So today I uttered my favorite new acronym in class while explaining what groups should be doing.Group work has become the new bane of my existence because I both realize it’s importance, and also recognize the fact that I have not done it well. …yet.  My new favorite acronym, HDYK  (How Do You Know), is hopefully going to help with that, along with new roles and what I learned employing those roles today.

For a number of reasons, I tried to get kids to focus on the process of group work, not necessarily the outcomes.  These were the roles that I suggested in order to get students to focus on listening to each other:

• Involver – Your job is to make sure that all of your group members are involved in the task.  Ask questions to other members to make sure they have their ideas included.
• Task master – Keep track of the task that needs to be done and the amount of time required to do it.  Remind people of the work the group needs to finish if it seems people are off task.  Let people know when they are ahead of schedule as well.
• Summarize and Share – Keep track of everyone’s thoughts and prepare to share all of the thinking with the whole class.  Also be prepared to let others in the group know what is going on if anyone gets lost.

This was a pretty interesting switch on group work (which I totally stole from someone else, but I can’t remember who) and it delivered some success.  It seemed nice to see people flocking to certain roles.  Perhaps next time I will find ways to immerse kids more intensively in these roles.  One thing I may do with would be to have little conferences with the different roles, like ask the Involver to give me a report on the groups functioning or pull out the Summarizers to meet together and share ideas.

The task for this class was also one which I hoped to hear a lot of “How Do You Know” from kids. Each HDYK  was hoping to get kids to justify their response to the following question which could hopefully get us to start thinking about permutations, combinations and other ways of counting:

Dimoni is going to make a new restaurant.  He promised it would be fancy, gluten free, paleo-friendly, vegan, low-carb, high-fiber, seasonally appropriate, locally grown, and tasty.  This left him with the following ingredients.

Sweet Potatoes, Radishes, Carrots, Onions

…and some other stuff.  Given that he has such few ingredients he wanted to make as many dishes as he could using all of these ingredients.  He planned to say he could make 50 different combinations of these items.

Is it possible to make 50 different arrangements of these items?  Work together to detail how to figure out all of the possibilities.

In how many different ways could you describe an arrangement?

When the students were in groups I realized how this could appear like a “What’s the answer” kind of task.  Many kids would come over and say “I got 12, is it right?” To which I would say “How do you know it’s 12?”  Students were supposed to come up with some way to justify that they have whatever answer they have.  Many instead focused on asking me whether or not I could justify their answer as “right.”  After some direction most of the groups got to a place where they felt they could justify the choice and many were saying things like “Yes, our answer is 12, because he shouldn’t be trying to act like radishes and onions is a different arrangement than onions and radishes.”  In the future I think I would replace the word “possible” with “reasonable” to suggest that kids should have a reason for what they say.

It seemed a little more conceptual than some kids were able to latch on to, and with so many people expecting me to guide them, it was really easy for kids to get left out.  I probably should have done a Next time the task will need to be really clearly laid out to show that we are emphasizing the HDYK and not the answer.  My role as facilitator has to be reduced too, perhaps the involver could be the person who is allowed to ask me questions, and can only ask me questions when they have heard from everyone in the group.

Next time I see this group will be on Friday and we will spend that time comparing all of the responses from each of the different groups.

Seems like one of the side effects of my new emphasis on large scale problems is getting kids caught up when they come in late, weren’t paying attention, or otherwise find themselves lost.  I think tradition trains students to shut down when they are lost, as if the key to getting un-lost will be someone telling you what to do.  Like if you get lost in the choreography of a dance, you need someone to let you know what the next step was, or even to prompt you to look at the previous step, or just to show you the steps so you can follow it.  The “math-as-dance-step” metaphor breaks down once you want a student to do more of the creating themselves.  I mean, I don’t go to someone who is used to dancing ballet and say “Make a routine to this hip hop song” (unless of course I’m the producer of that Julia Stiles movie).  So when I want students to explore all the different ways of solving a complex problem, how is it that I let them know the steps?  Not the algorithmic steps to the specific math problem but the dance steps for thinking about and solving any kind of problem?

Today I tried to get students to work on a counting task from MARS and as they struggled, I wrote on the board the steps from Polya, about how to solve a math problem.  These steps had a lot of meaning for, but I don’t think the kids got it.  Abstracting the problem solving process is not a good thing to do when your kids just had a break down in their problem solving process.  Tomorrow I am going to roll out a whole bunch of problems that various people can have success with, and then afterwards ask them to share, and use that share out to abstract the steps required to solve a problem.  Hopefully if the problem comes from them, they will be more likely to apply it the next time they get to a place where it would have previously felt safe to just “wait.”