Real-time math collaboration

After a conversation with Geetha today, I agreed to share a little bit about my collaborative stroke of luck with the IB Math SL 1 students this week.

An essential, but often slightly boring, part of this year is the introduction of the "function families" and their respective properties.  These are the essential shapes of graphs that students will use for modeling for the next two years.  It's imperative that they understand and engage themselves to the lesson, so I hate to stand at the board and talk.  My solution has usually been to divvy up the functions to pairs, then let them each present at the board.

We brainstormed all of the functional characteristics that should be recorded, such as domain, range, x-intercepts, and such other mathematical falderol.  I suggested that students explore these functions and prepare to report back... then, a light bulb glowed neon above my head, and I said, "Wait!  I'll just create a spreadsheet and a presentation, and you can put all your findings in there!"  Cheers all around, what a great feeling for a math teacher.  They worked on their collaborative documents for about 40 minutes in class, then finished them up at home.  

Besides that the students seemed to enjoy the activity more, and be more engaged, I found some other advantages to this technology integration.

1. They were able to create perfect graphs that illustrated the functions much more accurately than a whiteboard drawing would have done.
2. They were able to do MORE graphs, and truly explore the behavior of their "parent function" and others like it, using graphing software.
3. The collaboration didn't end in class.  Everyone contributed, and I could see their contributions popping up in the revision history.  
4. As a homework assignment, students refereed their peers' work, and made many comments and responses in the spreadsheet especially.  Any unresolved questions were discussed in class, and this included formalizing notation and mathematical language as needed.  
5. They have created a resource that will be highly useful to them, and available at any time, when they are considering which functions to use for modeling.  

Take a look at the files below to get an idea about how the "finished product" looked.   Cheers!