Why some children don’t get numbers

This post is strictly for educators and parents with children who hate maths.  No esoteric stuff this time…

When I was a teacher, for some reason I always used to be given the top set for maths – year after year.  (I’m not going to get into the ‘Is streaming children for maths a good idea?’ debate, by the way; just saying that’s the way it was.)

Well I enjoyed working with the school’s brightest and best very much, but then one year, the head teacher told me he’d like me to work with the lowest set.  That got me really excited!

I always loved a challenge.  I spent most of the summer holidays pouring through the finished maths books of my new group, trying to work out why a bunch of hard-working and well-intentioned 10 and 11 year olds had apparently failed to understand the very basics of number, while their classmates had made such excellent progress.

Finally, I had it.  There was one simple step that this group of youngsters had somehow missed – and this was the key that would help them to understand.  It goes something like this:

In English, we have 26 letters:         a b c d e f g h i j k l m n o p q r s t u v w x y z       which we use to make words.

The words can be one or more letters long:        a  my  box  daft  every  garden  quickly  unlikely  difficult…

In maths, we have 9 digits:        1  2  3  4  5  6  7  8  9  and one gap-filler  0               which we use to make numbers.

The numbers can be one or more digits long:                 3    27    154    2013    53196   100481…

So how was I to get that message across to a bunch of kids who by now were approaching some kind of number phobia? They were happy to work with numbers up to about 20.  From 40 onwards they got somewhat panicky, and if a teacher tried to introduce three- or four-digit numbers, they’d start shaking and ask to go to the toilet.

Close-up of a bucket full of midi-sized Hama b...

My solution was to give each child an abacus.  The ones in educational catalogues were hugely expensive, coloured to appeal to 3 year olds and far too big to fit on their tables.  I paced around the local shopping centre for a while and ended up with a couple of packs of self-hardening clay, a bargain tub of those little fusible plastic beads and a stiff yard broom.  The bristles made sturdy but flexible and non-dangerous abacus sticks.  I set four of them into a little strip of clay and cut them off at exactly the height of 9 beads.  That way, the children would be able to make the numbers 1 to 9 on the ‘unit’ stick, but would be forced to take them off and start again on the ‘tens’ stick when they wanted to show the number 10.

These are my updated versions - note boy and girl-friendly versions to help children feel relaxed.

These are my updated versions – note boy- and girl-friendly versions to help children feel relaxed around numbers.

The picture shows how I now make them for individual students, using a loop of wire, with beads safely trapped into the abacus.  There are, of course, only 9 beads on each wire.

We spent many days ‘building’ numbers from 1 to 99 on the abacuses and writing down the equivalent number.  Suddenly the 4 in 46 was understood as ‘four tens’ and the purpose of the zero in 20 was clear.

I insisted that they were forbidden to use the other two sticks, until they were completely begging me to allow them to make ‘hundreds numbers’.
“Nah,” I grinned.  “You don’t like big numbers, remember?”
“We do!” they insisted.  “We can manage it,  We promise.  It’ll be easy!”
“Well, if you’re sure…” I said, looking suitably doubtful and working hard to suppress a triumphant grin.

Within weeks, these children were working confidently with three- and four-digit numbers; not just building and writing them, but using them in calculations.

The next stage was to turn the abacuses round and use them to show decimals. Instead of labelling our four sticks as Thousands, Hundreds, Tens and Units, we now had Units, Tenths, Hundredths and Thousandths.  There was a clear decimal point marked between the whole numbers and the decimals and I showed them how, in this looking-glass world, zeros had to be used as gap-markers from the left, not the right.  Otherwise, they were in familiar territory.

By the end of term, the class was happily creating numbers to four decimal places, and comments like, “I get maths now!” and even, “Actually, I LIKE maths!” were heard around the room.

Now, to my great delight, I’ve been asked to work with Simeon: 14 years old, great at English, clueless at numbers.  Here we go again!

No Such Thing as Coincidence

This image is a derivative work of Gamepad.svg...

