From students' "what I've learned this week" summaries, the instructor also gains a peek at students' (possibly distorted) mental snapshots of the mathematics.
"In doing [homework] I did not have many problems except I do not know what the slash symbol...in Pr(E|F) means"Since conditional probabilities were the primary focus of the homework, this is a student who thinks they are a lot less confused than they are! Thanks to cover sheet, this is revealed now, while there is time, rather than only on the next test.
"Why is composing functions important?" -College Algebra Student
"...the discussion we had in class helped me to understand inverses more so than if I was just to read the book. When you picked on me to explain a question to another student [it] helped me to understand because I had to explain it verbally instead of just saying 'yes, I understand'".
"The little word problem workshop that we had last week did help me..in figuring out what to look for and how to get the problems started. This is very helpful because this is one of my biggest problems. If I can just get it started then I am usually fine. The workshop really did help and I am glad that we did it"
Instructor can gain and maintain the attention of students in class by launching a lecture, discussion, or activity with words like:
or
This can help foster the instructor's role as "coach" or "guide"
rather than "grader". It also encourages student writing and solving
for understanding -- focus is on learning rather than on
"points".
Students tend to genuinely appreciate and cite this as evidence of instructor's caring, listening, and trying to help them.
In addition to modeling correct mathematics for the students, the
instructor can model an attitude of enthusiasm and generally of caring
about and taking the material seriously.
Instructor's responses to cover-sheet comments can include reminders for struggling students of available resources, including (repeating if necessary) general "study tip" suggestions and information, e.g.:
and even a polite
tends to be appreciated by students.
"Dr. Barzilai, I am so excited because I am finally grasping this material..."
--Nursing student in College Algebra (Test 1 grade: 48; test 2: 84)