Yesterday, I looked up a former classmate of mine, B. We were in high school together; I haven’t really thought about her since we graduated. She is now a pediatrician back in my home country.
When we were in high school, she was what we used to call (loosely translated) a “crammer.” A crammer would be someone who crams, someone who works really hard at memorization, who just stuffs information into their head, without necessarily asking why or how any of it fits together.
The system I went through was different than in the US. In high school, you’d choose a profile (mine was math and natural sciences), and once you’d chosen a profile, your curriculum was set. In math and physics, we had tests, but we also worked on the board in front of the class. I distinctly remember her (and several other people, of both genders) really struggling to set up and solve problems. I don’t think she was dumb, but she put in enormous amounts of effort and still could never get an A in either math or physics, even though she had all other As. I also remember a couple of other people whose GPAs were not very high, but who were good at reasoning through math or physics problems.
Why did I think of B?
Because I had the first midterm a couple of days ago in my large undergraduate class. Usually, I hold all-day office hours before the exam, so I got to see a number of students and work through problems with them. And a few reminded me of B struggling on the board.
I am not sure what to do for these kids. They all came in with high GPAs and were among the best students in their high schools, but a good 60% should not be in this major or any physical science major at all. Yet, here they are, and they are not going anywhere, because their tuition dollars are coveted. I have been trying to figure out how to describe what I see, and it’s not easy. It is a perfect storm of being sloppy, having inadequate math background despite having cleared all the calculus courses (whenever I see people trying to take the curl of a scalar field, or they tell me that the divergence of a vector field is a vector field, I die a little inside), and just not being willing or able to think things through. All this manifests itself as overarching shallowness. I see these students trying to just somehow quickly tunnel through problems, pulling out equations from the book or memory that make no sense while on the surface seem like they do (i.e., they involve many of the right letters), but the actual thinking is completely absent from the process. There are no words that I say more often in office hours than, “Stop. Don’t rush. Think. What is going on here?” I spend a lot of time in class and discussion setting up each problem: drawing, describing the framework out loud, explaining what each step means and and how it translates to math, then solving the resulting equations. I know I try my best and I assume most of my colleagues in the courses before mine do their best, too. And for many students it all clicks and they do great. But for 60% it doesn’t seem to, almost as if they don’t want it to. They come to office hours not to learn, but to do well on the test. I post practice problems and they don’t even attempt to do any of those unless they have solutions. These kids just speed through everything and just want to be done. As if they deliberately don’t want to retain anything, or as if turning on the brain requires too much energy.
(An aside: It blows my mind how bad people are at drawing. I am not talking about becoming a comic-book artist here. I am talking about sketching simple geometric objects better than my 5-year-old: a circle or an ellipse; a disc, a cylinder, a sphere; a cube — oh, my God, the crimes against art committed on the cube! Very few students can sketch what looks even remotely like a cube in perspective, rather than like something that Picasso vomited. A surprisingly high fraction never resort to sketching anything, even though, in many courses, visualization is immensely beneficial to solving problems.)
Our colleagues in the humanities often argue that the humanities courses are necessary in order to instill critical thinking. I feel like we in STEM really try to do the same, but with the help of math. I don’t think we are particularly successful; it’s just that our STEM crammers come out with degrees that on the surface look more employable, even though these degrees — sadly — don’t guarantee that their holders can actually apply reasoning to problems within their discipline.