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(and common enough not to need an explict demonstration)
Also vital to good teaching but difficult to acquire if not already present to some degree:
Awareness of surroundings, particularly how well the students are paying attention and abstraction the essence of the lesson. The lack of this sense is called being oblivious.
A teacher's familiarity with the course content is *secondary* to the relationship with students.
What kind of relationship would *most benefit* the students' learning? Does the optimal relationship depend on the instructor's personality (Brian Mastro vs. Milton Nash, for example) or on the distinct experiences each cohort of students brings from their prior mathematics training?
As to the first question, Dan Meyer in a 2009 CMC North conference talk suggests that we in the education field practice *being less helpful* in the classroom. Avoid the trap of training the human equivalent of Clever Hans.
Let students struggle with open-ended problems (the kind they're likely to face in real life) so they become comfortable with *irresolution*. Working against this teaching strategy is the powerful force of episodic TV, whose tidy screenplays and storylines actually rewire the viewers' neural pathways to make them impatient with irresolution.
To set the stage for productive struggle with open-ended problems in the classroom, the teacher should help the students develop information literacy (i.e., "to practice reading the textbook," as Jessica B writes in a Jan 2016 post to the academia stackexchange). Even with a small class size, "there isn't enough time to answer every question from every student, so they need to be able to learn from a mathematical text." Building students' proficiency in reading for understanding can be as simple as holding a short reading quiz at the start of each new lesson.
Jessica B's expectation that she will receive a plenitude of questions, even from a small class, requires further justification. Students might not be ready to put their confusion into words the first time they encounter a new concept. Most likely, Jessica B has trained her students to make their first encounter with new material *before* the in-person discussion (i.e., the flipped classroom model). This model allows more time during class meetings to jump straight into the crucial second step of the general procedure for understanding new concepts:
1. Find out the definition.
2. Play with basic examples to understand the definition.
3. Use the definition to prove simple things.
4. Gain intuition, understand unusual examples, extremes and pathologies.
5. Prove more complex things.
6. Write out clear solutions.
Because step 1 (information transfer) is usually not the best use of lecture time, experienced educators like Jessica B have gotten "buy-in" from their students to undertake this step at home.