It’s such a glib phrase: There’s no such thing as a coincidence.   Usually spoken with a knowing smile, as if something deep and meaningful lies just behind the words.

What’s more, it seems to fly in the face of our everyday experience.  Odd, coincidental events appear to crop up all over the place and are usually shrugged off with a grin or a casual, “Oh, that’s weird…” or “Wow, I was only just thinking about…”.

What if there really IS no such thing as a coincidence, though.  Where does that leave us?

I, Damace, took this picture of my cat at dusk.

For me, the answer is that it leaves us with synchronicity.  We notice the weirdness of the situation, and that puts us on alert that something significant is happening.  It’s like that bit in The Matrix when Neo notices the black cat walk past the doorway twice.  For him, it’s just something a bit strange, but for those who are more experienced at the way the program runs, it is a highly significant clue that helps them to deal with what is coming up.

Fortunately, we’re not about to run into Agent Smith/s when we spot some synchronous event.  However it should put us on alert.  Life is reminding us that nothing happens by chance, and something is going on that we need to take notice of.

There’s more detail on this in the following extract from my book  Life: A Player’s Guide, in which life is considered as if it’s a highly sophisticated virtual video game:

Have you ever noticed that the characters in novels you have read, or movies you have seen, tend not to have random meetings and encounters?  In almost every story or narrative film, only the relevant encounters are included.  Any meeting or conversation the main character has is important in some way to the storyline.  Of course, this is particularly true in a thriller or a whodunit, but when you consider it, it tends to be true of most types of fiction. An apparently insignificant encounter might change the way the main character thinks, give them a clue about how to solve a problem or even change their lives.  We just know that the seemingly trivial conversation with the waitress in the diner will make a big difference somewhere along the line. That, of course, is why the author or scriptwriter included them.

In a computer game, there’s a slightly different convention.  Because you – not the scriptwriter – are making the choices about who you interact with, the game designers have to find a way of nudging you towards significant meetings.  Consequently, your avatar will meet other characters from time to time who will be identified in some way – usually by having special lights or symbols bobbing about over their heads.  This, as all RPG players will know, is a sign that they have some useful part to play in your story. Perhaps they have some information to give you or they can answer a question that will help you on your way.  Maybe by following them, you will find a hidden passage, or a hitherto unsuspected part of the level, and this can gain you valuable riches, points or experience.

So how does this relate to The Virtual Game?  Well in the widest sense, of course, every encounter is valuable, in that it provides experience; from the grumpy bus driver or the cheerful checkout assistant onwards.  However, there are certain individuals, just like those characters in the computer game with shiny things above their heads, who will have particular messages or significant experiences for us – people we would be wise to stop and talk to.

Since it’s a great deal more sophisticated than the games you play on your console, in The Virtual Game, these key characters don’t generally come with a helpful coloured blob hovering above their heads to enable us to recognise them.  Once you have read this section, though, you could begin to get seriously good at identifying them.

What a coincidence?

Look out for synchronicities.  At first sight, these may seem to be no more than strange or lucky chances, but trust me – they are far more than that.  We might not immediately spot the link but they are definitely meaningful; and they are important – always.  You have designed and planned The Game meticulously and, just as in the carefully scripted murder mystery story, there’s no such thing as a coincidence.

Here’s the way it could work:

You get chatting to someone, or are introduced by a mutual friend, and discover an ever-increasing set of things you have in common.  You find that you were born two streets away in the same town, that your mothers have the same birthday, that you both have a Springer spaniel and two goldfish – that type of thing.  These synchronicities act like a sort of mental sticky plaster and are strong enough to hold the two of you together; to keep you talking and interacting until you both get the information or experience that you need.  This can last from ten minutes to the rest of your lives, depending on how much experience there is to be had, or what form it takes.

There has been a huge amount of synchronicities turning up in my life over the last week or so.  I’m fascinated to see where they’ll lead me.

