Hope the following article will help you
http://journals.sfu.ca/flr/index.php/journal/article/view/44/89
Your ideas may presume that teacher engagement is universally understood and emotional intelligence is also universally understood. These two concepts may prove to be too diaphanous to apply metrics.
That notwithstanding, arbitrary measures could be used although the utility of such a method may not be useful: an attempt at a repeat of the experiment in an alternate population could yield marginal results because of context.
In the ETS cited, an arbitrary set of definitions was base lined to provide a framework for the end scale. While this may make the "metrics" look good, many can take issue with the initial presumptions/definitions. In other words there are many variables to nail down, or in the vernacular "different strokes for different folks"; but...that is the point of testing your ideas. I recommend you go forth and discover.
The key engagement factors are
Teacher's ability to engage with students can perhaps take into consideration; students' learning outcomes, assessments, enthusiasm, motivation and other variables that are pertinent to the syllabus.
Dear Gitanjali Roy,
Your question is quite important. I added a file about teacher democratic classroom management . You may review it.
Thank you all.
Yusuf, How shall i operate the file you have mentioned?
collaborative engagement scale
https://broadleafconsulting.ca/uploads/3/5/3/5/35353475/tools_for_measuring_collaboration.pdf
