Psychological test for Euclidean geometry

Question

There is the so-called FCI test. It contains a list of questions such that anyone who can speak will have an opinion. Based on the answers one can determine if the person knows elementary mechanics. I learned about this test from the lecture of Eric Mazur, which is an interesting lecture, and it describes an application of such a list.

It seems that there are no analogous tests in mathematics. Or did I miss something?

Sergei Tabachnikov shared a couple of questions that might work:

• One needs to peel potato. What is faster and why: peeling a pound of large or small potatoes?

• Why does the reflection in the mirror interchanges left and right, but not up and down?

• Two persons are walking down an escalator (that is moving down), counting their steps. Who will count more steps, the one who is moving faster or slower?

Could you share more questions of this type; please make one question per answer.

Answer 1

The FCI is a "concept inventory" test for classical mechanics. There exist several such tests for mathematics. Some may be implemented as "peer instruction" (as Eric Mazur advocates), but they can also be taken individually.

One example is the Function Concept Inventory test, designed to investigate undergraduate students’ understanding of the concept of function.

Another is the Precalculus Concept Assessment to "assess essential knowledge that mathematics education research has revealed to be foundational for students’ learning and understanding of the central ideas of beginning calculus."

A third is the Calculus Concept Inventory, to assess "the most basic principles of differential calculus".

A fourth is the Elementary Algebra Concept Inventory.