Attempting to organize my thoughts around Jurow’s article “Generalizing in Interaction: Middle School Mathematics Students Making Mathematical Generalizations in a Population-Modeling Project” took me back again to her conclusions and then again to the abstract. I believe that this statement is very important, “The analysis suggests that mathematical generalizing is the outcome of processes distributed across students, tasks, embodied activity, and modeling tools” (p. 279)
On page 297, Jurow concludes, “Mathematics students do not unproblematically see general patterns through exposure to or experience with multiple, similar cases. Rather, they need to orient to and be guided to recognize what is relevant in and across situations.”
With these two statement bracketing, as it were, her article, I then wondered who in my experience would be benefit from reading this article. I decided it would be classroom teachers and teacher candidates with whom I work on a weekly basis. Primarily I’d want these folks to see examples of how the tools and activities play a part in learning outcomes and how the affective relationships between students are every bit as important as the classroom management of the activities and manipulatives. I’d want to emphasize these two points because these are regularly points of difficulties for teacher practitioners in the field.
Furthermore, it is these points of difficulties that most often obscures or inhibits the teaching points / learning outcomes that a teacher hopes a student will appropriate.
One of Jurow’s questions, “How do students use and develop new resources (e.g. symbolic notation) to describe general mathematical patterns? (p. 297) is a question that the folks I work with could, as a community of learners, spend a good amount of time on, to our and our students’ benefit.
So, thanks, Jurow, for a fine ethnographic description of students participating in an open-ended, problem solving activity in which the materials and task and participant relationships are drawn so clearly. This provides a great opening artifact for my community of practitioners.
This archive was generated by hypermail 2b29 : Wed Jun 01 2005 - 01:00:04 PDT