After attending Mattie and Chris‘ morning session at Twitter Math Camp, I really wanted to try and get students talking more in class. One idea (of many) that really stuck with me was doing a Socratic (Paideia) Seminar in my geometry class. After talking to Mattie at lunch, I decided that doing it as an introduction to proofs was a great place for it.

Geometry is typically taught using two-column proofs. However, I wanted my students to be knowledgeable about all formats of proofs and make the decision for themselves. Every format speaks to students differently, so I wanted to give them the autonomy to decide.

Every unit, my students receive a new booklet from me. This booklet includes all of the material they need for the unit and acts as their textbook. The first activity for this unit was proof exploration. Students had to examine two-column proofs, paragraph proofs, and flow-chart proofs (these were given to them) and find one other source about proofs. In order to prepare for the seminar, students had show they activity read.

**Ways to show you actively read: **

- Highlight
- Notes in the margins
- Questions in the margins
- Answer all questions

Students filled out the pages below before coming to class for the seminar. If you are interested in seeing the entire booklet, it can be found here. unit-3-introduction-to-proofs

When students arrived to class, I had the class organized in two circles. The outer circle had tables and the inner circle only had chairs. I assigned students their “circles” and then asked them to take out their notebooks and computers.

The inner circle could use only their notebooks during the seminar. The outer circle would be on their computers. I used PowerSchool for students to “backchannel” during the seminar. On this “backchannel” students could engage in conversation with the rest of outer circle about the conversation going on in the middle circle. They could also talk about anything else as long it revolved around the subject. Many students chose to answer the questions being asked to the inner circle, and agreeing or disagreeing with comments being made.

Before we started, we went over the rules for each circle.

It was amazing how much students were talking and engaged in the activity. I heard very insightful comments from all ranges of students. A lot of my students actually asked for deeper questions for next time (I went easy on them). They said they had a deeper understanding of parts of proofs and why different parts needed to be included. They all also picked their favorite style of proof which they are allowed to use the entire year.

We look turns switching the circles as well! Below are some the questions that my students were asked. I did not reach the questions out loud. I just added a question when signaled by the students.

A video of part of our seminar can be found here!