I really love the website Math Pickle. There are so many great resources, activities, videos, etc. I wish there was more!
Here is the founder of Math Pickle giving a great talk about problem solving. Inspiring stuff.
On of the activities I used to today was their Symmetry search. The kids start with an image like the one below;
Next, they have to find all the lines of Symmetry in the shape (rotational and mirror). These include lines and rotations in each individual piece of the puzzle, but also as pices combine to make bigger shapes that have lines of symmetry and rotation. In short, there are a lot.
The point of the activity for my students today was not to find lines of symmetry. They know what lines of symmetry are. Today was all about organization. How can you keep track of how many lines you have found, and how can you communicate those lines to your classmates clearly? That was the task.
Many of them used tallies, different colored markers, letters to show rotational vs. mirror, etc. One thing that happened during the activity that I found very interesting was how the students self organized with the people around them. I made no reference to group work, nor did I say it wasn't allowed (this is on-purpose). I noticed that the students immediately went to work within the groups with whom they were sitting. However, since we all sit in very close quarters and noise travels quickly in a small space, they realized that they were using similar strategies for keeping track of their numbers with other people in other groups. At this realization, they began to hurriedly move about and readjust the groups to work with people who were using the same strategy.
What is happening here? I believe that they are searching for elements in a group that allowed them to increase their efficiency. They need an environment where their ideas can bump into each other, be challenged, and move forward. When we talked about it afterwards, they said that is was a simple matter of working with somebody who understands them. That is part of it, but there is more to the story, and I will tell in the coming weeks as I continue to hash out the details in my head.
For the time being, if you are interested in the topic, I highly recommend talking a look at some of the articles by Brent Davis (University of Calgary) website. He writes extensively about Complexity Science and Education.