advanced degrees

How did one earn an A.M. degree in the United States before the Civil War?  I am researching Marcius Willson (1813-1905), a textbook author who claimed to have an A.M. degree and was called "Professor," but I can only find evidence that he received an A.B. from Union College, Schenectady, NY, in 1836.  He went on to a few other teaching posts at prep schools and academies, but the most advanced post was at Poughkeepsie Collegiate School, where he was listed as a faculty member with an A.B.

Many thanks to the H-Education subscribers who offered very useful clues both on- and off- the network, all of which appear to apply to the Union College situation.  For those interested in this particular case, Union College's laws of 1815 did provide:

Chap. XI. Of Commencement and Degrees.

It was fairly typical for antebellum colleges to award an M.A. or A.M. based on the graduate's experience (often several years in the ministry) or upon his good character. I seem to recall that this practice was common during Eliphalet Nott's long tenure as president of Union College (1804-1866). Eventually, the practice became somewhat controversial and in the post-Civil War era it was mostly abandoned in favor of earned graduate degrees.

Possibly a long shot, but I believe that before the US Civil War, several institutions in the Northeast would admit graduates of other colleges and universities ad eundem gradum (at the same degree). If an AM from Harvard, for example, moved to Connecticut, he could apply, pay a fee, and be admitted as an AM at Yale. He could then participate in the collegiate life of an alumnus without having to travel back to Cambridge. It seems to have been a relatively common practice in the US throughout the late-18th and early-19th centuries.