Student Perspective-How do students interact purposefully about inquiry-based learning

This video is evidence of what students think about inquiry-based learning. It is also evidence of what a purposeful interaction among students and between students and teachers.
Context: The vice-principal was on instructional rounds and walked into my classroom. She gave a context to my students and asked them for their input on what inquiry-based, open-ended, student-generated learning means to them. We had been working on an inquiry on creating generalizations and algebraic equations for areas of regular polygons. Through our explorations, we addressed the curriculum expectations and went well beyond them. The vice-principal asked if students preferred learning and activities based on the curriculum or exploring mathematical concepts and let the exploration take its course even if it meant going beyond the curriculum. This set the context for a very purposeful interaction where students were having a learning-focused classroom, listening and speaking their mind respectfully. It was very empowering to be part of such a group of thinkers. While analyzing this conversation, it was made clear to me that students will use the language of assessment if we use it, they will think deeply about their learning if we give them an opportunity to, and they will interact respectfully if we model what accountable talk moves look like, sound like and feel like.