I recently was helping to create the last abode presentation on Tools and Representations for our board, so I have been thinking a lot about this pillar of the pedagogical systems. We have also been working on this at the schools I work at and a recent lunch and learn brought up a great example to help highlight the importance of annotating the representations of the student thinking no matter what tool they have used to do it.
I wanted to start with some quick pictures of possible tools that students use to create representations of their thinking. (Click on the picture for the names of each tool)
Once these tools have been formed into a representations and annotated they become a representation of the student thinking. Here are some examples:
As you noticed above, the representations are annotated using sticky notes. A student can also annotate their thinking orally by explaining what their model represents. Here are couple pics of two tools that are drawn on paper. The closed array model and the open number line model.
I have included some descriptions of why these tools become a representation once they are annotated.
The last part of this post is a video that I did just explaining what happened at our lunch and learn last week. I have redrawn the models for this video to put it all on one clear page for when I was recording it. I think it helps make clear why it’s so important to annotate the student thinking in the representations.
I want to thank Shelley Yearley for reminding me of the importance of annotating the models to clearly show the student thinking in the representations. She made a point of showing us at the last fraction inquiry meeting and it inspired me to make this post. Again thanks for taking the time to read!