Reminds me of https://en.wikipedia.org/wiki/QAMA_Calculator - a calculator that won't reveal the precise answer until you supply an estimate (physical hardware in 2014, I think the current version is an app.) The website makes claims about the pedagogic value, but I didn't see any actual citations at https://qama.world/the-science/ just "everyone knows" kind of things... but if they had research supporting it that would probably inform your approach?
