Sometimes that means the teacher has to get out of the way and let kids talk, wrestle with materials and information, and struggle against obstacles. I've written recently about losing the art of teaching to the science, concerning the current trends in our profession, but engagement, in my opinion, must lean heavily on a teacher's ability to creatively guide students and provide freedoms without losing control of the class. All the data collection in the world will not allow for that kind of magic.
Speaking of collecting data, however, we even have the opportunity for more of it in the area of student engagement. Some of the staff in our school take the time, a few times a year, to roam from room to room to analyze how deep students are getting, how engaged they are in conversations, and how high their thinking levels are when provided tasks. After this, the collected data is pooled and reported to the teachers. We discuss it and think of ways to improve upon it for the future. We make suggestions to each other about how more teachers can achieve more engagement for more students.
We don't always stay at the highest levels since some instruction is best presented during direct instruction, but we want to avoid times when the class is disengaged completely. Whenever possible we want to push the envelope and let students do the thinking.
So, if your child reported to you that we had a bunch of people visiting our class, Monday, this was the reason. They were collecting data to see how engaged we were.