Create debate is a social decision making tool that we was built to spur conversation and critical thinking. There is a debate forum and online community that is an ideal setting for people to debate topics and ideas they feel passionately about. As an educator there is a free service you can use, a trial use, then one's you have to pay money for. If you are comfortable having your students create their own for free instead of grabbing the special for about 100$. For free you receive a sub-domain and unlimited debates. The 100$ a year gives the educator a grading tool feature and your debates can be set to private. You can get a 30 day trial free if you would like to try it out first.
I created my own debate and it can be found here: http://new-to-teaching.createdebate.com/debate/show/Going_1_to_1
I was very doubtful on how it would look, but it turned out really well. My question was posed and if you click the link at the top you can add your own argument.
If you used this in the math classroom I could see very useful ways of creating your own debates and having your students use this well. Students could either create their own questions or the teacher could post questions or exploratory assignments for the students to look up then discuss. Very cool!! Here is the link for the website: http://www.createdebate.com/