studies that have shown a correlation between not believing the .999... and likelyhood to make algebraic mistakes
People did studies on that? That just seems so frivolous!
It seems frivolous to me too.
But I think if someone had a proper, almost religious respect and gut intuition for the separation of levels and meta-levels, it wouldn't seem so at all.
I'm mostly asking this open question to those among us who are well-versed in developmental psychology (I'm mostly thinking of children) . Although, failing the actual scientific research on the topic, I guess some testable hypotheses would be great too.