2. Reason abstractly and quantitatively.
How are middle school teachers helping their students reason abstractly and quantitatively?
How can students be helped to:
- make sense of quantities and their relationships in problem situations?
- decontextualize — to abstract a given situation?
- represent a problem symbolically?
- manipulate the representing symbols as if they have a life of their own?
The CCSS states:
Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
What are you doing to help students develop this practice? What makes it hard? What challenges are you encountering?
I think that one of the biggest problems for me is that I am afraid I won’t have enough “real-world” situations and ways to demonstrate at my hands when needed. When the teachable moment comes it can be difficult to come up with examples and models to help students bring their reasoning together. So, one piece that become critical is planning ahead thoroughly to attempt to anticipate student questions. Also, I need to keep better records of student thoughts on a variety of situations to help my anticipation of questions from year to year.