Teaching, Optimized

Bit of an afterthought after seeing patrick winston’s talk

Mainly applicable to middle/high-school and smaller university classes. Depending on your country’s school system.

Minimize Distraction

  • preferably blur out windows at eye height when sitting. Having something going on outside can completely destroy how information flows, however good your teaching is. This is often not something you can do something about as a teacher. But you can try to pick a room with as least distraction as possible.
  • Have students take notes. The error that a lot of lecturers make is that they expect students to make notes by themselves, but if you start without a notebook in front of you you are in no way inclined to grab it when needed. Start the lecture with a short question “does everyone have their books in front of them?” and also give them some time to write down what you say. A subtle clue can also be to say that people to not have to write down x thing, implying that the rest must be written down.
  • Talking people are the death of any lecture. The best way to minimze this is to make sure you are well audible and also to show that you (and all other students) can hear it when a student is talking. Preferably have semi-small groups of no more than ~20 students or a room that is setup such that sound seems amplified, how counter-intuitive it may seem.

Minimize cutoff

  • Never, ever, have a slide full of text or even worse, equations to talk through. People will lose you, and probably wont catch on later either if you take too long. Break problems up into smaller sets, and preferably leave out duplicate information.
  • Give people a chance to jump back on after a while. Give people something to think about for a short time and then start a new part-subject. Make it obvious that you are restarting from scratch so people have a chance to get on.
  • Don’t be boring, but also not too hyper-active. A boring teacher will make his students bored, but a hyper-active teacher will probably also lose out on the energy of students really quickly. A teacher that likes their area is way more likely to generate interested students than one who seems to be bored. (if the teacher is bored then why would you ever want to learn more about it)
  • Be sure of what you are saying. If you have to think a long time of what you are doing people will quickly lose trust, start talking about it, and dropping off.
  • Mainly for math subjects: You do not have to rigorously prove complicated things in your lectures. Students don’t care and they sure as hell don’t have the time to take it all in during the 1 minute that you have your slide up. Students really like to know “why” something is true, but giving intuition is often a thousand times better than plomping down a complicated formula and just reading that off of the slides.
  • Similar to last point. Don’t just show definitions. Show examples. A student cannot remember all your definitions, but they will remember examples. If needed show them many edgecases that implicitly or explicitly explain the definition.
  • Again mainly for math: Where possible, use a blackboard or even digital drawing instead of slides. It is extremely important for students to grasp the steps of solving a problem, and doing it step by step allows you to explain your reasons, allows asking more specific questions from students, and better overall intuition. Blackboards are a lot of work, but what works similarly well is a drawing tablet projected on a screen. You don’t have to lose time and focus when clearing out the board, can go back to show how something correlates to a previous assignment, and share the results for later reference. Do make sure that you have a cheatsheet next to you so you don’t make any big mistakes. Or do and show how students can check themselves when they are solving problems.
  • Lectures often build on eachother, but may be spread out. If you are handling a lot of information in a single lecture then it’s a good idea to have recitations after a day or two to help students remember.

Optimizing tests

  • Tests are not for teaching, please do not include too much new information that might confuse students. Application of the actual course content is of course fine or even imperative.
  • Give everyone their test back after they are graded. Show people where they made errors even if they do not want to redo it. Tests often give a great amount of different topics to see what you know, and re-reading a test is a great way to see what errors you made and where your ideas might differ from the teacher’s. (notationwise, etc). Don’t have students go somewhere to view their test or have them wait a long time. Stimulate them to actually take their time and take away any barriers.
  • Offer a demo-test. This is a great way to prepare students so they have a nice checklist of what to learn and a way to test this. If you think most of your students aren’t making the demo-test include one of the demo-test questions on the real test. This will give them a good reason to use the demo-test when learning and will greatly improve their grades. (don’t re-use more questions, don’t be that guy)
  • Make sure students have enough time. Your goal is to check if the student knows what you told them. Not how fast they can read and write
  • Use a lesson to talk through items of the last test that didn’t go well, and add a small question on the next test with that same item for a couple of points. If you have no reason to want them to still learn it then why were you testing them in the first place?

