Fishbowl in a Math Classroom

I was challenged by Janice Schwarze to use a fishbowl model to differentiate in my math class.  I tried it today in my Honors Algebra 2 class and I can't wait to do it again.

When I 1st considered doing a fishbowl lesson, I had no idea what it was supposed to look like or how to execute it well.  I went to one of our LSCs for help getting started.  She arranged for me to see fishbowl in action in a Social Studies classroom.  This made all of the difference because I saw that the success of the fishbowl was in how I introduced the activity.

I began by asking students: when have you done a fishbowl (inside-outside circle) in other classes and what did that look like?  I followed that up by asking: what would a mathematical discussion look like?

I posted my success criteria for today's activity on the SmartBoard.

-Mistakes grow the brain - This is a learning experience for you and your peers, no one is expected to have the right answer right away.  
-Use mathematical language
-MP1:  Make sense of problems and persevere in solving them.
-MP3:  Construct viable arguments and critique the reasoning of others.
-MP5:  Use appropriate tools strategically (Whiteboard, Calculator, Chromebook, Your choice)
-Make eye contact
-Everyone must speak
-Connect your thought/idea to the previous student's thought.  Don't go on a tangent that doesn't make sense.
-Don't move on to a new problem until everyone on the inside circle understands it.
-Outside circle is listening for understanding.  Specifically listen to your partner.  Did you understand their explanation?  Did they use mathematical language? Did they accomplish the 3 math practices?  

As we were going over these bullets, I made about big point about saying that "Getting the right answer" wasn't my biggest objective today.  There's more to understanding mathematics than finishing a problem.  Our goal was to grow in being able to construct arguments and critique each other.

My original lesson for today was 6 example problems that I was going to show the class.  It was originally a very teacher-directed lesson.  I put students in readiness groups based on an exit slip from the previous day.  I was purposeful in picking which questions I wanted each group to work on.  I gave each group 3 of the 6 questions to work out together.  I also gave each group a pattern to figure out.

There were 3 circles going at once.  I had 4-5 students on the inside and 4-5 students on the outside.  Each inside student had an outside partner who was specifically listening to their contributions to the discussion.  After the 1st group went, I had the outside partners give 1 praise and 1 critique (Math Practice Standard 3).  I think this was my favorite part of the activity.  It was fun to see students encouraging one another.  And even cooler to see that we have a classroom environment where students feel comfortable offering constructive feedback.

Afterwards I had students talk as a class about the benefits of this kind of activity in math.  They appreciated that time wasn't a factor today.  There was no point in racing to finish the problem.  Students felt like the had space to ask questions and approach a problem more slowly for better understanding.  A few students commented that they liked hearing the different approaches to solving problems from their peers.  If they didn't understand the problem when one student described it, someone else was there to offer a different perspective.  Students felt that they had a better understanding because they had to speak and explain.  There was also a lot of pride expressed that they were able to figure out the problems as a group, without any teacher help.

Next time I do a fishbowl activity in class, I want to give students the opportunity to made decisions and have choices in their discussion with activities like Would You Rather Math or Which One Doesn't Belong.  I'd like to see their personality come out more in the discussion by having to defend their opinion.  A big thanks to Steve Stack and Megan Plackett for helping me plan such an engaging lesson!