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Tuesday, September 13, 2011


Pre-school storytelling

Sometimes I watch television with my son. In this culture, even this simple statement feels like a confession: good mothers are supposed to do non-television activities all day ... but y'know, sometimes I have to go into the kitchen or up to the bathroom and a bit of educational TV in the background can be a good thing. I take him out and play with him and read to him and so on as well, but I might as well out myself: I am a CBeebies fan.

CBeebies, for those of you not subject to British television, is the children's channel for pre-schoolers, the younger counterpart to CBBC (Children's BBC). It runs from morning to evening, has a variety of presenters and regular shows ... and it's really very good. Rather than running Tom and Jerry non-stop, almost all the programs are educational one way or another: The Green Balloon Club is about environmentalism, Mr Bloom's Nursery is about growing your own vegetables, Octonauts is an adventure in marine biology, Waybuloo (my personal favourite), is a kind of Buddhist idyll, Zingzillas (my son's favourite besides Waybuloo) is a pretty impressive introduction to all kinds of musical styles as well as a rather good portrait of productive artistry, and all in all I feel practically no guilt about sitting him down in front of such fare. They're informative, they have a reasonable commitment to racial diversity (the Rastamouse controversy notwithstanding*), they all feature at least some female characters (though male characters in leadership roles tend to predominate), and generally speaking they're pretty nice.

There's just one that really gets up my nose. And it strikes me as an interesting example of the problems you get when you try to mix fiction with the sciences.

Let us consider Numberjacks.

The Numberjacks, our heroes, are a bunch of numbers (the male ones are even, the female odd) who get called in to solve problems. Odd things happen because of various villains - Spooky Spoon gets things out of order, The Shape Japer changes the shapes of things, and so on - and the Numberjacks have to sort things out. The idea is that by showing the problems caused, children get introduced to the concept of numeracy...

But here's what I can't take. They solve the problems by turning on a machine, charging up with some mysterious substance called 'Brain Gain', which somehow mysteriously solves the problem by doing something mysterious.

Now, I am no mathematician. But am I wrong in thinking that a discipline founded on the study of cause and effect is not best served by magical hand-waving?

I'm not a mathematician; I'm not even a particularly numerate non-mathetmatician. But as a writer, I can say categorically that the correct term for 'Brain Gain' is actually 'cheating'. It's terrible storytelling: creating a problem and then solving it with the same universal substance every day is basically promising your viewers a climax and then refusing to give it any content. Suspense and plot are both destroyed: we know exactly what'll happen at the end, because it'll be exactly the same every time. And worst of all, it's a supposed tribute to brainpower that doesn't actually use any brainpower - that actively avoids it, in fact. Solving a problem by switching on the Brain Gain is solving it by saying, 'I don't want to think of a more involved solution, so let's all agree not to think about this too hard.' Calling this Brain Gain is a bloody cheek. It's like solving scientific problems by waving a Magic Wand of Science at them.

The thing is, the sciences can be a tricky issue in fiction. One can, of course, write science fiction, either by playing around with scientific laws one understands or by using a certain amount of Gizz - that is, by presenting the existence of certain things as a given fact that has to be accepted. But you can't Gizz a plot event. Things can exist because of a Gizz, but they can't happen solely because of a Gizz. That's just a non-story.

But when one's trying to educate children, there is information to get across. And presenting it in a way that's both fun and accurate is obviously a challenge.

For instance, I admire Nina and the Neurons. I also enjoy it. Nina, the presenter (a female scientist and authority figure at that!) has five CGI friends in her head, the Neurons, each of whom represents a different sense; children ask Nina questions, and she recruits one of the Neurons to help her demonstrate the answer. The questions are questions that children would definitely find interesting (why does my ice lolly melt? why do I get eye grit in the mornings? how do you stop bread going mouldy?) and in answering them, Nina uses basic science. Finding the answers to questions makes for an engaging 'plot' of sorts: Nina goes step by step, and there's a definite progression towards an answer, and I'll admit there have been times I've delayed a task because I was curious to hear the answer. Nina and the Neurons is a documentary, but it manages to balance entertainment and education very skilfully.

