First, I am a teacher preparing to give a discrete mathematics course, in which I will not do any computing, but the students will (in Python). I want them to make empirical estimates for the growth of their (short) recursive programs by putting in some sort of "counter" in their programs, and then run it on several sets of data of varying sizes. (I will also ask them to analyze theoretically, but that is not my question here.) But since I am not a programmer, I am not sure how to do this.
The Attempt at a Solution
Simply have the program count the number of operations seems to me to be incorrect, because different operations will take different amounts of time and/or memory space. I am also aware that different machines (not to mention different versions of Python) will give different answers, but they should be within a linear factor of one another. Reading off the time for the completion of the program is not going to work, because the programs will be short. Some websites classify some operations complexity, but not all of them, and besides, that brings us back to a theoretical approach. Anyway, I don't want to actually give them the Python program construction (my students can program; I can't), but I will be suggesting the mathematical steps to put in. (Therefore an answer in mathematical language rather than computer language would be appreciated. I think the first mathematician to have seen a computer program reading "n=n+1" probably had a heart attack.)
Thanks for any hints.