If you have no reason to want them to still learn it then why were you testing them in the first place?

(Math) Textbooks


The following example is taken from a friend’s mathematical textbook, but any student who has done math at a decent level will recognize the kind of text. It being in romanian only helps prove the point.

Mixing math and normal language is funest for learning. Take mixing french and german in a text. You can’t read it easily even if you know both languages. Let alone remember the content. For most humans, the language processor cannot switch between such different languages efficiently enough (though i’m not aware of any scientific research on this). Books like this want to be mathematically rigorous, but end up being completely useless. If you look at for example MIT’s mathematics for CS book and this the difference is as day and night. MIT has formulas cleanly separated and focussed on their relation in written text, while other books often have this mixmatch of inline unreadable math that makes most people want to stop reading and just watch youtube videos instead.

Asking questions

This is something that many education systems struggle with, and it’s almost become a culture thing in a lot of countries.

Educators often ask themselves why students are not asking questions. Even though it’s obvious from the next test that they didn’t understand everything well. And it’s a sad by-product of mass education.

The amount of questions asked is often already decided in the first lecture by the speed and thoroughness of which an educator anwsers it. If a student has to wait a long time and the subject has already passed, the student (and for one question-asker many others) will already have missed the point, and having to go back feels like you are wasting everyone’s time.

If an explanation is too short, the student might not understand yet or feel dumb, which will stop them from asking more questions. If the explanation is too long the other students will quickly get distracted or the student will feel like it’s a waste of time. Try to keep your answers to questions to the global audience and make them part of your lecture, don’t just look the specific person in the eye and talk softly to them as you will surely lose all other students. The trick here is to gauge what level of understanding all students are on, but this is an extremely hard if not impossible task.

What my university did very well was create a discord group with specific channels for each subject for asking questions. Being able to ask them semi-anonymously (under your real name, but no face) helps a lot with getting people to ask questions, and you have a lot more tools like a LaTeX bot or images. It would help if there was a bit more of a culture of also anwsering those questions. Perhaps by having TA’s anwser some of them, but this fills a very important gap. Somes universities have specific question-hours but these are often not very productive as people are not actively working on the content at those moments. It’s better to allow asking these questions when people are working on the content at school or at home.

Electrical filters

Filters are quite an important application in Electronics. You may want to filter out lower or higher frequencies, or perhaps a band in the middle. This is very important in audio systems (think bass etc), but also in for many other electrical components.

Passive Low pass

Low pass filters simply let the low frequencies “pass” while not letting through higher frequencies.


A capacitor has the function

capacitive reactance equation

or 1/(ωC). (ω = 2 * pi * f)

You can see if f increases the bottom part will get larger and as a result Xc will get smaller and smaller. This will make the capacitor have a lower impedance and thus a smaller voltage drop (X = U/I -> U = X * I) which means that Vout will be lower when increasing the frequency. This is the basic idea of a filter.


low pass filter bode plot

The difference between Vout and Vin is often defined in Gain (dB), you might recognize this scale from how loud sound is, but it is important to know that we are talking about voltages here, not directly sound.

Gain is defined as 20 log(Vout/Vin) where the 20 comes from the 45 degree slope that can be seen at the right of the image. 45 degrees ends up at -20dB/Decade where a decade is a factor 10 on a logarithmic scale.
normal: 1, 10, 100, 100
decade: 1, 2, 3, 4

The cutoff frequency is the frequency at which

Cutoff frequency

The cutoff frequency Fc is the frequency at which the gain is -3db and the slope is exactly 45 degrees. This is is ultimately the magic that decides where your filter should start cutting off.

The cutoff frequency is defined as follows:

Where R is the resistor’s resistance and C is the Capacitance of the Capacitor

You will see this RC factor come back below

Time constant

The time constant t (greek tau) is defined as R * C.

This time constant is an indicator for the time needed to charge the capacitor. To be exact the time from 0 volts to approximately 63.2% (1-1/e) of the value of an applied DC voltage.