How do you prepare talented students to fill small gaps in their fundamental physics and math skills? Data from 30+ years of teaching PhD dynamics to 1000+ Stanford students showed that some gifted students (particularly from elite universities) regard basics as intuitive, obvious, or remedial - even when they are wrong. This pretest helps overcome overconfident certainty and provides a growth mindset -- which is critical to avoid failure in the real test of nature (which is unaware of prestige and PhD degrees).
While working with Professor Thomas Kane for 15 quarters and teaching graduate dynamics at Stanford for 25+ years, we encountered students from elite schools who were impatiently frustrated during their first months in advanced dynamics with what they considered "review" material (vectors, rotation matrices, differentiation, angular velocity, etc.).
Unfortunately, some of these elite students performed poorly on the midterm (compared to peers) and criticized the course and its instruction. After a conversation, many acknowledged their misplaced certainty in knowing basic material caused them to overlook critical small details. Their performance on the final exam was dramatically better, but their midterm angst was discouraging.
This concept test has seemingly simple true/false and multiple choice questions, which actually require a deep understanding of fundamental concepts. The average pretest score of hundreds of Stanford graduate students from all over the world is 35%.
High-confidence students who have a more positive growth mindset for "review" material and who avoid intimidating peers with their misplaced certainty about "trivial" early topics.