Numberjacks ... well, I can see what they're aiming for. Showing how patterns and systems work through showing what happens if they're changed is a good idea. And if the purpose is to show that things have structure, then how do you solve the villains' machinations? In the real world, numbers do come in the right order and blue things don't magically disappear or any of the other things that get the Numberjacks in a tizzy, so a realistic solution is out of the question and a more fantastical solution is spending finite minutes on something that isn't the to the purpose. The purpose is to showcase systems.

But if the purpose is not to solve the problem the story has created, then you aren't actually telling a story. You're telling a 'what if?'. All you really need to do is say 'Wouldn't it be confusing if it were like this?' and then move to 'Aren't we all glad that it's not?' That would be fine; I can picture Nina doing it very well. But for some reason, Numberjacks decided it needed an epic and exciting story format ... despite being averse to telling any actual stories.

You can mix stories and science. Octonauts does it: the (regrettably male-dominated) crew discovers surprising new creatures in the sea, then has to help them, and in so doing, has to learn what how that creature works: for instance, when the ship gets full of panicking humuhumus, the Octonauts need to know that humuhumus hide when they're scared and can lock their spines to wedge themselves into safe places, because that's a necessary piece of knowledge for dealing with the situation. And it also happens to be an interesting fact of marine biology. Science and story combine to good effect.

Now admittedly, numbers are rather less easy to anthropomorphise than fish. But surely there must be a better solution than this. The way I was taught mathematics as a child drilled into me the 'fact' that maths was boring from an early age, and indeed, the way I was taught, it was. But children have to study maths until they're sixteen, even if they abandon it after that, and if you associate it with boredom, it's a wretched experience. Numberjacks is boring storytelling; this is not a good start.

How should one teach mathematics to pre-schoolers? Any thoughts?

*Some Rastafarian people object to having their culture portrayed by a mouse, feeling it's a demeaning animal. Others have said that while the accents aren't very accurate, at least it presents a fairly positive message. The BBC received six complaints from people concerned about racism, and ninety-five complaints from people objecting to the use of Rastafarian slang. This is a truly discouraging ratio.

I have pondered the same problem myself when forced to watch the Numberjacks (around 6 years ahead of you with that particular joy.... argh!) and I guessed that the original idea of the "brain gain" was that it would show how by working together and using the mental resources of many brains you can achieve much more. That many brains working together can solve the problem. That's why they show all the "agents" answering questions. All this brain power is then loaded into the one brain and fired at the villain. This has definitely been lost somewhere in translation though!

As an aside I have a friend who refuses to let her children watch Rastamouse on the grounds that "they don't speak correct English". She gets quite angry about it in fact!
Show, don't tell.

Preschool kids do stuff with math all the time. Does this shape match the other one? What shape is it? How many sides does it have? Can I fit my train through this hole? Can my train climb over this pile of blocks?

All of those are math problems. While showing the exact working out in a formal way may not be within a preschooler's understanding... they can still understand how it works in practice.

There's also a whole host of fairly complex math ideas that a very small child can understand and use. Infinity is a concept that most kids love. Same with things like triangular numbers and square numbers. Simple logic puzzles are good too. And Venn diagrams are a bit tough for most preschoolers in the formal way, but they love showing you why this thing is like another thing, or talking about how two things are different.

If you tie it into art, you can get even more complex. Kids that age pay attention to different art styles, and there is a ton of math underlying how various sorts of perspective work. And kids that age know that you can't have two things in the same place at the same time, but they don't always know how to show that in a picture.

A common thing to hear in math classes as you're getting on towards classes in a math degree is... "can you draw the picture of what happens?" This is a really fundamental part of math. It comes up all the time. Starting kids off with the idea that math is visual and artistic is a good solid foundation.
@Tequilamonkey: your friend is linguistically underinformed, because there is no such thing as one 'correct' English. Every dialect has its own consistent grammar and is a perfectly legitimate form of speech; it's just that BBC English is a high-prestige dialect among the middle classes and Rastafarian slang isn't. BBC English is no more grammatically correct than Rastafarian English. It's just a white dialect rather than a black one. Mind you, if she objected that it wasn't proper Rastafarian English, she might have a point...

