The point being (about the pillowcases), that no-one in direct contact with the children should know what footwear they have on, as this could, consciously or unconsciously affect the teaching and influence the result. If 'catters can come up with any better suggestions, go to it! Another way would be to have the teacher teach remotely with screens showing only head and shoulder views of the children.

Ridiculous and impractical, sure, but in a clinical trial every effort has to be made to eliminate anything which could possibly affect the outcome, other than the thing for which you are testing. If you want a statistically valid result, that is. However I suspect academic scholastic research is somewhat less rigorous!