I struggled with high school calculus. I just couldn't wrap my head around the concept. My teacher kept making noises about "rate of change" but it made no sens

I struggled with high school calculus. I just couldn't wrap my head around the concept. My teacher kept making noises about "rate of change" but it made no sense. Luckily for me, I was taking physics at the same time, and we ran an experiment to calculate acceleration due to gravity. So we ran the experiment with a weight and a ticker tape and a little hole punch tool and we got these data sets measuring the distance between each consecutive hole on the tape. Plotting distance against time on a graph, we produced a curve somewhat reminiscent of a y = x^2 function. Then, given d2, d1, t2 and t1, we were able to calculate a set of velocities between each point. Plotting velocity against time on a graph, we produced a sloped line somewhat reminiscent of a y = 2x function. And then, of course, given v2, v1, t2 and t1, we were able to calculate a set of acceleration rates between each point. Plotting acceleration against time on a graph, we produced a horizontal line somewhat reminiscent of a y = 2 function. Then it hit me. Looking at the three graphs, in a flash I suddenly understood exactly what "rate of change" meant. I understood why d(x^2) = 2x, and why d(2x) = 2. Calculus made perfect sense, and I plowed through all the exercises that had plagued me since the start of the year. So when I clicked on the first video in this OCW set [1] and watched Professor Strang put distance/speed and height/slope side by side as his two canonical examples, a big smile spread across my face. [1] http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/big-picture-of-calculus/ http://ocw.mit.edu/resources/res-18-005-highlights-of-calcul...