I’ve been thinking, reading and listening to a lot of things about maths lately….and maybe as a consequence, or maybe it’s a chicken-egg thing, I’ve been seeing a lot of maths in Kai’s life, too.
But i’ll get to that later.
Firstly, I was thinking about maths ‘readiness’. You see SO MUCH about reading readiness, and even the schools are finally starting to realise that kids all learn to read differently, and at different ages, but you don’t see a lot about maths readiness.
I was thinking about it because, suddenly, number ‘literacy’ seems to have twigged for Kai. At nearly 10. Calculations that would have stumped him only a few months ago, he can do quickly in his head. Complex addition, subtraction, money…he’s even figuring out telling the time, down to how many minutes to x’oclock, etc.
In lots of ways, it mirrors how he learnt to read. But the numbers thing has come later…about 18 months later, to be exact.
Like reading, it wasn’t the linear progression that schools make-believe happens…it was sudden, and it was all areas of understanding. He went from not being able to do simple calculations, to doing complex one’s in a matter of months. All of which suggests, to me, that number literacy is like letter/word literacy – you can’t do it until your brain is ready – and when it is, it happens naturally and painlessly.
For someone who found school maths absolutely impossible to comprehend, this comes as something of a kick in the butt! All those years spent struggling when actually it’s likely my brain just wasn’t number literate until later than many kids. Which also explains why, when I went back to Uni at 25, maths was easy and fun!
In the meantime though, after I left school at 16 (I failed my maths GCSE, for the record!), I was using maths ‘in the wild’…I really love this term, and I’ve heard and read it a lot lately! I think Joyce maybe coined it? I saw her writing at this awesome page on math where she mentions it…But Pam Sorooshian also said it in a recent podcast I listened to. Anyway, whoever it was who first used it, it wasn’t me. But I’m going to use it now, all the time!
Back to my meanderings as an older teenager and in my early twenties. At 16 I was working in a typing pool in an office, typing share certificates (yes. I’m *that* old!). We had to tally everything up at the end of a round of certificates. My boss said I had a ‘head for numbers’. This was news to me…and all my maths teachers!
After that, I worked at the RSPCA. I looked after dogs that had been mistreated, often starved. As part of court cases against owners, I logged how much weight they gained each week. I weighed them, subtracted my weight from theirs (I picked them up to stand on the scales!) and converted pounds to kilo’s. If that’s not wild maths, I don’t know what is!
Then, I travelled around the world for 6 years. I negotiated time tables for buses, trains and planes. I converted money from one currency to another (back then, in Europe, that was a LOT of conversion!). I managed my finances, bought food, paid for rooms. I worked in bars adding drink totals in my head. Wild. Maths.
And when I went back to college to do the course that allowed me to go to Uni as a mature age student, at 25 – I whizzed through the basic maths. And was soon enjoying (yes, you read that right!) algebra and differential equations! In first year Uni I also loved statistics! The wild maths I’d been doing, and the fact that my brain was now ready to be number literate, made all the difference in the world!
So. On to Kai and unschooling and how he’s learning maths in the wild. I’ve seen a bunch of graphics showing how kids learn maths through unschooling, like the one’s Sue Patterson has at Unschooling Mom2Mom (scroll down for it, but the whole page has great resources, too!).
But I thought i’d try something different – a side-by-side comparison. ‘School’ (or ‘caged’?!) maths beside ‘Wild’ maths. I picked school maths examples from Grade 4, as that’s what grade he’d be in (I know this because his cousin is the same age and goes to school :p ).
The examples are all from Kai’s actual life – he plays a lot of video games, so a lot of our examples will come from gaming, but i’ll try and think of some others too (in case you don’t have a gamer….erm…I’m sure there must be kids that don’t like gaming?! Right!? Yeah, nah…doubt it!).So. Let’s begin with addition and subtraction – caged vs wild.
Addition and Subtraction
Now, I have taken steps to make sure to also include school maths that is, in essence, trying to masquerade as wild maths – like the Minecraft worksheet in this example. But guess what – actual Minecraft is addition and subtraction too, for real reasons! And dice/money games like monopoly, Pokemon game cards (or any cards with stats and powers on them), stat pages for games like ARK: Survival Evolved…and even a bit of actual schooly looking maths in Naruto!
