict most of the discussions and questions from students before they are shared.
This is in contrast to his research group, where the progression is more fluid. The participants are welcome to bring data, video, particular challenges, to the group for discussion. The group is a community and no one has "the answer". In the group, there are several understandings: everyone is there seeking knowledge, the authority is the accepted standard of the explanations and there is trust: people are free to share and have ideas compete without personal biases.
Schoenfeld goes on to explain that throughout the semester in his problem solving course, he encourages the students to judge the solutions for themselves, not to look to him for validation of their ideas, but to prove it with mathematics. Indeed, he points out that in a mathematics classroom, the authority is really the mathematics itself, not the teacher.
Overall, Schoenfeld feels that in both the research group and the classroom, the community needs to understand:
a) they are all seeking a particular kind of knowledge and answers are not known in advance
b) the authority is not the teacher, it is the explanations and what is right
c) there is a feeling of trust.
The part of this article that struck me most was the constant and purposeful use of the word community when referring to both a classroom and a research group. This is the core of the article and how he has created a community of learning in both situations. A happy, fruitful community can be a happy place of learning, of discussion, of debate and disagreement; exactly as classrooms should be. I admire his willingness to be fallible. Perhaps, as he is considered an expert in his subject, it is not such a risk for him, but it shows his commitment to acting in the best interests of his students and also his colleagues.
I agree with Schoenfeld that there are 3 elements are essential in a community. I have noticed that in my classroom, it is particularly difficult to convince students that they do not always need to get approval from me, as their teacher, that I am not the expert. The most helpful way I have found is by pointing out my errors and making a list of my mistakes. Students seem genuinely surprised that a teacher not only makes mistakes, but celebrates them. They are highlighted as a learning experience. It has made students more willing to participate, take risks and try out new ideas.
Do you think you have a community of inquiry in your practice? Do you have all the tenets Shoenfeld mentions? Do you think there are times in teaching when the teacher should be the expert?
ReplyDeleteThe teaching model I am using in my robotics program gives more time for students to pose questions by reducing the time spent in direct teaching to 10 minutes, compared to the 20-30 minutes outlined in standard curricula. The inquiry community is based on what-if questions. A “what-if” question might be “how can we calculate the area of a circle if we only knew its diameter?” The question requires further analysis of the formula presented at the beginning of the class. Instead of being discouraged, most students feel like this is an interesting question that needs more investigation. The participation and engagement in the robotics program have been great, with a large proportion of students demonstrating improvements in standardized tests after participating for over half a year. But, I am bit hesitant to acknowledge Schoenfeld’s first tenet, acknowledging that each student is seeking particular answers. I noticed that in situations when students believe that teacher has a “correct answer”, they are less motivated in inquiry-based learning and some will change their goals to getting an A. To be an expert in this case, rather than knowing answers, I think it would be more important for teachers to treat questions with passion, and spend time to plan and share solutions with an open mind.
Whenever I asked students some questions (not limited to mathematics), they often look at my face after she/he gives their first idea. Then they change their answer if my face does not change. If I ask them “so your answer is xxx (confirming their second answer)?” without expressing any emotion, they again change their answer… I suppose it is not easy to invite students into free opinion/question atmosphere in mathematics classes (at least in Japan). Students might think they have to respond appropriate answers/questions that teachers and classmates accept as correct or incorrect ones. I think it narrows students’ point of view and also makes mathematics as a difficult subject to connect to other fields. Additionally, this reinforces the idea that teacher should be a perfect person because everyone in class feels anxiety to answer inadequate contents.
ReplyDeleteI agree with your idea Nancy, and your idea is very interesting to me since some students believe teachers never mistake. I think teachers should be an expert in mathematics education, however, it does not mean they have to be PERFECT when teaching or answering questions. Even when they accidentally make mistakes, they have to behave as an expert who can eventually help and lead their students to the goal.