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Stephanie. I think it is graph a because a Ferris wheel goes round.
Tara. Graph a goes backward in time.
Laura. Time goes forward this way, along the x-axis, so it cannot be a.
Quavis. It goes down like this. That would make it go back in time.
Stephanie. Yes, but that is how a Ferris wheel goes.
Stephanie and Quavis gestured animatedly as they stood in front of the graphs, shown in figure 1, that had been drawn on the board. Tara and Laura were speaking from their desks, and the rest of their second-year algebra class watched intently. We will subsequently share more of their discussion as we discuss an example of a Socratic seminar, but we first notice how these students struggled to "organize and consolidate their mathematical thinking through communication" and to "communicate their mathematical thinking coherently and clearly to peers, teachers, and others" (NCTM 2000, p. 348). The students were arguing vigorously and seemed disappointed when the bell rang to end the seminar.
Mathematical discussions with this high level of interest and involvement are a goal of the Standards and are stimulating for both students and teachers. At Forest Park High School in Forest Park, Georgia, the entire mathematics department uses Socratic seminars to create classroom settings that are conducive to this type of discussion. Each mathematics teacher conducts several Socratic seminars a year in each class-with the whole class. For the sake of this action research, each teacher who taught secondyear algebra did the seminar described in this article with at least one class, but each teacher had a control class, as well. As teachers compared students' achievement on tests that focused on the concept of function, they found that students who had participated in a seminar did better on the chapter test and on a posttest instrument used to measure students' understanding of the concept of function.
In this article, we share the basics of using Socratic seminars in a mathematics classroom.
BACKGROUND
For an example that indicates how Socrates taught mathematics, we turn to the dialogue between Socrates and Meno (Rouse 1956). Socrates used what we have come to call Socratic questioning to teach the Pythagorean theorem to Meno's Greek servant boy. Socrates later said that...