I am searching for the relevant materials related to the time allocation in class according to the varied types of teaching:autonomy supportive versus controlling.
Any suggestions for the design of measuring the time proportion are welcome.
The classic study is "The Subject Matters" by Stodolsky. In mathematics education, the recent Grouws/Tarr work does analyze this. Stigler et al. also analyzed this for the TIMSS video study.
My focus is on how an autonomy supportive teacher attaches more importance to the satisfaction of students' basic psychological needs by allocating more time to listening to students, explaining rationales, offering suggestion. A controlling teacher, as expected, prefer to invest most of time in the instruction by the way of supressing. Therefore, the measurement of the time allocation is very meaningful and convincing of the awareness of teaching style.