# all you (maths) ideologues unite

The Christmas season is now at a full blast on, and with it the call for singing all in tune with each other. I am looking forward to it – my neighbours and I will, for a little tradition that is worth three or so years – meet in my cosy little house and enjoy the mince pies, mulled wine, and the few ours of messing about with the Christmas carols. I hope John from down the street will volunteer to play the piano again, otherwise it will have to be me, in which case the said mess of finding the tune will be considerably greater.

Which brings me to the other different messes or messi or the one great mess that mathematics education sometimes is. It’s hard isn’t it, to think of something so pure and beautifully clear as circles and cubes and number 3 or 5 or some such, and consider it messy in any way. If you ask, as philosophers would, what is actually a circle, or a cube, or 3 or 5, you may be forgiven as long as you pose such question in an adult company or pose it purely rhetorically.

But if you were a teacher would you ask the 11 or 12 year old such a question? I did. I still do if I find some 11 or 12 year olds, or even a 5 year old. Just recently for example, not only did my 5 year old (clever Kitty) engage with me in a discussion about the nature of number 5, but was, the next day, able to tell me that after she thought about our conversation some more, she discovered she could count in zillions:

1 zillion, 2 zillions, 3 zillions, 4 zillions, 5…

I found that pretty impressive. But then again, it didn’t surprise me really, as I learnt that the greatest surprise of all in our culture, is how little we value the intellects of children. For some reason, we seem to put all the emphasis and value on the experience, the accumulated knowledge, and maturity. Could actually one tell when the supposed peak of wisdom occurs? 11, 12, 22, 27? I dare you. And then I double dare you to test it in practice.

Likewise, we seem to be quite precise to identify where exactly is maths learnt best. It must be something with the method. So why don’t we take the method and run?! We’ll surely make some progress, like the Chinese or Singaporeans or Finns have done.

Well we are not alone, with that kind of thinking, and those kinds of ideas…

But as the film shows you, unless you are actually a criminal it’s going to be very difficult to behave like one. You need to have the mindset, the language, the spelling, and the behaviour of a criminal to actually do criminal stuff, to take the money and run.

So let’s not try to be something we are not: in maths education or in any other way. To learn from others is fine, but to become someone you are not is kind of Frankensteinean in the worst sense, or Woody Alleny in the best. (Although I have issues with both.) And we don’t actually need the money, neither to take nor to run with it.

So my pearl of wisdom while preparing for the festive season is this: to sing in tune is fine as long as it is enjoyable and it comes naturally to you and your friends. But equally, we need to let kids to think on their own and mess about a bit. Forget the ideologies, get them some mathematical gems and mathematical mince pies of kinds to nourish their young brains and intellects, and they’ll find their own songs in time.

Next time: just before Christmas, I’ll show you how start counting the presents you’ll give to your loved ones over the 12 days!

# do you need to be weird to be good at maths?

I promised you last time that I’ll talk about this, so here it is. But I can’t talk about it in any of the normal ways available to me, as I’m supposedly weird (as I’m supposedly good at maths too) or so it goes. Let’s be mathematical about it. (I am weaving the story, remember, so I can pick whatever basically I like as the starting point. And I’m picking the exclusive or operation for some reason.)

Exclusive or is a logical operation that outputs true only when both inputs differ: it would be true if one is true and other false. If you have more than one input then the things begin to become more interesting, until you get to the point that you realise that XOR (exclusive or) is true only when an odd number of inputs is true… So in other words it’s reasonably easy.

Why am I going on about this? Well you will see that, plus a few other things in the following video.

Did you get that? (Oh by the way, do you know who Paul Erdős was?) Well what Sidon really said was mathematically quite correct. You have three operands here:

1. you are turning up to see him (this would always be true as you are determined to see someone – a mathematician presumably)
2. there is a person to see
3. that person is in a place that you are coming to.

Now you have three inputs, and you would have to have all three true for this exclusivity principle to work out. So all of the above have to be true for this principle to work, and your visit to be successful. Ah, I’ve forgotten to tell you something. Exclusive disjunction could also be interpreted that ‘if and only if one is true, the other cannot be true’.

In the above case, you have a person who doesn’t want to be seen. Unfortunately for you. So you would have to make all the other inputs different – you wouldn’t turn up to see him, there would be no person to see, that person and a place you are coming to are not there.

Well to be a kind person as mathematicians are, and Sidon obviously was, he just excluded himself, rather than the whole story. So you see, he said that you could

1. turn up to see a person
2. there is a person to see
3. that person is in a place that you are coming to

it’s just not him.

He wasn’t weird at all in my books.

Why I used XOR however may remain a mystery. If it is true, then the story (or title even) can’t be or something like that.

# Why oh why and when oh when will we ever need this (maths)?

The summer past and gone, and the blog I did for my first co-edited volume out, I still keep going through some of the questions that bothered me in the first place (first with the book, then with the blog). The one that is a common question that every maths teacher will come across many a time in their career: “when will we need this?” is the classic, and perhaps deserves some further exploration.

Let me start from the post I came across on  facebook recently. It said something about how  little we need algebra.

Boohoo I say to one and all wanting to reduce all effort in our lives all round. We live once and have one opportunity to learn as many things as we can, do as many things as we can. And not only because I Love Maths do I say maths is worth learning.

In school all kinds of things are offered to kids to learn, so they can enjoy and participate fully in their society: and we don’t tend to ask why do they need to learn music, or literature, or business, or anything else they are learning about. If anything, my question is: why don’t we teach our kids more, or give them more options and opportunities to learn, not less. Well, for one, does the facebook exist so we can post things like the picture above? Its inventor, if anything, must have been really bad at algebra…

Then I get back to think about the actual purpose of education in general and maths in particular. Why teach maths at all? one suggestion is to find a crystal ball and ask it.

“When will I need quadratic equations?”

I dare any maths teacher to think of the answer to that. I think in my case, I needed it on 14th April 2002, 17th May 2011 and a few other times. Then also I need it every day because I find it beautiful to switch from one way of solving it to another, and from investigating how completing the square was done about 4000 years ago and has been done ever since. Or to see all the possible solutions to a problem that looks so simple to begin with and which starts from having an area of a rectangle being equal to some value….

In short, “I’m very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical”

Coming up next week:

do you have to be weird to love maths?