My 5-year-old son recently brought home (from kindergarten) a worksheet that he had done at school. 6 boxes were given. In one box were 3 kites, in another, 2 bears, in another 8 drums, and so on. Each box had a list of 3 numbers at the bottom to choose from. The instructions were:
“Count the objects in each set. Draw a circle around the right number.”
As we all know, such exercises are common for young students, but I have always wondered whether such exercises were teaching something that would later have to be unlearned, namely, the false idea that members of a set are always all instances of the same thing. Anyway, at the very least we should ask when in their academic career students finally encounter the truth that the members of a set can be things of different type. 8th grade? senior year of high school? College? Only math majors in college after their first year?