In Multivariable Calculus, I assign problem sets as the major learning tool. Kids can collaborate, but must solve and explain their solutions to algebraically challenging and conceptually challenging problems. On the latest problem set I collected, I had kids solve two optimization problems, and then create two of their own (or find one somewhere other than our textbook, and create one of their own). They then have to solve it. I’m okay if they don’t get the solution 100%. I’m looking for an interesting and innovative problem.
In the past few years, I haven’t gotten so many good problems. Maybe one or two good ones total.
Today (Saturday) I started grading these problem sets. It took me from 9:45am-1pm and from 6:30pm-11:50pm to completely grade them. (I have seven students in the class.) What took so long was going through each of the fourteen problems that my kids posed. I was INSANELY impressed with over half the the problems I read. Unbelievable. They got me thinking in interesting and challenging ways. I was utterly nerdsniped. I was learning and my mind was whirring while I was working through these problems. I was forced to consult winplot for one, I made a geogebra applet for another. I had so many pages filled with scrap notes. And all while doing it, I was loving it. It is so tough to come up with interesting problems. But my kids did. And because of that, even though I graded an INSANE amount of time for just seven papers, much of it was joyous mathematical fun.