Category: teaching

Socrates and Shoelaces

 

 

 

 

I have quite some time to think these days. Thinking is a process that is frequently non-linear, arbitrary and sometimes causeless. I rely on tools, mostly mathematical and sometimes probabilistic which shape the next part of the thread. Thinking is exhausting, especially when a degree of conscientiousness is required. It has been suggested, erroneously in my view, that ten thousand hours of practice can turn a novice into an expert, irrespective of innate ability.  Building neural pathways to solve specific problems is not enough. Until we learn and appreciate the value of lateral observation, thinking becomes no more than a mechanistic, hence unrewarding activity, which, dopamine-addicted as we all are, is counter-productive. Great teachers are not those who can manage gigantic classes and convey some information. Great teachers ask individuals, who then deduce partial solutions from which greater understanding comes. It comes as no surprise to learn that tutored students do better by a measurably significant amount than those who sit in large classrooms and are lectured along with a large number of others. It takes intense concentration for individuals to engage appropriately with the material in such a setting with little or no feedback. ‘How am I doing?’ is the perennial question, the answer to which is what every student really wants to know.

For these questions, you need to ask someone else the how-am-I-doing part. There aren’t any right answers, just interesting lines of enquiry. For each of them, you have to ask subsidiary questions, the accuracy of which will determine the quality of your final answer.
First, Fermi estimation. This is the process of coming up with estimates of the correct order of magnitude for various real-world quantities often with little or no hard data. Here are a few examples.
1. How much does a cloud weigh?
2. How many people could fit into the Island of Manhattan?
3. How many piano tuners are there in Chicago? [a classic example- I’ll post the standard solution in a comment – you might like to try to compute the uncertainties in the calculation]
4. If the average temperature of the sea were to rise by a degree, then by how much would thermal expansion cause sea levels to rise?
5. How many molecules from Socrates’s last breath are in the room?
Now for some more difficult ones.
6. How do speed cameras work? How accurate are they likely to be? (The basic technique I’m talking about is taking two photos in quick succession.)
7. Why does a mouse survive a big fall when a human doesn’t? (There are many questions similar to this, such as why elephants have thick legs, ants can carry several times their body weight, etc.)
8. Somebody pours you a cup of coffee but you aren’t yet in a position to drink it. You take milk, and the milk provided is cold. You want your coffee as warm as possible. When should you put in the milk: now, or just before you drink it, or some time in between?
9. You are walking from one end of an airport terminal to the other. The airport has several moving walkways, and you need to stop to tie your shoelace. Assuming you want to get to the other end as quickly as possible, is it better to tie your shoelace while you are on a moving walkway or while you are between walkways?
This question comes from a blog post ofTerence Tao
10. You have a collection of suitcases, boxes and bags of various sizes, shapes and degrees of squashiness. You want to pack them all into the boot of a car and it’s not obvious whether you can. What is the best method to use? If you don’t like the idea of suitcases, try thinking about plastic containers of varying sizes and robustness, some with lids and some without. How can they be fitted into the least and most accessible space?
 
If these kinds of exercises bewilder you, that’s fine. A significant part of our time is spent wondering what to do next. Wondering is what we do best. I sometimes wonder in common with the comedian Mark Russell whether  the rings of Saturn are entirely composed of lost airline luggage.

