When applying for academic jobs in the US, one is often asked for a recommendation letter from someone who can attest to your teaching abilities.
How much experience should the letter-writer have with your teaching? Should they have observed you teach multiple times? (In my present postdoc I will teach 3 courses per academic year, should I be inviting potential teaching-letter-writers to visit each course? Or perhaps a selection of undergraduate/graduate courses/seminar talks?)
Are the answers to the above different for postdocs/tenure-track jobs? Within tenure-track jobs, are they different for research-focused versus teaching-focused jobs?
I am personally in mathematics. I am assuming the answers will not be too field-dependent (please correct me if I am mistaken), so I left it out of the main body of the question.
Answer
In a situation where "teaching matters", there are two significantly different tangible assessment types: student evaluations, and peer (or supervisor) evaluations, not to mention the more extreme sort of commercial sites which have the systemic problem that the commenters self-select, typically with skewing to negative, even ranting reviews.
The aggregate response in university-organized end-of-term student reviews is useful, not necessarily as a gauge of whether you're a good/effective teacher, but whether the students are "happy". For that matter, successfully generating no "complaints" during a term is some kind of success. This does matter.
Peer-evaluation (occurring not at pre-arranged times, but unplanned, yes), or evaluation by your director of undergrad studies in your department, is the closest to what hiring committees might care about. In particular, if you are doing what your peers or "boss" think you should, it doesn't matter whether the students love you or not... as long as they're not actually unhappy.
(Indeed, our goal surely isn't so much to make students "happy" in a superficial way, as to achieve certain pedagogical goals.)
The attributes relevant to undergrad teaching, especially lower-division, are essentially unrelated to seminar talks and even to graduate-level teaching, since the objectives (and the frame of mind of the audience) are invariably very different.
Edit: a "teaching letter" that merely reports that the student evaluations were positive, or that there were no complaints, is positive, but cannot count as a "strong" teaching letter, I think. This is a special case of the weakness of recommendation letters of any sort that merely repeat facts not known first-hand to the writer. First-hand information is better, and, further, lack of a first-hand-information letter-writer is not a good thing...
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