I don't think the 'brain gain' really does show brains working together, though, because they don't actually think. They don't get together and think of solutions; they just fire a blast of plotsolvium at the problem.

I console myself with the thought that it's not one of my son's favourites, so I probably won't have to watch too much of it. His tastes are almost entirely dictated by how much music a show features, which is fine by me.


@torrilin: that sounds interesting. Another idea that occurred to me was that children very often enjoy riddles - and a lot of riddles involve a degree of mathematics. There's the two gatekeepers one (you know the one: one always lies, the other always tells the truth, you only get one question), and there's the three-black-hats riddle, and then there are mathematical surprises like the Monty Hall problem; I'm sure you could get a lot out of those.

For very small children, though, I might just incline to shows that feature good, well-structured music. It'll work on similar parts of the brain, and it'll entertain them besides.
Jolie, one of the kids in our system love CBeebies, but not the shows (don't have them here, so we haven't seen them), but the website. It has lots of fun games that she finds enjoyable at age 5 -- some of them your son probably isn't ready for yet but he'll grow into in a year or two.


She does have a few accessibility complaints -- nothing's captioned since the target audience can't read and there are quite a few games that are unplayable due to information being conveyed only by sound, but she likes the ones she can play, and they do have print outs for fun ideas that would be totally cool if we had a printer.

For maths, what our parents did with us when we were very young was:

backgammon. We spent a lot of time playing backgammon at the age of 3, rolling the dice, counting up the pips, moving a piece that number of pips. We remember rolling a 56 and knowing it was a 5 and a 6 at a glance, but not being able to get to "that makes 11" without counting "one...two...three..." and our father was trying to get us to start with six. "You know this one is six, so count the ones on this die, say: seven, eight, nine, ten, eleven." It was so difficult! We could only count starting at one. :)

When I was about five, we learned negative numbers and the concept of debt with stones. He gave me a few and then set up the scenario that i'd been promised a stone for each task I did. He said "you cleaned your room so I give you a stone, and then the next day you raked the lawn, so i give you a stone, and the next day you tidied the bathroom, but I'm out of stones and can't give you any, so I have negative one stones, one less than zero, because the very first stone I get, I have to give you..."

We also did a lot of word problems to keep me still in the car. I really enjoyed it. When I was around four, he would say "Okay, so there are two men who live in two towns that are five miles apart, and one starts walking towards the other at three miles an hour and the other starts walking towards the first at two miles an hour. How long does it take them to meet"

This was really helpful to me. He also wrote a very simple computer program that quizzed me on multiplication or division or addition or subtraction (i could choose) and played a short bit of music for each right answer. The music only played for a few seconds, and I would try to keep the music playing continuously.
Oh, and I'm not remembering some of the other DOS games we had. There was one that drew stars -- I could type in any number it would draw a star with that many points. And I think another one that was like a spirograph which I played with a lot. There was also gorillas (which came with QBASIC which came with Windows 3.1) where you have to decide what angle and velocity for your gorilla to throw an exploding banana at the opponent gorilla. And there was another one, moon lander, which I'm pretty sure was a DOS game where you had to land a small craft safely on the moon, so you had to go in with a certain velocity and you had to steer. It was quite difficult, but it was good physics.

And this was more literacy than math, but we had this other DOS game with letters falling from the sky and I had to type them. It was just part of a larger typing tutor, and at age four it was very much "match the lowercase letter on the screen to the uppercase letter on the keyboard" and less about touch typing, but I did use the same program to learn to touch type when I was ten.

Also, about backgammon, it starts as a very simple counting game, but as the kid gets a bit older, it becomes all about probabilities and gets into some much more difficult math.

Cooking is also good -- learning about measurements. A small allowance is good, down the track, to learn about money and budgeting. Working out how much you'll have left in your jar of coins after you take out 35p for a bit of chocolate is good practice for later.

