Archive for the ‘Parenting’ Category

Amaze your friends, and confound your enemies!

Wednesday, November 4th, 2015

When I was young, I read lots of books with titles (or at least subheadings) along the lines of, “Amaze Your Friends and Confound Your Enemies” – a lot of them were filled with tricks and oddities like the Birthday Paradox, or the old saw about the elephant from Denmark.

It turns out that if you read and continue to read enough of this kind of thing, you can continue to amaze your friends well into adulthood! A lot of times this means appearing to be good at mental arithmetic. And the trick to being good at mental arithmetic is not to be especially fast at rote calculation. It lies in a web of knowledge about numbers.

An aside about maths teaching

I often think that number theory is poorly served by the mathematical curriculum almost everywhere. Kids learn times tables and are introduced to prime numbers, and then I think the number theory track more or less stops, and a student doesn’t meet it again until university-level maths. Which is a shame, because there are many interesting and fun problems in number theory that can be easily stated and understood by a ten-year-old but which still remain unsolved. Also, a more continuous (ha!) grounding in number theory would give us a better understanding of some very important features of the modern world – an obvious example being cryptography.

I was lucky enough, as a 12-13 year old, to have a recreational maths class at school for a year where we tackled problems together. It was distinctly constructivist in nature – whether by design or not – and it was a really fun class because we were typically all trying to solve a hard problem over the course of a few weeks. “Copying” other people’s work and building on it towards a solution was par for the course – as in real life! We took inspiration from the writings of people like Martin Gardner, Sam Loyd, Raymond Smullyan, Henry Dudeney and Eric Emmet. The teacher would ramp up the difficulty of problems as we went – and in mathematics there is almost always a way, having solved one problem, to remove a constraint or make it more general in some way to provide a step up to the next level.

A typical class exchange:

Teacher: Who can tell me how many squares there are on a chessboard?
Student A: 64!
Teacher: Ah yes. Correct. But I see you’re only counting the squares that are one square in size, as it were. I think there might be more squares there…
Student A: …
Student B: Wait a minute…
Class: *realization* *time passes, working-out*
Class: 204!
Teacher: Correct. For your chessboard there. But my chessboard has n squares on a side, not 8.
Class: *argh* *more time passes, probably a week*
Class: Um… (a few tries, and then)… n(n+1)(2n+1)/6 ?
Teacher: Right! But… hm… my chessboard got broken, now it’s not square any more, it’s n by m. Oh, and I want to know how many rectangles are on it.
Class: *mind blown*

Associations – it’s what brains do

Anyway, the human brain is fantastically good at constructing associations. And being “good at maths” is about having lots of those associations when it comes to numbers. Mathematicians often have this. Computer people have this facility, when it comes to powers of 2, and it looks astounding to muggles when it comes out in another context (eg Biology class):

Teacher (thinking he is asking a hard question): This germ divides in two every hour. If we start with just one germ here, how many will we have after a day?
Nerdette in the back row (instantly): 16,777,216
Rest of the class: How the hell…?

When you have enough associations, they start to overlap and provide multiple ways to an answer. I was recently out with a group of friends and at the end of the night we came to pay the bill. There were seven of us, and the bill was $195. I immediately knew it was about $28 each, and I didn’t have to calculate, because of some associations:

  • 196 is 14 squared, which is 7 * 28. Immediate answer. (Square numbers up to 20 or so – very useful to know.)
  • In the UK weight is often measured in stones. 14lbs = 1 stone, and I know that 98lbs = 7 stones or 7*14 = 98. And as 98*2 = 196, because (100-2)*2 = 200-4 = 196, so 14*2 = 28. Corroboration by overlapping association.

“Wizardry” with 1/7

Another second’s thought provides the exact amount per person, because 1/7 is a useful and interesting fraction to know. It has a recurring 6-digit pattern, and it cycles. Once you know the six digits of 1/7, it’s trivial to figure out/remember the other fractions:

  • 1/7 = 0.142857142857142857…
  • 2/7 = 0.285714…
  • 3/7 = 0.428571…
  • 4/7 = 0.571428…
  • 5/7 = 0.714285…
  • 6/7 = 0.857142…

This is a fun trick for kids: compute 142857 * 2, 142857 * 3, etc and see how the digits cycle. Then try 142857 * 7… and you get 999999. Neat.

Anyway, 28*7=196 but the bill is $195, which means actually everyone pays $28, less 1/7 of a dollar. So the exact figure is $27 and 85.714285… cents.

Fun for kids

When numbers are your friends, it’s easy to look like you’re a wizard. And it’s really just about forming those associations. When I see 41, I think of Euler’s famous expression x2 + x + 41 which is prime for every x from 0 to 39. When I see 153, I think, “Hello, 13 + 53 + 33!” And similarly for many other numbers and mathematical techniques, thanks to all that reading and playing with numbers as a child. These days I entertain my kids by having them do fun math tricks like:

Enter any three-digit number into your calculator (say 456)
Multiply by 7
Now multiply again by 11
Now multiply again by 13
The result is the original number “doubled up” (say 456456) – because 7 * 11 * 13 = 1001

I’m teaching them how to amaze their friends and confound their enemies!

