This year, I encountered the world’s worst calculus class, a mutant-frog specimen of undergraduate mathematics: UC Berkeley’s Math 16B. It’s an exercise in cynicism; a master-class in spite; a sordid and cautionary tale of everything that can go wrong in curriculum design.
16B is my blood-born nemesis. Neither can live while the other survives.
It comes as the second semester of a year-long sequence. Its predecessor is the respectable-enough 16A: a light, trig-free presentation of calculus. Accessible and coherent, it has a conceptual focus and lots of friendly graph-based questions. I enjoyed tutoring it.
But then comes 16B: a hasty meal assembled using whatever mismatched leftovers the fridge happened to have. The mathematical equivalent of Jello-olive tacos and bowls of mustard.
Simply consider 16B’s spaghetti-logic calendar of topics, presented here in precisely the order they’re taught. (No worries if you don’t know what these are—neither do the students completing the course, really.)
Like a blind driver on a six-lane highway, 16B veers madly from topic to topic, grabbing material from half a dozen different standard courses. Namely, it cannibalizes pieces of the following:
No discernible logic governs this sequence. No underlying principle unites the topics. 16B is merely Franken-calculus, stitched together from the corpses of actual classes.
As the semester wore on, the two students I tutored grew increasingly frustrated with the course’s haphazard path. “What are we even doing?” one asked me. “So… none of the chapters really relate to each other?” asked the other. They both wanted to know: “What’s the point of all this? How does it fit together?”
The exercises and homework questions rarely gave them trouble. Their biggest problem was the Kafkaesque purposelessness of the class itself.
A good course in any subject, from art history to chemistry, ought to feel gratifying and self-contained. It ought to build and develop, like a well-written novel or film. This goes double for calculus, whose beauty lies largely in its unity, its coherence, the harmony of its constituent parts.
16B possesses none of that. It just rambles on, like a shaggy-dog story.
This problem engenders another. In sprinting through so many disparate topics, the course can do justice to none of them. At every turn, it settles for computational shortcuts at the expense of conceptual depth.
Students learn the second-derivative test for maximizing functions of two variables, without even a whispered mention of the mystical formula’s origins.
When they encounter the normal distribution, it’s in a setting purged of calculus. Makes sense for a calculus class, right?
And don’t get me started on the class’s sham presentation of Taylor Series, so watered down that it’s practically homeopathic.
Though they fully understood the course’s futility, the students kept slogging. They had little choice. After all, 16B satisfies the university’s pre-med and pre-business requirements, despite offering absolutely nothing of value to any future doctor or entrepreneur. Accustomed to hoop-jumping and arbitrary tasks of academic strength, the students showed little outrage at being forced through this particular series of rat-mazes and hamster wheels. Hey, they’re Berkeley kids—school is what they do. Graduate first; ask questions later.
The best you can say of 16B is that its students have been “exposed to” something. That passive construction is the only appropriate phrase. “Exposed,” as if a man had thrown open his trench coat before their eyes. “Exposed,” like wheelbarrows left to rust in the elements. “Exposed,” that last excuse given by educators whose lessons leave no fingerprints, who justify wasted weeks with the remark, “Well, they may not seem to understand much of anything, but at least they’ve been exposed.”
You know the yearbook cliché: “Shoot for the moon; that way, even if you miss, you’ll land among the stars”? With 16B, Berkeley takes the opposite approach: “Shoot for the mud; that way, you’ll never miss.”
It all raises the obvious question: What the heck is the point of Math 16B?
As best I can tell, 16B allows someone, somewhere, to rattle off a long list of mathematical topics and say, “Isn’t impressive that all our pre-meds and pre-business students know this stuff?” It’s a class that serves the needs not of the students, nor even of the teachers (indeed, I pity the poor professors conscripted into teaching 16B), but of some distant curricular architect indifferent to them both.
I believe that good education comes from a compassionate expert crafting a course, like fine artisanal handiwork, to suit the needs of the students. In that sense, 16B is the unholy Manichean opposite of good education.
To their credit, UC Berkeley Math seems to be learning its lesson. One new course (Math 10, tailored to biology majors) is rightfully the pride of the department, a thoughtfully compiled toolkit of techniques and concepts. I only hope that someday soon they’ll revisit Math 16B and breathe real life into that rotting jack-o-lantern of a class.