SPARC preparation, SPARC itself, and two new classes to teach at Berkeley. I better have learned something. =)
Skill Harvest: Teaching
- Besides teaching a course without an established curriculum (Mathematical Cryptography) I have the dubious honor of helping Berkeley run its Putnam training (the Putnam exam is the most prestigious university-level mathematics competition), so I get free reign (mwahahaha!!!) to try different pedagogical techniques. Here are some takes that I haven’t often seen elsewhere:
- For my cryptography class, Math 116, starting with Problem Set 3 I’ve included one prose-form cryptographic puzzle per week that tries to capture some mathematical/cryptographic idea after stripping away the mathematical details (so non-math trained friends of mine have been able to solve all 3 puzzles so far), and a narrative has begun to form with Alice, Bob, and Eve, three people familiar to most students of cryptography. I’ve gotten a surprising amount of both positive (“made me forget it was homework”) and negative (“the prose obscures the point of the problem”) comments, which made me further convinced
that optimal teaching is much more like cooking than soylent.
- For the Putnam class, instead of doing the usual “teach topic A, give 10 problems on topic A; repeat” I do something like “teach topicA, give 10 problems such that 2 problems are about topic A, 3 problems are about topics in previous weeks in random order, 3 problems are “bridges” to topics I’m likely to teach in the future, and 2 problems are ad-hoc.” I haven’t seen this done much, so maybe I’ll call my way “horizontal teaching” and the old way “vertical teaching” (feel free to give me better words). It seems “horizontal teaching” makes students feel more lost (some are even angry!) and is in some sense more shallow, but I think it does 2 cool things: (a) it trains the skill of “what skill do I use to solve this problem?” much better than
“vertical teaching”; (b) spaced repetition is good for long-term learning, and this method inserts spaced repetition for free! For a personal analogy, I find that this is what my interaction with a climbing gym feels like (you have old and new, hard and easy, etc. problems kind of strewn together and I’m exploring all of them at the same time).
- For the Putnam class, I also have them turn in the scratchwork. Not only is it the case that “the journey is much more important than the destination” for Putnam-level problem solving, it is also a good place to teach strategic fundamentals of problem-solving by observing habits that are not visible in a finished product (does the student spend time generating small test cases? Does the student do visualizations or write everything in words, etc.?). I stole this idea from thinking about how apprenticeships of other crafts work, and the fact that the instructor is frequently there to see the progress and not just the solution (the art teacher gets to observe the students paint, the writing teacher sees intermediate drafts, etc.). I haven’t seen this done in other math classes ever, but mathematical problem solving is surely a craft.
- One of my favorite pieces on teaching (but also on dealing with human beings) is “The Lesson of Grace in Teaching”
(http://mathyawp.blogspot.com/2013/01/the-lesson-of-grace-in-teaching.html ) by Francis Su (with whom, for purely coincidental reasons, I met and solved a problem together over summer). The main idea is, as its name suggests, better understood if you are acquainted with the idea of “grace” usually associated with Christianity, but you don’t need to be
a Christian to use it. A short description that doesn’t do it justice is “you can (and maybe should) value human beings independent of valuing how good they are at skills” (as usual, the extreme version of this statement is a little too extreme for me. I do like people more when they are better at skills and I don’t think that’s unhealthy; I think what’s unhealthy is thinking a person is just a sum of skills). Over the last couple of years the idea has repeatedly pinged me whenever I felt frustration dealing with students, my mother, or any situation where I felt annoyed that I thought the person I talked to was missing something crucial knowledge/skill/”virtue” relevant for the conversation. I think remembering the concept improved all of those conversations.
Idea Weaving: Hoarding
- When I was in finance, many things about people’s lifestyles bothered me. Now that I’m in academia again, a different set of things bothered me, but strangely there was some thread that felt very similar to finance. I think I’m finally able to articulate it.
- One stereotype of a financier (or in general, really lucrative jobs) is like a dragon: they hoard gold, and then they sit on it without knowing what to do with it. (this is annoying since it is gold that other people now have less of). (There are other stereotypes, of course, like the people who make and burn a lot of money — I’m just focusing on this one. In a certain sense I actually like the people who burn a lot of money more – at least they are giving money back to the economy!)
- Well, it turns out you can hoard things that are not gold. You can hoard, for example, knowledge: just sit around all day and have people pay you to gather knowledge. You can also hoard social networks like a kid collects pokemon. This still feels inelegant and wasteful in the same way I find money-hoarding annoying (though a valid counterpoint is that knowledge can be duplicated and not removed from others, like money is). I think the part that bothers me about these stereotypical extremes is that resources are going into a hoarder, but the hoarder doesn’t even see a responsibility to generate output (especially if the thing being hoarded is something a lot of people value, like fame, knowledge, celebrity, etc.). So the common thread that bothered me about academia and finance is really a sustainability problem.
- a person that collects gold actually has the most options to generate output: spend the money! Support people doing good things. Help people out through charity. Invest in good businesses, whichever. If I collect knowledge, I can turn it into kinetic knowledge by building things, teaching people to build things, having the knowledge written down in a searchable way (write a book, blog post, wiki, etc.), share it with people when I think they need it. If I have a social network you can turn it into teams, friendships, introductions, romance, etc.
- I think of hoarding as a bad pattern similar to but distinct from “selfishness” and “fetishization” (you can fetishize truth and knowledge to annoying extremes, for example).