Some poems we like to read at bedtime

Tuesday, February 15th, 2011

We have a book of classic poetry that we often read a bit of at bedtime. Some of mini-Elbeno’s favourite poems:

  • Naming of Parts by Henry Reed
  • Tarantella by Hilaire Belloc
  • The Way Through the Woods by Rudyard Kipling
  • Ozymandias by Percy Bysshe Shelley
  • The Road Not Taken by Robert Frost

Taking Parenting Classes

Saturday, January 29th, 2011

I’m currently attending a parenting class on Thursday evenings, given by Brian Joseph from the Echo Center. It’s somewhat of a refresher class for me since I’ve taken a similar class a few times before, but it never hurts to have a refresher.

I wanted to blog a little about this class and about this philosophy of parenting in general. The Echo Center was formerly known as the Center for Non-Violent Education and Parenting. So that’s what the class is about – non-violent parenting.

“But wait,” I hear you say – “parenting isn’t violent in the first place!” This bears some explanation. This philosophy has a couple of key ideas:

  • Violence is anything that hurts a kid’s mind, body or spirit. That means not just corporal punishment. In a physical sense, it means also things like bodily moving kids without their consent (something we all do) or just giving them that extra squeeze when you’re angry, just to make sure they get the message. Things like that. In a non-physical sense, it also means verbal put-downs, shaming (“I’m so disappointed in you…”), threats (“Wait till your father gets home..”), and general unkindness in language and action.
  • All behaviours stem from needs being met or unmet. Everyone has needs, ranging from the basic (food, warmth, sleep) to higher-level needs like belonging, accomplishment, respect, love. Needs give rise to feelings, which in turn give rise to behaviours. When needs are met, we experience feelings of one sort; when needs are unmet, we feel differently.

So, the first class started with a simple question: what do we want our kids to be like when they are our age? And a short brainstorming session evokes a long list, of which some are:

Happy • Generous • Content • Fulfilled • Successful • Caring • Aware • Compassionate • Loving • Appreciative of others • Competent • Responsible

The list goes on. So the next question is: how will they learn that? The answer is very simple – and you already know it. Kids won’t learn the tools for such a life by being lectured to, by reading, by watching on TV, or by thinking about it logically. Overwhelmingly, kids learn by imitating what they experience in their families. So to bring up happy, healthy kids with all the qualities we want them to have for a good life, we had better start by modelling those qualities in our homes.

Here is how the non-violent paradigm differs crucially from the dominant paradigm of parenting: the dominant paradigm is behaviourist in nature. It seeks to control kids’ behaviour. The non-violent paradigm looks beyond the behaviour to uncover the feelings underneath and the unmet needs behind those feelings. It seeks to connect parents with their kids.

The tools of the dominant paradigm are fear, threats, punishments, rewards. And make no mistake, these tools work. Spanking. Go to your room. No more Game Boy unless you eat your dinner. Clean up your room and you can have a cookie. These things are all effective, after a fashion. They do elicit desired behaviour and prevent undesired behaviour. But they don’t foster a better connection between kids and parents, and they don’t work in the long term. Eventually, the kids are too big to spank. Their room has plenty of diversions. They aren’t particularly fussed about a cookie.

Just take a step back and consider treating an adult like this. It’s laughable. Imagine saying to your spouse something like, “If you don’t do the washing up, you can’t drive the car for a week.” Ludicrous. Threatening violence against your co-worker because you don’t like their behaviour? It’s ridiculous, not to mention that it would get you fired. Society and our legal system simply don’t tolerate such things. And yet, many (perhaps most) people in the US and the UK still support the right of parents to spank their children, and it seems that almost everyone thinks that the dominant tools of discipline like timeouts, the naughty step, withdrawing privileges, etc, are good things.

A central tenet of non-violent parenting is that these things don’t help – in fact, they harm the child’s relationship with the parent. And they do nothing to further our goal of raising kids with all those qualities we want. The dominant paradigm tools model sanctions, disconnection and conditional love. What we want to model is unconditional love and connection, which has been shown to result in the kind of qualities we want our kids to exhibit as adults.

So non-violent parenting is a radical idea, in the sense that it flies in the face of such entrenched dogma. And when you first hear about it, it immediately raises a couple of issues.

The first is doubt about effectiveness. If kids don’t have limits, if they don’t learn “consequences”, then they are going to grow up wild.

Let me be clear: this style of parenting is not about permissiveness. There are still limits and one can still be firm about enforcing them. I don’t give my son a cookie right before bedtime, no matter how much he wheedles, cajoles, threatens, and cries. What I do is try to connect with him and figure out what need is not being met. If he’s still hungry because he left half his dinner, this frustrates me, of course, but ultimately what can I do to solve the problem and remain connected with him? Maybe the need is something completely different, like him needing some time with me because he hasn’t seen me all day.