A Treasure Find

Had to share this. It made me smile – a lot !

Where is the Love?

This was a true gift to me. A friend of mine emailed this to me and I was grateful that I had someone who cared about me, who thinks about me enough to share something as beautiful as this short film with me.
I’d like to pay it forward and share it with you in the hopes that you watch it and it brings a Smile to your face =]

PS – I’d like to give you a challenge if i may.

Compliment one person today.

It could be anyone and in any way. But be honest with your words. And speak from your heart. Let someone know you love them, appreciate them, respect them and admire them. There’s no such thing as too much.

I love you.
I appreciate you.
I respect you.
I admire you.

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The Curse of the Question Mark

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Danny, despite his speech difficulties, has an interesting turn of phrase.  He’s just 10, and yesterday we had our first tutoring session of the new school year together.

“So what’s been going on in your life over the summer?” I asked.
“Dood stuff!” he announced, proudly. “I had my birthday, and I dot a digital damera and I’m detting a laptop soon!”

He must have noticed my raised eyebrows. I know his family’s financial situation isn’t great.
“The laptop’s from a jarity,” he explained. “I don’t know what ‘slexia is, but my mum wrote to them and they’re divving me a laptop so I can do my homewort.”
“Well that’s brilliant, Danny,” I enthused.  “Aren’t you a lucky boy!”

Lucky isn’t really the word that springs to mind when you first come across Danny.  The youngest in his year group, he does daily battle with all aspects of academic study at school.  Words appear to fly around the page and refuse to lodge in his memory; numbers resist all attempts to become bonded or otherwise related to one another.  Several speech sounds remain stubbornly inaccessible to him, despite years of therapy, and his tendency to writhe, fiddle, daydream or mumble his way through the interminable school day must have driven many a teacher to distraction.

Despite all this, Danny remains a cheerful child with a gift for optimism and humour.  He’s one of the many special young people who have so much to share with those of us who are willing to embrace different ways of learning and being.

“Do you really not know what dyslexia is, Danny?” I asked, despite my personal aversion to the term.  “Would you like me to explain it to you?”

‘Explain’ is one of his trigger words.  I should have remembered.

“No,” he replied hastily, “I thint I remember now.  It means I darn’t learn properly.”

Well that set off one of my own triggers!  I drew a quick cartoon brain.  I drew two dots and a straight line representing stimulus and response between two points in a neurotypical brain.  Then I drew the response to a stimulus in his brain – all manner of weird and wonderful connections firing off simultaneously and the resulting wavy synaptic line that connected them all in new and exciting ways.

“You learn DIFFERENTLY Dan,” I told him, as I traced the routes on my drawing with my finger, “and if the teacher wants a quick answer, that’s difficult for you.  On the other hand, if she wants an original answer – one that no one else would think of – then yours is the perfect brain for that.”

He looked slightly hopeful but sceptical.

Mario Kart DS Bundle

“What are you like at computer games?” I asked.
“Brilliant!” he grinned. “I’m the best in the family. I tan beat everyone.”

Several minutes of sound-effect laden role play followed as he demonstrated his prowess at Mario with an imaginary DS.

“I’m not surprised,” I told him.  “Your brain is perfect for that.  It can keep track of all the different things going on at once – the number of lives and energy levels, the route you need to take, dangerous enemies and obstacles…  All those bits of your brain that work at once can handle that far better than most ordinary people.”

Danny seemed happy with that, so we turned to some of the work I’d prepared – the gentlest of introductions to algebra, such as

9 + ? = 13   or  15 – ? = 10

Danny stared balefully at the page for a moment, then rose in his seat, peering down at it with great disdain.

“Dwestion Marts!” he announced with gravitas.  “My arch enemy!  I hate you, Dwestion Marts!  You never reveal what you are hiding!  Durse you to hell forever!”

And that’s the way it goes – a typical weekly session with Danny, the boy who can’t perhaps answer the question, but has penetrated to the heart of its intrinsic essence with a clarity the rest of us can only gasp at.

