“Do you guys remember the parachute man?”: Teaching tensions when managing students’ prior knowledge in problem-based instruction in mathematics.

Lecture by Dr Gloriana Gonzalez, University of Illinois at Urbana-Champaign, USA 

ABSTACT:
Reform documents in mathematics education in the US recommend problem-based instruction to enable students to experience authentic mathematics.  For teachers, problem-based instruction requires paying close attention to students’ prior knowledge.  Since students could have multiple ways to solve a problem according to the prior knowledge that they possess, students could propose ideas to solve a problem that the teacher had not anticipated.  I show a case where a geometry teacher tried to trigger students’ prior knowledge about similar triangles with a problem.  Instead, students remembered “the parachute man,” which was an anecdote that the teacher had used to teach theorems about the geometric mean.  I illustrate with this example the tensions that a teacher faces when managing students’ prior knowledge in problem-based instruction.  On the one hand, the teacher should allow students to make connections with prior knowledge on their own as they work on a problem.  On the other hand, there is specific prior knowledge that the teacher wants students to use so that their work on the problem becomes useful for doing other mathematical work.  Drawing from Systemic Functional Linguistics, my analysis of the parachute man anecdote involves an examination of the teacher’s use of intersemiosis—the visual displays, the mathematical symbolisms, and the discourse.  I propose that some teaching moves could strengthen students’ memory of a theorem, but could also jeopardize students’ memory of the reasons justifying the theorem.  I use the construct of “the collective memory of the mathematics class” to explain possible reasons that a teacher could have to use students’ memories of an anecdote while working on a problem.