In doing so, they would receive an education that no school could provide them with.

in 在这里是介词，表示"在...过程中"或"通过...方式"。 doing 是动词 do 的现在分词形式，表示"做"的动作。 in doing so 这个短语的意思是"通过这样做"或"在此过程中"，用来指代前文提到的某种行为或方式。