Value of written reflections in understanding student thinking: the case of incorrect simplification of a rational expression

Encouraging students to articulate their thinking when doing mathematics is a means by which teachers ascertain understanding. Reported here are the results from a content analysis of the written reflections of 67 undergraduate students who incorrectly simplified a rational expression. Although asked to write about the thinking that led them to their solutions, most did not. Instead, they recounted what they had done or had not done. Of those who did write about their thinking, most wrote of their confusion or uncertainty; only a few provided a rationale for the procedures they used. Nevertheless, insights into student thinking were gleaned.