Reflections upon Teaching a Poorly-Conceived Lesson

Using a “failed” mathematics lesson as a mini-case study, I explore some of the challenges inherent in teaching an inquiry-style mathematics lesson. The ensuing discussion centers around two issues: the preparation and subsequent scaffolding involved in guiding students to desired understandings, along with the tension inherent in “telling” and “not telling” in an inquiry-style pedagogy. I resort to personal reflection, as well as to Wenger’s (1998) theoretical construct of participation and reification in revealing the underlying link between the manner of lesson preparation and consequent engagement of students during the enactment of the lesson. Reflections upon Teaching a Poorly-Conceived Lesson One of the difficulties in attempting to transform one’s teaching practices from a traditional lecture format to a more student-centered mode of instruction is that one oftentimes relinquishes a certain degree of control and predictability in the classroom. As opposed to simply planning out a lecture with the expectation that students will ask questions when they do not follow the course of reasoning as set out by the instructor, the new practice requires one to more carefully map out—that is, to anticipate and be prepared for— various contingencies: in particular, such issues as, in what manner might the ideas be best embedded within activities (as opposed to directly telling them), what degree of scaffolding might be necessary and optimal for the different levels of students in the class, in what manner might one want to go down divergent learning paths depending upon student input, and so on. As such, in opening up the classroom discourse, by its very nature, student-centered teaching practices introduce new and necessary skills for the teacher to acquire both in preparation and in interaction with the students (see Lampert, 2001). When the lesson plan has been carefully thought out in these terms and more, the teaching itself can be a real thrill. It affords a richness of dialogue, and even learning opportunities for the teacher that lecture-based teaching does not often enable. On the other hand, when done poorly, this other way of teaching can leave both teacher and students alike in pedagogical predicaments that the traditional approach safely steers clear of for the most part. I am particularly interested in this latter case, of when things are not aright, of when such attempts can go messily wrong. I am interested in this, for I believe that it is in exploring when and how a particular pedagogical approach fails that one sometimes comes to a deeper understanding of how it might come to succeed. † [email protected]