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When applying for academic jobs in the US, one is often asked for at least one recommendation letter from someone who can attest to your teaching abilities.
If applying for a tenure-track teaching focused job, should one aim to have multiple teaching letters?
I am personally in mathematics. I am assuming the answers will not be too field-dependent (please correct me if I am mistaken).
Yes, I think it is advisable, especially if you are coming from a "research track": e.g., if you attended a university rather than a liberal arts college (or especially if your undergraduate degree is outside the US); if you are currently doing a postdoc at a research university, and so forth.
The SLAC [=Small Liberal Arts College] track is its own subcommunity within the academic community. Though many research-focused academics view the liberal arts track as being an acceptable second choice [in full disclosure: that is a rather faithful description of my own views!], the liberal arts college community does not see itself that way and is very wary of hiring academics whom they suspect (i) will not understand what a liberal arts college really is and turn out to be unhappy and/or bad at the job or (ii) will make good enough faculty members for a few years and then turn around and take a research job at their first opportunity. If you don't have "SLAC pedigree", then liberal arts colleges will -- correctly, I believe -- view your application with the above wariness.
To get past this wariness you have to demonstrate real understanding of the SLAC track and teaching interest and credentials which are both more intensive and also different from what one is expected / asked to do as a typical university PhD student / university postdoc. Teaching calc I/II/III every year, getting really good evaluations, and maybe eventually winning a teaching award is not a recipe for success on the liberal arts track. Whereas many research faculty teach calculus, graduate courses in their specialty, and advanced undergraduate class related to their specialty when they get around to it [again, this describes me pretty well], at SLACs faculty get called upon to teach a much broader course load, often including things that a larger university may not even be housed in the same department (CS, statistics, mathematical biology...). A good candidate for a SLAC will have a broader teaching experience.
Many research universities nowadays have some "broadening" alternative teaching choices for students and junior faculty interested in this kind of career. At my department all PhD students start teaching precalculus and then go on to teach calculus. They can also be involved in a Writing Intensive Program (WIP) and teach elementary education / math for future math teachers courses. If you are coming from such a place and want to make a good SLAC candidate, nailing your calculus teaching and having teaching experience -- and possibly even additional coursework / mentorship / administrative experience / volunteer work -- in less traditional teaching opportunities is somewhere between extremely helpful and mandatory. The best way to be convincing in the breadth of your teaching success and skill is to have multiple people write letters about the different aspects of it. So...yes, two teaching letters sounds wise.
Added: Any additional teaching letters you get should not come at the expense of research letters! As I wrote in an answer to a related question by the same OP: don't be afraid to send along 1-2 more letters than the application specifies.