- While it may be interesting to argue about whether hoarding (or selfishness, etc.) is “bad” (or get into meta-crap like whether this idea about hoarding is a sign that I’m hoarding ideas) I think I want to end the pure intellectualization for now and focus on some thoughts that I had that will hopefully turn into concrete personal change for the good (in a similar vein as selfishness, where I think you can be a pretty respectably cool person while being utterly selfish, I don’t think it is useful or even right for me to criticize other people for hoarding -* I just think I don’t want myself to hoard and I suspect many of you have similar tastes in ethics, so it may help you as well):
- I’ve always had this vague idea that an academic hoarding knowledge is more noble than hoarding money. Well, I’m still hoarding – some money is being put into me (a combination of parents, taxpayer money, people who get fooled by mine and other people in academia’s grants, etc.). It is worthwhile to have some sort of output that’s commensurate with the input. I think the concrete important result for me is that I shouldn’t have an inflated ego about hoarding knowledge as opposed to money. I can be an irresponsible academia much like I can be irresponsible making $$$ in finance (and I can also be responsible in both!)
- motivationally, for me personally at least, having an idea of “responsibility to give back more than given” is a good compass to have. I think this is something I stole from the Boy Scouts, of all people. (real Boy Scouts: feel free to comment)
- Like fetishization, while money, power, etc. are the main things to hoard, I think there are a lot more niche ones (it may be fun to think about what you may hoard)! For me, Yan, personally, the realization that struck the nerve most is that not only may I be hoarding knowledge, I think I may be hoarding “skills.” I like collecting skills, with the pretense to myself (and others) that the skills will be useful later, even though it may be something not immediately applicable like Go, climbing, or fashion. Nothing needs to be immediate, but I think it would be pretty unpleasant to die without converting these skills (probably more likely the network + mindset that comes with these skills, as opposed to the skills themselves, which also counts) to something interesting for the world.
Idea Weaving: Elephant Questions II
- the Elephant Questions idea in the last post seems to have been pretty popular. Here are some responses and additional thoughts:
- Will on social games: “We like to refer to social reality, which is the commonly-acknowledged set of public information, which is quite different from what everyone is perceiving and what is actually happening. :) Basically, we think there are positive externalities to adding information to the set of common public knowledge, and it does often make people feel a lot better. Then why do these weird social denial games even exist? And why don’t I always just bring everything into the open? Basically, I do think that resolving another person’s emotional problems is taxing on some mental/emotional resource. Openness is effective an invitation to have the person unload stored emotions…” This model seems to be fairly similar to my own, besides an important “obvious” point that Alex also addressed:
- Alex on elephants: “- Re: elephants. The elephants you mentioned all have a component of vulnerability, which is why I think people often fear bringing them up. – asking a very basic question might make you look dumb. Talking about emotions in business meetings involves, well, talking about your emotions, which we’re often scared to do. While it might rationally be that people rarely actually judge us for asking such questions, we still fear it on a gut level.” I think this is a good (unprompted!) complement to Will’s points.
- Gavin, on concrete ways to ask elephant questions: “- As to elephant questions, I’ve been clearing a few out of the air recently – all elephant questions that are about potential hostility. I am feeling so great these days, to suddenly realize that I’ve run out of such questions! … And it’s largely because elephant questions can, I find, be just magical at helping turn arguments or disagreements into bonding experiences. But I’ve been stumbling towards a formula for doing so that I find is crucial for getting that rewarding bonding out of exposing an elephant in the room. First, all the obvious things: like, make the question nonthreatening, never corner the other person without a way to save face, etc. But second, recognize that elephant questions come with sort of a built-in timer. If people are used to not talking about them, changing gears like that is exhausting after a
bit. And that tiredness can cause good feelings to be less cathartic. SO I am developing a very deliberate philosophy of thinking of such questions NOT as a way to start a conversation which goes as long as it takes to “solve” a “problem”. Instead, to me they’re now more like a valve. I bring difficult things up, let us both blow off a little steam for some set amount of time, then gently but firmly suggest we move on to having some positive, emotionally rewarding experience next. Again, not super helpful for when the elephant in the room is not emotional, but for disagreements I’ve been finding it an incredibly helpful formula lately.” This seems pretty concretely helpful. Thanks!
- I had several conversations where the concept turned up (spurred by my email or not) where people talk about when/how to bring up elephants, etc. I think a lot of resistance is justified because there seems to exist some people for whom bringing up elephant questions is a way to be an asshole while gaining virtue points of being “honest” and “truth-seeking,” and this really rubs certain people (myself included) the wrong way, in the same way that I get annoyed/sad when good debaters use their logic and rhetoric skills as a way to knock people down or as a intellectual phallus symbol. I think for any culture that wants to develop “tell culture” or anything like being more accepting of elephant questions, they need a good way of dealing with these defectors. (Prisoner’s Dilemma again! … yay. -_-)
Misc / Meta:
- People seemed to have also liked the bit about my model of Mastery as “understanding = knowing + feeling.” Thanks! I’ve actually been using that as a way to think about teaching, which is pretty effective. Maybe there will be a Idea Weaving: Mastery II sometime. =D
- there is a particular half-sleep state where my brain generates improvisational music, but I’m utterly not creative otherwise (I also have no music training, so this weirds me out. I mean, I understand that if I practice Go problems a lot I start seeing them in my head, but…). The most frequent case is when I wake up but stay in bed, sometimes lingering on the cliff of unconsciousness I get tunes and I have to save them with a sound recorder. When I was semi-meditating today in a restaurant I also generated a song, but I became less creative when I realized this and became more awake. Does anyone know what this state is?