Our thinking around inquiry-based teaching and learning is that it develops 'disciplined' ways of being and thinking. That is, inquiry is more than students just 'doing projects.'
Rather the purpose of taking an inquiry approach is to structure learning so that students can tackle problems, generate possible solutions, share and improve each other's ideas, and demonstrate their understanding in a variety of ways. The end goal of inquiry is students developing deep understanding of key ideas and concepts. With that in mind, much of our school's understanding of inquiry comes from the Galileo Educational Network and their Inquiry rubric.
Seen that way, the purpose of strong mathematical inquiry is to get students thinking, acting and working like mathematicians, not just doing math. This movement from students 'learning math' to students 'learning to think like a mathematician' can be a difficult concept to understand.
With that in mind, this video produced by our two grade 4 math/science teachers (Amy Park and Deirdre Bailey) does a fantastic job of capturing and sharing how an inquiry-based approach develops mathematical thinkers by putting student problem solving, idea generation and collaboration at the forefront of the learning.
This video is also an exemplary example of teacher inquiry where you have two teachers carefully and critically documenting and then publicaly sharing the learning that is occurring in their classrooms.