I'm a math PhD who has been asked to interview a high school student and determine what he/she is interested in and how strong the student is.
Usually I would want them to talk as much as possible about what classes they've taken and what parts of the classes they like the best. Generally I'd like to allow them to get comfortable talking about what they like rather than what they think I'd like. However, that might not work this time as the student is a non-native english speaker and may get less comfortable as I try to get him/her to talk more.
Thus far I'm thinking about watching how he/she solves different problems in different areas of math, but I would like to know if anyone has done this before or has any suggestions for evaluating a student who might not be comfortable talking much.