Multiplication and Division
Yep. I have an App in the school side. It’s an app we used to have (eek!!), even ‘fun’ looking apps aren’t wild maths though. And they aren’t really fun, either! So – wild math – yep, we divide up chocolate blocks ALL the time! In order to build symmetrical buildings (well, any building or structure, really!) in Minecraft you need to use multiplication and division. We love playing Yahtzee and that uses multiplication all the time…In order to build enclosures, feed animals, and balance the books, Zoo Tycoon uses heaps of multiplication and division.
Measuring and Weighing
Like really – why would you measure a jug on a worksheet when you need milk to make waffles in your real actual life!? The Cave Bear example is (as are all of these) real examples from Kai’s actual real life lately. He watched a few YouTube doco’s on Cave Bears, and the comparison size between a cave bear and a grizzly (including that it’s skull is 2 x bigger – also multiplication!). We use the geocaching app, which tells you distance to the cache, weighing and measuring in the kitchen, measuring our caterpillar to see how it fast it grew, and measuring a koala skull we found to try and determine if it was male or female (we think male, for the record!).
What about maths that seems more complex? More advanced? Like those pesky percentages that plagued me as a school girl (that’s a neat alliteration…just as an aside!). Turns out fractions and percentages are WAY more fun on the wild side! Pizza anyone!?
Fractions and Percentages
I included the ‘school’ example on the bottom left, as I thought it related to Zoo Tycoon on the right. The exercise on the left is just that – meaningless work making a grid into different habitat types. In Zoo Tycoon, you do that (choose the percent types of cover/vegetation) but it costs different amounts of money, and helps keep your animals alive! Way more interesting!
Most video game stats charts are full of percentages, fractions and decimals – like the one’s in ARK. And seriously- what kid hasn’t watched their game load or checked the percentage uploaded on an app, on Steam…almost everywhere! Oh, and the cute dragon in the top, it makes you 1,963 coins/1 hour!
What about geometry, map reading and coordinates? Well…we *actually* do a lot of that wild math in the wild….geocaching and hiking!
Mapping, grids and coordinates
Nearly every video game Kai plays has a map. That one at the top left on the ‘wild’ side is from ARK, but Zoo Tycoon, Wizard 101, Dragon game apps, every game I can think of, has a map! In Minecraft, you can install a Mod called REI’s Minimap that lets you plot home coordinates…Battleships is all coordinates (and strategy!), Geocaching is coordinates and map reading. And let’s not forget Google Maps! Kai is my primary map reader in the car these days!
Moving right along….Telling the time, estimating time, converting time. Wild time isn’t like school time – for one thing, it doesn’t go excruciatingly slow (haha!) – and analog clocks are likely to be the very last way an unschooled kids learns to tell time.
Telling time is something I stressed about somewhat, since Kai only just recently learnt to tell the time at all. But since it *just* happened, the how’s are something fresh in my mind. Mostly the how was YouTube! Watching YouTube videos – if we are going out, i’d say ‘How much of your video is left?’ – YouTube handily lets you know that in a fraction/proportion format at the bottom of the player. Many games make you wait until your creature matures, or egg hatches, and it gives you a count-down..We skype with friends all over the world, but mostly Canada, so Kai has a good idea about differences in times across the world (also the UK, for my family). You can change the time in some games, like Minecraft, which can help you do stuff….and finally…the computer has a clock on it ALL the time!
And lastly – I made a kind of general category for *other* mathematical concepts and mathematical thinking…including algebra, patterns, probability and chance, and more…
Probability, Patterns, Algebra etc…
Jigsaws, chance games like Uno and Backgammon, card games, geometry/pattern games like Blokus, strategy games like Chess….all awesome fun things that, as a side effect, build mathematical thinking and algebraic reasoning skills…In the middle, crossing the line, I’ve put the App Dragon Box. We like it here, I like it more than Kai, though. But we’ve deschooled for a looong time. It might be too schooly for newbies who haven’t deschooled….which is why I have it straddling the two sides… it’s a fun game, if you can see it only as a fun game ;)
So. That’s it. Hopefully the graphics illustrate what I wanted them to – that schooly math is dull, uni-dimensional, not related to real life and arbitrary. Wild math is ,well, Wild! It’s inside, outside, dice, computer games, cards, jigsaws and more….it relates to your real life, and helps you get stuff you want – like cookies, dragons, pizza, geocaches and road trips!