I believe reducing this gap can start from linking their prior knowledge of introductory theoretical principles/assumptions to the more advanced concepts that they are currently studying. I remind students of the relationship between some basic statistical theories and application rules and today’s lecture and assignments by asking questions or reviewing the related summary pages in lecture slides. Also, I focus on giving student questions, not direct answers; this encourages them to establish their own rationale or premise for refining the problem and reaching an answer in lab sessions. Students come to be familiar with the complete cycle of statistical analysis, i.e., when to use certain methods and to how to interpret the results. For instance, more students in my class earn partial points for assignments by showing their choice of application rules. 

--I would change the sentence in the fourth paragraph to--: The Quantitative Methods class is often considered lacking in such communication. 
--This makes it seem like it’s not just your class that lacked the communication, but the subject in general, in multiple universities. Which, I think is what you’re going for.--

--I understand what you mean about the verb tenses. I tried to make them all present tense verbs, so that it didn’t sound like it applied to one specific class, but went to your teaching strategies and philosophies in general. So, I would change the example you gave me in parentheses (I arrive early and left late) to-- “I arrive early and stay late.â€ --This way it is an ongoing thing.--

Some students who are hesitant to participate at first tend to participate more actively in class when I ask questions. Also through interactions with students in lab sessions, I am able to identify... 

--Again, it keeps the teaching current and not totally done with. Hopefully this makes sense, and helps. Let me know if you have any other questions--