Those conventions depend on the school, in my experience, but it's not crazy that a lecturer without a Ph.D. would call himself "Professor." I don't know how they roll at Columbia.

I went to a tiny undergrad, and we called all the professors with Doctorates "Doctor" and all the ones without "Professor" and the nuns "Sister".

Where I work, you are only allowed to be called professor if you are appointed in a tenure track professorial position. Which leads to problems, because most teaching faculty in our nursing school are non-tenure track, but the students tend to call them "Professor" anyway and then they get in trouble.

As adjunct faculty, and one who is indifferent to what students call me, I get a good amount of "Miss Hobbs" and a few "Professor Hobbs", and a lot of students not referring to me by name.

I tend to tell the story of trying to get my 4th and 5th graders to call me "Mistress Hobbs" after I got my Master's, and how they thought I was funny and wouldn't do it. That joke, however, requires that you know that "Mistress" is a feminine of "Master", which is a bit much on the first day of class, apparently, even at the Undergrad level. I think any student who did refer to me as "Mistress Hobbs" would get massive brownie points.

Wikipedia informs me that in the UK and some other countries, the term 'professor'

refers to a senior academic who holds a departmental chair, especially as head of the department, or a personal chair awarded specifically to that individual. [...] In the United Kingdom, Ireland, South Africa, Australia, New Zealand, The Netherlands, United States, Canada, and Hong Kong it is a legal title conferred by a university denoting the highest academic rank.

Which makes sense of my experience of who we get to call 'professor'. There are two professors in my department, both chairs of sub-departments within it.

Do Americans really call *all* college teachers 'professor'?

As an undergrad, I did. As a grad student, Ph.D.'s were "doctor."

Well, when I was an Instructor, I was always teaching in French, so mostly I got Madame.

Elsewhere I was a Visiting Asst Professor, so Professor was appropriate, and I'm pretty sure was used by students even for people that were Lecturers or Instructors. I mean, what else are they going to use?

If someone is a Professor, either Assistant, Associate, or Full, I do use Professor rather than Doctor in letters since that is the higher title.

Unless you're Al Gore, it is unlikely you would teach at Colombia without a PhD, or other relevant degree. Or say, multiple interviews and presentations, and articles to your name.

This is where I tell the story of my professor, who was a nun and a Ph.d. Her last name was Hoctor. So, against all conventions, we always called her "Sister Doctor Hoctor"

I mean, what else are they going to use?

I've always called all my lecturers* by their first names. Without exception. It was a bit odd as a first year undergrad, admittedly. But my current dissertation supervisor is younger than me. If I'd called her 'Dr --' instead of 'Anita', it would have made her laugh rather a lot.

So, against all conventions, we always called her "Sister Doctor Hoctor"

Hee. Did she have a sense of humour about it?

*in the UK, we use this term used for university teachers generally. You can have tenure-track lecturers or fixed-term (adjunct) lecturers, etc.

Oh yeah, we would have adjunct professors, etc., which is different from being the Smith Professor of Blah Blah.

I had a philosophy prof. who insisted on being called by his first name, Fred. He told his students that if they had a problem addressing their instructors by first names they should call him, "Mr. Fred".