The science is psychology and the particular field within psychology is Self-Determination Theory (SDT). I did research on patterns of motivation in two alternative schools for my psychology degree using SDT. In order to enable students to access their motivations teachers need to support the students psychological needs for autonomy, competence, and relatedness. Of the three schools tend to be most unsupportive of autonomy by being too controlling. To help differentiate between them here is a resource: http://www.teach-kids-attitude-1st.com/autonomy-support.html
That page also identifies the seven barriers to autonomy supportive teaching.

So you are right about the fact that how the teacher teaches is a critically important factor. There is great art in applying the science. But, what is required can be specified much more clearly than you know. All the terms from the student’s letters involve some combination of the basic needs and providing support for meeting them. There is still tremendous skill required to create a classroom situation in which the basic needs of students can be met in the same way that knowing the chemistry of oil paints does not remove the necessity of great artistic skill when applying it to canvas.