I don’t know how my daughters’ mathematical abilities compare to other children their age. I’m simply not interested in comparisons because I know ‘the norm’ is arbitrary. There are children who far exceed what is expected of them in school curricula at this age and others for whom the curriculum is far beyond their current capabilities. I’ve written about this before here.
Like all home educated children, Lily’s and Katie’s education is more patchy than that of formally educated children. They know lots about some things and not so much about others.
Lately I’ve been thinking about maths, and the varied ways the girls are developing their mathematical abilities. We use a combination of methods to encourage the girls to become familiar with and to enjoy playing with numbers. Some of our methods are planned, others happen in a more random and arbitrary manner.
In the past few months Lily has got her head around hundreds, tens and units; she can add two digit numbers with ease and subtract two digit numbers with some difficulty. Katie can write her numbers; she recognises and can explain the differences between basic geometric shapes; and she can count to twenty.
We use some more traditional approaches – some great maths workbooks we picked up in Portugal that Julian and I translate page by page into English as we go along, and maths copybooks where we set problems to be solved. But these are only the beginning of our adventures in maths.
The internet is a wonderful resource. Julian has found some great maths games online and we’ve noticed that Lily’s ability to add numbers in her head has increased dramatically since starting to play these games (example games). They also both love to watch episodes of the CBeebies programme Numberjacks on YouTube. Only this morning they watched an episode about square numbers. When the episode ended Julian saw an opportunity to further develop the concept using Lego and Lily was able to make a tangible physical model of some square numbers.
I don’t bake with the girls as often as I should, but when I do I am conscious of the mathematical learning possibilities it presents us with. I always get Lily to read the recipe, and to read the weight displayed on our digital scales as I add ingredients to the bowl. Last weekend when we baked I even tried some subtraction (‘Right, I’ve got 100g of flour in the bowl. How many more grams do I need to add until I have 150g?). And while Lily’s helping with the reading and the scales, I might get Katie to work out how many fairy cake cases we need, or if we only have enough icing sugar to ice half the fairy cakes, how many will that be. They are unaware that they are learning maths. Instead they are contemplating the bowl and spoon licking opportunities that await them when the cakes go in the oven!
To get them comfortable with recognising numbers we have often played the game of asking them to tell us house numbers or car registration numbers as we walk down the street. And we play board games such as Home Run that involve the use of dice, counting, number recognition and simple addition and subtraction.
Colouring pencils, felt tips, clothes pegs, books, clothes, dolls and teddies – pretty much everything aboard Carina has the potential to be turned into an adding, subtracting, multiplying or dividing activity.
Besides these mathematical activities and games, they are also exposed to Julian and I regularly discussing money – budgeting, working out our finances, discussing the weekly shopping (see Julian’s golden chicken rules!). Through these conversations they learn about the applications of maths to ordinary everyday life.
Perhaps no other way of life is as obviously mathematical as sailing. Navigation involves working out distances, tide heights, tidal streams, wind speeds and directions, and boat speed. We have to play around with various combinations of these to work out the appropriate depth of anchorage, how much chain to put out, what course to steer, optimum arrival and departure times, and when to not even bother trying to go anywhere. In a gentle way, they are starting to think about the mathematics of sailing. Looking at a map of Europe, we discuss how long it has taken us to get from Plymouth to Aguadulce, and the distance between the places we have been, and we talk about where other sailing families have gone, and how long it will take them to reach their destinations in the Caribbean or the Canaries.
As time goes on, I hope they will develop an interest in navigation, and will have fun with the mathematical possibilities of it.
For probably the first time in my life, I’m having fun with maths. I’m relearning concepts alongside Lily and Katie. I’m thinking about numbers in a whole new way, I’m learning that problems can be solved in multiple ways and not just by the single rote method that was drummed into me at school. I hated maths as a kid and didn’t understand the point of it. I remember crying over my maths homework and teachers shaking their heads at my inability to grasp seemingly simple concepts. Rediscovering the wonders of mathematics alongside Lily and Katie is giving me a second chance to fall in love with numbers.
(PS..an article on unschooling that I published in Life Learning magazine in September can be viewed here).