# Teaching Recitation, 5.0

This semester is my fifth as a recitation instructor for 6.004, a core undergraduate class in MIT’s Electrical Engineering and Computer Science department. The course covers everything from transistors to operating systems. My recitations during my first semester were a little painful, but at least the students (who came) knew I was trying. The second semester, a little less so. The third? Okay. The fourth: I was tired. Tired of working out problems in front of them. I made them do the problems instead. This was a step in the right direction, but it felt a bit forced. The fifth? Damn good.

Last Friday, 40 or so students had just spent the hour hurling questions at me, populating a Google spreadsheet with their free-form answers to exercises for me to review and discuss, and occasionally coming up to draw Complementary Metal-Oxide-Semiconductor (CMOS) gates in chalk on the board, live, in front of their classmates. A student walked out of my classroom on a Friday afternoon, saying, “That was the best recitation… ever!” And he wasn’t the first to say something along the lines of… *“I like your style.” *I thanked the enthusiastic student for making my weekend, and walked back to my office with a gigantic spring in my step. I won’t let it go to my head, but I will acknowledge that something is going right. And I want to figure out what it is.

My students just watched a 50 minute lecture by an expert the previous day, and now they’re expected to answer questions and design circuits that reflect that knowledge they just “received.” Whether my students are loud or quiet, I don’t think either end of the volume spectrum is inherently better. The real determiner, in my mind, of recitation quality is how free students feel to ask questions and make mistakes.

To generate questions in their minds, I ask my students to immediately start solving a problem by themselves or with a friend, and to enter their answers in a Google form so that I can see everyone’s responses in real time in a spreadsheet on my computer at the front of the room. It’s not multiple choice. I can skim free-form answers from 30 students to judge the distribution. Of course, sometimes a significant fraction of students can’t even start, and I’ll launch into a mini-tutorial, so they don’t spiral into that familiar “I’m so lost I don’t know where to begin” place of quiet doom. After a significant portion of the class has entered their answers, I’ll identify the common answer(s), and ask students to volunteer explanations for which one is correct.

If the problem is to *design* something, like a circuit, I ask them to compose their answer on paper, and let me know in the Google form if they are done, need more time, or again, don’t know where to start. Without the ability to see their designs, I have to rely on their generosity and courage to share them with the class on the board. On these days, I am particularly thankful that, in engineering, there can often be multiple right answers.

Last Friday, I asked students to design a CMOS circuit—a network of two different kind of transistors—that implemented a particular function. The lecturer just told them the previous day what a CMOS circuit is, along with a recipe for how to build them! It’s not enough to be told; students had to generate their own bounds on what a CMOS circuit is. They were unknowingly illustrating Variation Theory, summarized by the contradictory saying, “He cannot, England know, who knows England only.”

**Student A: **What is, and what is not, a CMOS circuit? **Me:** It has to have [a], [b], and [c], or it is not a CMOS circuit.

**Student B:** Is this thing I made a CMOS circuit? **Me: **It’s close, but we need to reattach this here because…

**Student C: **Can we remove the top half? It will still work, right? **Me:** It would still work, but it’s a different kind of circuit; what would happen when it’s switched on? How much power will it dissipate?

At the risk of sounding grandiose, we were playing the “What if?” game that these budding engineers need to play, to understand the rules of CMOS gates, so that they might later break them and invent something new. Most future variations they play with in a lab won’t work, if they go down the road of research, but every once in a while…

Later in the hour, I invited students to offer their CMOS designs to the class. Five designs went up on the board, and we made every possible mistake (me included), on our way to the actual answer. Students were coming up to “fix” the previous design, only to have us collectively determine that it was *closer* to working the way we wanted.

It is a little risky. Some students are more immune than others to what can be a little embarrassing—to make a mistake in front of their peers and a course staff member. I thank them for their designs, and find what’s right about them, as well as what isn’t quite right *yet. *And when they correct me, I laugh and fix my mistake. I hope they’ll meet me in the middle, where we all have a little less ego and learn a little bit more.