> you'd think a math teacher of all people would know not to use "average" when they really mean "median".
I think a math teacher would be well aware that "average" can be used for "median", "mode", "arithmetic mean", or any of the other means (geometric, harmonic, etc.), as well as other computed values that are somewhere in the space bounded by the extremes of a data set, and would likewise be aware that, while in a formal context "average" should -- for that reason -- be avoided in favor of identifying the specific measure more precisely, it was acceptable and unambiguous to use "average" for any of those, including the median, where context made it clear which was intended.
I think a math teacher would be well aware that "average" can be used for "median", "mode", "arithmetic mean", or any of the other means (geometric, harmonic, etc.), as well as other computed values that are somewhere in the space bounded by the extremes of a data set, and would likewise be aware that, while in a formal context "average" should -- for that reason -- be avoided in favor of identifying the specific measure more precisely, it was acceptable and unambiguous to use "average" for any of those, including the median, where context made it clear which was intended.