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Icebreakers

As I sit here by my pool, watching the sun go down on another near-perfect day, my thoughts have inexplicably turned to my many friends who are still labouring at the chalkface in various parts of the world. With no end in sight, I thought they might enjoy a little commencement encouragement, as it were. Perhaps they could show this to their new classes over the next few days as a kind of icebreaker. I’m sure it would be genuinely valuable. Pin it up somewhere next to the Discipline Policy document. 
“It’s the first few days of the school year. Everybody’s grown a bit and after an exchange of pleasantries you can get down to the serious business of School which, as everyone knows, is to make your teachers’ lives as miserable as possible. Also, you get a first peek at the freshest lambs to the slaughter, the New Teachers.
Going to an international school is quite fun because the staff there don’t often last very long and you get to torment a new intake quite regularly. Some of them do have a trick or two up their sleeves, but as long as you keep your heads you’ll have them all sobbing in the corridors in no time at all. Remember, low-level disruption is a first line skill, not a last resort. If you can get him (or her) to stop talking and demand quiet enough times in the lesson – this can be done with relatively minor whispering and muttering while their back is turned – you can actually hear them grinding their teeth in frustration. Falling off one’s chair can often waste several minutes, especially when you paste a look of injured surprise on your face while clambering very slowly to your feet. It’s particularly amusing when the teacher asks you if you are ‘all right’. Since you’ve been practising break-falls in your judo class since you were five, you have come to no harm at all, so a little  judicious elbow rubbing plus pained expression might get you a chitty to see the Nurse, which effectively means that you get the rest of the lesson off. Don’t make the elementary mistake of taking your stuff with you – it arouses suspicion. A well-briefed colleague will offer, kindly,  to take it for you at the end of the lesson. 
Missile-throwing is an advanced exercise, not to be attempted by the faint of heart, but, as long as you watch for the mirror above the teacher’s head – a nasty, underhand ploy which means they can actually see you while writing on the board –  you can sometimes get a quick whiplash shot off undetected. It takes a brave soul with quick reactions and good aim to get a rubber right on the back of his head without any trial shots first, so try it out on classmates in break. Practice makes perfect.
Having mastered the basics, we can now move on to more sophisticated techniques, the business of cheating – such an unfair way of looking at things, I think.
Class tests are the Nemesis, the spirit of divine retribution against all who succumb to Promethean hubris and imagine that they can get away with doing nothing. The implacable executrix of justice – and sacrificial goddess of all educators – gets her own back. So, here are a few simple tips on how to circumvent her mendacity with minimal effort. I make no reference to any people groups in particular, but, you all know who you are….
·                     If asked to write a critique about a poem, write the title of the poem followed by the words “is about man’s relationship with nature.” This will appeal to your teacher who’s probably a tree-hugging anorak.
·                     If you’re going to permanently tattoo answers on your forearm, make sure a) they are correct – have a grown-up check them first for you – b) you tattoo them the right way round – important for physics – and make sure it’s for an exam in a subject you really love.
·                     Have everyone take out their textbooks and cheat all at once, sometimes referred to as the ‘Oh, Captain, my Captain’ principle. They can’t fail everybody. Or, can they?
·                     Offer the teacher money. You get more pocket money than their salary so it sometimes works, really it does, if the price is right. Physicists are expensive. Be advised.
·                     When passing notes that have answers written on them, be sure not to label the note “Test Answers”, ’cause it’s a bummer if you get caught.
·                     Some schools equip classrooms with hidden cameras to catch cheaters, or entrepreneurs, whichever you prefer. A simple low-inductance capacitor bank appropriately modulated with a three-way phase adapter discharged into a single-loop antenna can send out an electromagnetic pulse capable of disabling all cameras within a three-block radius. This will give you a two point five minute window at the most. Use it well. Regrettably, however, your iPhone upon which you had been relying for external text updates, will also fail to function. Don’t get caught plugging it in, will you…
·                     It is notoriously difficult to cheat on most applied mathematics tests, since the teacher might actually expect you to apply what you have learned. It’s probably best to avoid taking these classes altogether.
·                     Visits to the bathroom can be a most productive method for harvesting information. Holding your breath until your face gets really red before putting your hand up usually has the desired effect and a crabwise scuttle out of the door adds a nicely Thespian verisimilitude. You are not advised to write the whole of Hamlet’s soliloquy on the wall of Cubicle Number Three, since this might arouse suspicion from an overzealous cleaner.
·                     No matter how small, crib notes can be conspicuous, especially when used as missiles. As an alternative you could commit them to memory for an innovative, unencumbered cheating method.”

Carpe diem.