The second oft-raised concern is: the world is not like that. “I’m only preparing my child for what (s)he’ll encounter in life.” But is this really true?

First, do you think the world should be violent? Wouldn’t it be nicer if it weren’t? And how will it change? The only way it will change is for us to be the change we wish to see in the world.

Second, I don’t think the world really is that way. People are not, in general, motivated by punishments and rewards. Extrinsic motivations like these are a distant second to intrinsic motivations. People in the working world will often take a pay cut in exchange for a job they feel is interesting, meaningful, and that fills the need for autonomy. Similarly, the reason most of us don’t commit crimes is not the fear of legal punishment. It’s that normal, well-adjusted members of society have an intrinsic sense of morality. Our morality comes from an evolutionary history of the value of living in a harmonious society.

The lack of rewards in this philosophy is a particular challenge for many people, in a world which emphasizes the value of “good job!” But rewards, like punishments, are a poor long-term motivator, and do not put a child on the trajectory that we want for success and happiness in life.

Non-violent parenting is not easy. Most of us were raised in the dominant paradigm (not to mention being surrounded by it in the media) and have learned the tools and language that go with that. Non-violent parenting requires us to step back, and frequently, to ask ourselves: does it really matter? If I’m a little flexible and allow a little more time to deal with this, we can all reach a happy outcome. It’s about really recognising the rights of kids as members of our families.

I’ll keep you posted as I attend future classes.

He likes a challenge

Friday, July 2nd, 2010

I was wandering around upstairs this morning and heard the mini-Elbeno playing downstairs. He was playing “Twinkle, Twinkle, Little Star” on his glockenspiel, a tune he has known for a while.

When I came downstairs, he said “Look what I’ve done!” and I saw that he’d swapped around the keys of the glockenspiel in pairs (C&D, E&F, G&A, B&C were each swapped). And he’d been playing the tune on that variant of the keyboard…

The hardware is out

Friday, June 25th, 2010

Micro-elbeno had his final op today to take out the internal hardware which has been holding his jaw together for the last few months.

Mrs Elbeno got up at an infeasibly early hour to take him to the hospital, where they arrived at 5.30am. She called me just after 8am to tell me he’d just been taken into the OR. The procedure took a little under 2 hours and he was out in recovery and doing well.

The plan was originally that they would keep him in overnight but they had no room, so he was sent home this evening and he’s now sleeping in his own bed again. He’s a bit swollen under the cheeks and stitched and taped up there, but overall doing great. In a few weeks he’ll be right as ninepence.

Little Bro is home

Sunday, March 14th, 2010

Henry Holding Archie at Home

Archie came home on Thursday and the screw-turning is now complete (we did the last couple of turns at home). He’s had one paediatrician appointment and tomorrow we’ll be making an appointment for him to get the other screw removed. With any luck that will be soon.

He’s doing well and is pretty mellow, all things considered. He’s letting us sleep pretty well in the night and the feed-burp-nappy-back-to-sleep routine is working out. One consequence of the jaw procedure seems to be that the left side of his face is palsied. It looks like there is some neural damage as there is no motor activity in his left cheek. Of course we don’t know if he can feel there or not. It’s too early to say whether this will be a long term issue or not, but this was always a risk. Unfortunately it seems to make it hard for him to close his left eye – he only gets it about 3/4 closed most of the time – which makes getting to sleep that bit harder. It doesn’t seem to interfere with eating though.

Quick update

Saturday, March 6th, 2010

The op today went well, and now he has a nose trumpet in rather than an ET tube. So that must be a bit more comfortable for the little guy.

Now, we wait another 7 days for the distraction to run its course (again).

Latest – a setback

Thursday, March 4th, 2010

The plate that is in the left side of Archie’s jaw broke a couple of days ago. This has caused his jaw on that side to slip back by some millimetres. The rod is partly sticking out and the asymmetry of his jaw is visible from the outside. So after an x-ray it has been determined that he needs to have the distraction done again on that side.

This means another 2 weeks in hospital just when we were gearing up to have him at home (otherwise he has been doing well, bottle feeding, off the IV, etc). He will have the operation at 7.30am on Friday. There will be 7 days of screw-turning this time, followed by the op to remove the external pieces again, followed by a period of convalescence which will, with luck, be shorter than before.

Tubes out

Thursday, February 25th, 2010


Archie is doing well and as you can see he’s been extubated for a day or two now. He has been in a bit of pain what with the jaw stuff coming off again, so he’s got some meds for that and also probably as a consequence of that he didn’t fully cooperate with a swallow study yesterday. Slow but steady progress is the order of the day. For the moment he still has the NG tube in, but should be bottle feeding soon.

Archie’s progress

Sunday, February 21st, 2010

This morning was the last turn of the screws. They have reached the predetermined end of their travel. Archie’s scheduled to have the hardware removed on Tuesday. It’s made a huge difference to his jaw, as you can see from this photo taken a couple of days ago.

Archie, 6 Days After Surgery

Otherwise everything is going well. He’s feeding well (35ml a time and increasing) and he’s on a small amount of Fentanyl for pain.