Interesting query, this woman was a student here ca1870 and then later went to Japan to found Hokusei Gakuen University in Sapporo, Japan. A Jim Allison there is looking for info on her school years etc. Here is a Wikipedia article on the school and its founding.
I found her in the student register, the only entry I see is for 9/23/1872, Sarah C. Smith, from Painted Post (quite far!), # months taught 4, Presbyterian.