95. The Last Enemy That Shall Be Defeated is Ignorance

(Epistemic status: a slightly weird framing backed up by plenty of personal and professional experience. For IL, SP, and everyone else I've ever taught anything.)

The last enemy that shall be defeated is ignorance. Not death, not scarcity, not suffering, not evil - ignorance. The foggy darkness that lives at the edge of the universe is what stops us from knowing what to do and how and why, which after all is most of the battle; the rest is just implementation and mopping up.

And everyone is ignorant about almost everything. That's nothing to be ashamed of in itself, and I really do mean "everyone". You, me, everyone you've ever met, everyone I've ever taught anything - both before and after I taught them; everyone knows nothing about almost every topic. This is no moral failing, but rather the prevailing condition of sapient existence. Notice - it is not the ignorant who are an enemy bur rather ignorance itself, the reified not-knowing. The enemy is not the people who lack for knowledge but rather that lack simplicter, empowered and manifested by its servants, those who cling to their ignorance or who keep others in ignorance.

And if our foe is ignorance, then our joyful duty is to learn hungrily, and our prosocial sacrament is the act of teaching well. Learning something new means reshaping your soul just a little; it means reshaping the way you think and work on a fundamental level, just a tiny bit. Learn a subject more deeply and be further changed; in extremity, the topic becomes such a part of you that to do it wrong - to deliberately write an unsound proof, to knowingly strip a screw, to consciously misinterpret a text - is a bane for you, and might make you feel ill. Math especially is like this. I sometimes remark that a doctorate in math requires you to reshape yourself, and that ever after, you are a creature made partially of math and rigorous reasoning; to make a wrong argument or write a bad proof comes to hurt and sicken you on some core level, but your blind intuitive leaps of reason seem somehow to nearly always land pretty close to solid ground.

And teaching, too, comes with mysteries of its own. Inasmuch as humanity's decisive advantage over other animals has to do with cultural transmission, teaching is a core part of what make humans human; I posit further that it's a core part of what makes prosocial sapients be prosocial sapients more generally. So while it's good to be able to learn things on your own and in effect teach just yourself, it's even better to teach others.

There are three miraculous and magical aspects to teaching: kindling, unveiling, and empowerment.

To teach is to kindle: quite apart from the intensely scarce nature of goods, time, and energy, not only does teaching a student some skill or topic not leave you lacking that knowledge for having taught it, or even leave you the same for having spent the effort, it generally makes you understand the topic you've taught in a better, stronger, and more nuanced way - students frequently have novel frames and insights; the precious beauty of the beginner's mind. And what's more, once you kindle that tiny flame of understanding and fan it higher, the fire that you have conveyed can spread on its own; every student can become a teacher themself.

To teach is to unveil: it allows you to open a student's eyes to all sorts of subtle and unseen worlds; to see old things in new ways and new things in old ways. You get to bring someone to look at beautiful, profound things for the very first time, to see in their eyes the insight clicking into place, to pass on the enjoyable revelations that you yourself once delighted in.

To teach is to empower: giving a student new knowledge is to give them more power over the world - power to see their will enacted in ways that are surer, cheaper, or subtler than they might ever have managed on their own. And that empowerment isn't even necessarily an unalloyed moral good; especially as goes STEM teaching, which most closely touches on manipulation of and power over the world of things.

For fire burns as well as warms and lights, and knowledge reveals both wonders and horrors, and power can be used both well and poorly. Not all of wisdom brings joy; ignorance is indeed bliss, but it is the bliss of those who dine on poppies and lotuses. And knowledge has its price in tweaks to your brain and marks on your soul, but that pain is the pain of excited overexertion, of a hard day's fullfilling work, of a cleansing grief; the pain that unambiguously tells you that you are alive.

So - enough of something ambiguously between strategy, motivation, and theology. What are a few things to keep in mind if you want to do a good job of teaching a student a chosen topic? And shouldn't we be worried that the teaching of different topics will call for very different approaches? To that latter, thankfully not. Teaching has a generalizable substructure to it; if you teach enough people enough material from enough different topics and you'll come to see that, even if you don't at the start. To that end, understand that the first thing to know about teaching is that the overwhelming majority of possible students can learn any topic they pick, if they truly want or need to learn it, and inversely that an unwilling student, however capable, can refuse to learn any topic, however simple. Math itself is a good example: it needs little justification, just some motivation, and the abstractions it demands people build for themselves are effortful but ultimately mostly not that bad - but all too many would-be students have been badly burned by indifferent teachers, incompetent course design, and the unreasonable expectations of institutions and authority figures; not for nothing have I remarked that teaching math well requires a good splash of trauma counseling.