Making lamps for my dollhouse with LEDs was really fun. I'm glad my parents were a bit more modern about gender rolls. I had a dollhouse, but I learned some basic engineering to provide lighting for it, was allowed to solder things with supervision, and unwanted dolls were not forced upon me. When I begged them to tell the people at McDonald's that I was a boy so I could get a HotWheels car instead of some stupid barbie, they went along with it.

(Thinking back, I'm sure we learned some intuitive things about physics with those little race tracks, even if there weren't any numbers involved.)

Also, I had a skip-it, which was really fun, and when I found out that the numbers decreased when I put it on my other leg instead of increasing, it was a fun challenge to work out why that happened (and the presumptions the company had made about which leg a child would be putting the toy on)

and of course, I can't recommend highly enough learning an easy programming language as a child. I had so much fun writing computer programs in BASIC, it was such an sense of accomplishment when I wrote a bit of code that worked -- even really simple stuff -- and I've never lost that feeling. BASIC isn't really around anymore, but I'd recommend python for your son. Maybe after he stops teething though ;)
*now remembering, not "not remembering.

*gender roles, not gender rolls. I wonder what gender rolls taste like.

gah. I did study inglish in collidge i prommiss.
pthalogreen, I remember the exploding bananas! They were great fun. I wonder whether they still exist. Someone with better javascript skills than I have could do a web-based version fairly easily.


open source python version (works on all operating systems):


with links to a flash version as well for online gorilla goodness :D
Yikes. What a poorly thought-out show. One thing worth noting -- while, as you say, in the real world numbers don't go missing, etc., sometimes you mess up and it sure seems like they have! Then you have to go back and figure out where the problem is. I suppose if you carry out this line of thought, the villains would spread subtly wrong misinformation, and the heroes would have to find the mistakes... but I have to wonder to what extent that would work if you didn't have a little understanding already. "6+7=11" doesn't really work as a convincing error -- well, I mean, it is believable if you haven't yet gotten good at mental arithmetic with small numbers, but it's not wrong for any interesting reason!
I never heard of Rastamouse but it put me in mind of this proposed series for Speedy Gonzales that never happened. Artwork by Fwak! Animation.

How should one teach mathematics to pre-schoolers? Any thoughts?

I went to a Montessori preschool, which was run by subversive geniuses who had things like this.

This is a set of eight blocks: two cubes and six rectangular prisms. One cube is red and has a side of length A; the other is blue and length B. Three of the other blocks have two A sides and a B side, and the other three have two A sides and a B side. They fit together as shown. The relationship between the lengths of the sides, the areas of the faces, and the volumes of the blocks illustrates the concept of squaring or cubing a binomial (a sum of two maybe-unknown quantities). You don't know the value of A or B but you know that the painted square is one red square, plus one blue square, plus two rectangles that are A on one side and B on the other.

None of that is talked about in the activity. The Montessori system avoids verbal explanations of math concepts, as they make verbal ability a prerequisite for learning anything else. The binomial cube is a great example: the language we would have to use to explain the concept is far more complicated than the concept itself, which can be learned by a three-year-old playing with blocks.
Re: your critique of the "Brain Gain" conceit:

you're in good company here; I recall Richard Feynman writing disgustedly about a similar situation in an introductory science textbook. The front of a page had a handful of questions: what makes this bicycle move? What makes this lightbulb light up? What makes this bird fly? And so on.

Feynman, looking at the front, thought that this was a good conceit. On the back you'd work your way through the various steps--the bike is moved by the child, the child gets energy from food, the food grows in the sun, etc.--back to the sun (in most cases), illustrating the complex relationships between different sorts of energy. Then he turned the page.

The answer for every question was "energy makes it go."

Feynman pointed out exactly what you did: that such an answer takes real and meaningful scientific understanding and mystifies it. Rather than actually teaching children to think about energy, it taught them that the word "energy" appeared in the Great Dogma of Science.

I think the way to teach math, then, might be a lot like what Feynman suggested: to revel in the detail. Rather than be concerned with a particular sort of math (lesson plan before the story), pick an age-appropriate story in which some (age-appropriately) fiddly math bits happen, and let the characters work through those bits. Easier said than done, sure. But it would be an interesting approach.
When I was about eight or so, I was extremely fond of a kids' math show called Square One. Many of the segments were math-based parodies of grown-up TV shows, where the characters worked through the math problem that had been substituted for a plot while making terrible puns. For example: today on General Mathpital, can Dr. Mal Practice help Dr. Precisely double a patient's area?

