Students have complained that I have no right to ask the above question in a mathematics class, but my better students really seem to appreciate the point I am making. Words matter, whatever discipline you are discussing. We should never attempt to make a conclusion or take an action based on a word or words to which we have attached no meaning. I believe that we can overcome this problem, once we acknowledge its existence. Instructors are encouraged to try variations of the above experiments, but not to take the results too much to heart.
Students come into all classes with a certain amount of intellectual baggage.
Unfortunately, I have observed that part of this baggage is the belief that terminology and definitions are not important in the study of mathematics. When an instructor is defining his or her goals for a course, she or he should make a list of the basic vocabulary. Having the students develop a deeper understanding of the basic terms should be one of the primary goals. This is true of all mathematics classes from first grade through graduate level courses. References Boyer, Clark, Kett, Salisbury, Sitkoff, and Woloch.