Barker served as trustee for MIT, Northwestern, Robert College, and the Newberry Library during his later years. Perhaps his most important trusteeship was on the MIT Corporation. Education, and especially humanities and linguistics were of personal importance to him and he was quite active on committees steering these topics at MIT. In 1964 while serving on the Visiting Committee on Modern Languages and Linguistics Barker became involved in a dispute with Noam Chomsky. Chomsky had been a professor of Modern Languages and Linguistics at MIT since 1955, and Barker disagreed strongly with his theories on the evolution of language. They entered into a debate over the merits of these theories which resulted in a heated letter writing campaign by Barker to other members of the committee that year. In 1970, Barker made a sizable donation to MIT for the construction of a new engineering library that would be named after him, and the series also contains correspondence and materials from the dedication and opening of the library. Materials from the Newberry Library pertain to building improvements and financial concerns, and the Northwestern University and Roberts College materials are of a similar nature.