For a few more widely applicable pointers on how to teach well:

• Get people to listen and pay attention. Comport yourself as someone whose words mean things and carry importance; ideally not just the desperation that exam stress induces.
• All the same, make it clear that there will be fair evaluations - ideally ones whose rough structure and general topics, you will tell your students in advance, maybe with a little bit of nondeterministic spice.
• Tight feedback loops are crucial. The quicker you and your students can check understanding and touch the object-level, the better. Clicker questions and brief in-class asssessments are much maligned, but it's possible and valuable to do them right; they should never be part of a grade.
• Trying to keep as many of your students in the Zone of Proximal Development as long as possible is of extreme importance. The Zone of Proximal Development is a degree of mastery over a subject that's just a little bit past a student's grasp - neither comfortably within their ken nor so far outside their reach that they have no hope of performing at that level. Make them stretch; promote their growing pains.
• Mnemonics basically always help. The wonder of plucking truths from the air and grounding them in the world can be flashy and nice and all, and it can help the facts stick, and ultimately you want for your students to inscribe the methods and the facts on their own souls, but for an initial inking, mnemonics are pretty valuable. No need to ask them to memorize by rote. Make the mnemonics shocking, if you can; anything to make them stick as well as possible.
• Repetition legitimizes. Make sure to say things repeatedly to compensate for people zoning out, mishearing you, or not quite getting it the first time. Talk about the material in multiple ways, from multiple angles, and through multiple frames. One of them will probably stick, and it'll be different for each student. When you give tests, make them cumulative; don't let your students cram and then forget. Spaced repetition is a big help here, too.
• Make sure that there's a framework or throughline for a student to hang the knowledge on rather than have to try to carry it all in bare hands. If you give students a framework, a story, or a path to attach all these facts and methods to, then they will reliably learn them far better. Show them how each topic feeds into the next, and the one five after that. My favorite way to do this in math is to make my students construct tools for themselves, and to use methods from earlier in the course to ground or prove later material.
• Cultivate a capability to live in the student's head, in both senses. Be able to inhabit their frame, taking the perspective of honest ignorance; what don't they know yet? Know where your audience starts and how much you'll have to lead them. On the other hand, be such a figure as can live in their head; phrase things in a memorable or playful or idiosyncratic way; tell them to talk to their imagined version of you, who advises them to check their work and to explain concepts to them. It's not cheating if they're running you on their own wetware! 
• Learn the territory well for yourself. If you don't understand something solidly, then you're probably not fit to teach it. Conversely, be all but annoying about eliciting from your students what's going right, what's going wrong, and what people need; unfortunately, too many students (at least in academic settings) are so burnt out and justly mistrustful that this might not work.
• Bluntly: don't be a cop if you don't absolutely have to. Don't impose additional restrictions beyond what's strictly necessary. Don't restrict freedom of movement, don't demand people do things in a specific way unless that's really necessary to confirm learning, and try not to be too much of a hardass about deadlines, makeups, and absences. Try to paint yourself as being on your students' side as much as possible. Obvious exceptions include matters of safety, basic peer respect, and actual retention of the material. Do no harm, but take no shit.
• Accept that attraction is worth more than repulsion.  Be someone safe to ask questions of, to give your attention to, and to admit ignorance to. Give rewards and not punishments whenever feasible. Make your office welcoming to come to and bend over backwards to accommodate students' schedules. I always liked keeping a dish of lemon sherberts in my office.
• Generally, make use of applied cognitive psychology - intelligences share patterns. You can learn and make use of those patterns. Being a teacher does not except you from being a student - quite the opposite.
• Don't just empower your students by way of knowledge - empower them emotionally and psychologically as well. Show that they are stronger than they know; that they're not stupid or lazy, just lost and dealing with a lot.

Manage this decently well and call forth the stuff of legends. I've walked into a midterm room to a standing ovation. I've wrangled dozens of scholars in a research stream doing original work. I've so thoroughly illuminated numerous students in introductory calculus courses that they switched their majors to math-based majors. It's not actually that hard; all you need to do is care and try and practice. All you need is to take teaching seriously, as a sacred and joyful unveiling rather than humdrum mercenary transfer of information.

And as a student and as a teacher, always keep in mind this humble but powerful truth: that knowledge never falls out of the sky on a stone tablet. It's never handed down by the gods. Someone somewhere long ago figured it out for themselves for the first time, by their own strength. They did that, and you can do this somewhat easier thing, too.