Intellectual
First is the obvious area of intellectual growth. Broad content knowledge: in science, in history, in literature, in mathematics and so on.
Growth in intellectual knowledge is easy to measure. I can recite the US presidents by name, or can spell all the provinces in my home country.
However, broad content knowledge is available on any smart phone with a 3G connection. Although it's easy to measure growth in this area, it's also limited. We want more for our students...