I have a lot of questions that can be summed up by "whats the history of independent and dependent variables?" Here is a list of those questions:
Where does our conception of independent and dependent variables come from? When did science get a notion of variable? How was this notion distinct from one quantity changing as another changes? What did they call measured quantities in science? When were these measured quantities first called "variables". Was there ever a time when mathematical variables were regarded as a distinct notion from measured quantities? Where does this particular terminology come from? When did this terminology become so established as it is today? Was it always central to science and hence a part of all science curricula or is its prevalence due only to some educational reform?
However I look into these questions I always get an introduction to independent and dependent variables as if I have never seen them before, and those sources always present the material as if the ideas have been around forever with no historical dimension. The most insight I've gotten into these questions so far has been on this sight here: Is it true that Leibniz introduced "constant," "variable," and "function"? . So variables, at least in mathematical contexts, have been around for a while, but nothing else is mentioned about variables in experimental contexts. I've also searched for the 'independent and dependent variables' on the Stanford encyclopedia of philosophy but those articles will at best discuss "causally independent variables" or "probabilistically independent random variables". There is no discussion even acknowledging the basic ideas learned in school. All of this suggests to me that the notion of independent and dependent variables is a modern invention for teaching science, but I don't have any proof of this. Also, even if this were the case the notion would have taken from some established ideas in science and I'm curious what that history would be.