The math curriculum I use has a recurring character who shows up in the student workbook to help them identify computational and algorithmic errors. His name is Puzzled Penguin. I haven’t really spent much time on the workbook activities that utilise Puzzled Penguin but he came up in a conversation during a recent inquiry group discussion about troubleshooting strategies.
The idea of troubleshooting is pretty simple: the students are given a solved problem with errors in it. The first thing they do, though, is not correct the errors. Instead, they figure out what was done right. Then, and only then, do we go back and look for the mistakes. As students identify the mistakes, they are able to review the processes used to solve similar problems.
The most empowering way to do this troubleshooting is to use a student’s own work, but you also want to make sure that the student isn’t embarrassed or humiliated. So there needs to be a culture of cooperation and collaboration. We are still working on establishing that in our classroom, so I decided to use Puzzled Penguin as an intermediary. Still using student work, I explained who Puzzled Penguin was (most of the students already knew) and had them help him figure out what he did right and what he needed to fix.
It was a great strategy and helped many of my students better understanding the standard vertical algorithm for multiplication and how it connects to other strategies we’ve used, such as the open array model. I am hoping to see my students use these strategies with their own work. In the meantime, we will continue to help Puzzled Penguin become less puzzled!