On the website, "Old Fulton New York Post Cards", there is a roster of teachers who received school assignments. The list appeared in the newspaper, New York Sun (January 26, 1939, page 28, 29). The information includes assigned schools in New York City, Brooklyn, Queens, & Bronx; some specialties & some school names.
For page 27, "818 New Teachers Appointed" enter the following in the search box:
New York NY Sun 1939 0874
For page 28, enter the title (including quotation marks) "Teachers Assigned by the Board" (or you can write: New York NY Sun 1939 0875--but the newspaper listings are very long this way).
***Note: There are buttons to enlarge the image, move, print, save, etc.--they are not visible (at least on my computer) until you move the curser along the bottom right side.