Probably the math (and puns) were too advanced for preschoolers, but I don't see why the basic gimmick of the characters talking through a math problem wouldn't work with younger kids.
Learning Math through Music is effective and great fun as well. One way to look at music is to break it down into three elements:
1. Melody (determined by the lengths of the notes / sounds and the rests / silences as well as the lengths of musical phrases and sentences).
2. Harmony (the lengths of the pitch differences)
3. Rhythm (number of beats in a bar, the patterns of stress in the bars).
The relationship between these elements (and other Math-related musical concepts) can be picked up unconsciously as one enjoys the music. There's also the Constructivism / Objectivism debate in teaching Math but that's a whole other can of worms.
The Kidd.
Mathnet was a regularly recurring feature on Square One - it was a Dragnet parody, and it was *awesome*.

I don't know enough about preschool learning to know appropriate levels, but I like the story/puzzle ideas. It seems like some fun fables and myths could be merged in there nicely.
@torrilin : I agree with you on making math visual and artistic, and I'd add one, especially for preschoolers : make it tactile. Have them play around with beads and bottle caps and coins, having them add and subtract thing that way (and multiply and divide, too).

Note that there is an issue of brain maturity though - before the ages of 6 or so children don't understand conservation of volume (as in : if you transfer a liquid from one glass to a differently-shaped one, they'll think the amount of liquid changed with the level) and I'm pretty sure that makes it harder for them to do basic maths. It's hard to figure out that, say, 2+3 is the same as 3+2 if you don't even realize that 2+3 has a single, consistent answer.
Mathnet! The names are made up, but the problems are short...

Oh I was such a huuuge Square One fan.

Team Umizoomi seems to do alright with basic preschool-type pre-math stuff. I haven't paid a lot of attention, though. And blocks are made of win.
I have no idea why I wrote "short."
"The names are made up, but the problems are real." And I do believe I had a crush on Kate Monday.
Teaching math to preschoolers? I'm pretty sure that preschoolers have other things to learn, that are more pressing for their developmental level.

My thought is just to focus on communication and real-life situations.

Songs that help them get the numbers and counting-words memorized in order are good. Knowing the sequence of counting-words is essential, but the connection between the sequence and "counting things" doesn't need to be made immediately. Just have fun singing.

Using counting-words in daily situations, such as if you have the child with you for grocery shopping, count the apples you need, together, is good. Maybe counting two things separately, and then together, such as choosing three apples, and then six pears, and then counting together nine pieces of fruit. Or choosing "one apple for mommy, one apple for daddy, one apple for you, is one, two, three apples." The exact numbers aren't the point, the point is that you can count one thing, then another thing, and then both together.

Math is something that is part of daily life. If you make a habit of talking to your child about whatever you're doing, as you're doing it, and giving them tasks to help you, you'll teach a lot of math without stressing about it.

It also makes life easier for you as a parent. For example, in the grocery store, if you keep your child interested by counting apples together, asking them to look for a particular type of cereal in the cereal aisle, having them ask the butcher for three chicken legs, etc. they'll be focused on the task at hand and less likely to fuss.

(Be canny about this. Asking "what vegetable do you want for dinner" is a clever question to encourage interest in a healthy type of food. Asking "what cereal do you want" invites the answer "Super-Sugar-Junk!" and will make your life harder. So in the cereal aisle, you ask "help me find the big yellow box of Healthy-Yummy-Stuff.")

Almost any grownup task can be made interesting for a child, because they're curious about the world. And involving a child in grown-up tasks teaches lessons in math, language, ethics, etc. in a natural way.

Some of my friends thought I was odd when I was proud of my two year old niece for spreading butter on her bread for lunch. But spreading butter on bread is a task people need to master, and it is as worthy of praise as any new skill. (She did a great job, using a small knife to take some butter, and spreading it neatly and evenly, without wasting any.)
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