How utterly dull our world would be without the likes of Danny.

Even More Alternative Communication

Animation of a Foucault pendulum (showing the ...

Animation of a Foucault pendulum

The messages come from somewhere.  I can’t say where.  If I try to define their origins, I begin falling down quantum rabbit holes and end up where We Are All One in any case.  At that point, of course, the source doesn’t matter.

So I’m not going to try explaining who or what Koimul is.  I’ll just tell you that when I sit at my computer keyboard, relax to a point where I know I will receive responses to my questions, and hold a quartz pendulum over the mid point (between G and H), the pendulum moves to swing over different letters and then circles gently when a word is complete.  Sometimes I get random letters that make no sense, but about 90% of the time, I get sentences – clear coherent and eminently wise sentences.  The clarity and coherence don’t impress me that much any more (although they tend to freak observers out quite often) but the wisdom does, which is why I’m sharing it with you.

Some will say my own subconscious thoughts or intentions are controlling the pendulum.  I won’t argue.  If that’s the case, there’s a deep and wondrous knowing hidden within me that I’m proud to connect with.

Some will say I’m contacting someone who has passed over, as I did when I developed this 21st Century ouija board to speak to my friend Nina.  (if you missed my earlier posts about this, the link to the first of them is here.)   Again, I won’t object.  I’m just humbled that this being which calls itself Koimul is such a wise and patient contact.

There will be others who believe I am channelling a spirit guide.  I tend towards that explanation myself, for the simple reason that Koimul had ‘told’ me that is what he or she is.

So be as sceptical as you wish, or believe me totally.  I’m easy either way.  While my pendulum keeps swinging, I’ll keep writing down the messages.

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Here, so that you can judge for yourselves, is a recent discussion we had.  It has been slightly edited so that it will make sense to a wider readership.  Koimul has a rather strange turn of phrase sometimes, but I find it easy to tune in to the meaning behind the words if I read them through a few times, and I trust you will too.

I’d asked whether I had inadvertently caused pain to someone else.  Koimul not only answered my question but went on to explain ways in which we can heal other people’s pain.  The methods weren’t new to me, but the explanations as to how and why they work certainly were.

Koimul’s words are in large case, mine in small:

I  know that what I create is my reality.  Have I created his pain?

IF YOU IMAGINE HIM TO BE IN PAIN YOU CREATE THAT

Yes.  I get that.  But in his own reality he has experiences.  Yes?

YES

And is he experiencing pain?

YES

And if I ask whether my actions caused that pain, you’ll tell me that only he can create his own pain, I suppose.

HE BELIEVES OTHERS CAUSED IT  BUT THAT IS NOT POSSIBLE

What if I stick a knife in someone.  Surely then I will hurt that person – cause their pain?

NO  YOU CAUSE THE CUT

And what causes the pain?

THE CUT GIVES THE PERSON THE CHANCE TO CAUSE PAIN TO THEMSELVES

Oh.  In a weird way that makes sense, although it’s not the way we perceive it in our everyday lives.

JUDGE FROM SOUL PERSPECTIVE

So from a soul perspective, I can imagine him feeling happy and free of pain.  Or I can send him the intention of healing.  Do either of those affect his reality?

YES  BOTH DO      THE FIRST CAN BAKE INTO YOUR OVERVIEW AND SUPERIMPOSE ON HIS

This is some kind of quantum effect?

IT WILL OPERATE ON KIND OF ENTANGLEMENT

So we humans haven’t quite worked it out yet, but an effect something like quantum entanglement?

YES

Right.  And how about the healing?  How does that work?

YOU PROJECT THE IDEA THAT HIS DARE TO HEAL IS GAINING STRENGTH

Hmm.  I see.       Now what of a third option – sending love?

EASILY THE BEST

Because…?

OPENS YOUR HEART TO LINK TO HIS

Must his be open too?

YES  IT OPENS AUTOMATICALLY TO LOVE       REFLEX ACTION