This article reports on an analysis of episodes of invalid or controversial arguments that occurred while two different groups of students worked on similar fraction tasks and examine the role that these types of arguments played in the development of students' reasoning. One group consisted of suburban, middle-class, fourth graders who worked on…

A great number of teachers in the United States have found themselves wrestling with an internal conflict between their teaching beliefs and a need to revert back to traditional modes of teaching in order to have their students demonstrate proficiency on high-stakes tests. While they want to include more non-traditional methods in their repertoire…