don't make your child multiply - primary mathematics instruction

If your school tells you to cram times-tables or fractions into your child, but they don't want to do that or don't enjoy doing that, don't make them multiply. If they don't enjoy the maths they are doing at school, don't try to force them to do it at home, that's only going to make them dislike it even more. Instead, play games with them, do things with numbers and shapes yourself, show them mathematics unrelated to anything they do in school, and give them fun maths books to read and videos to watch. I realise this is harder for most parents than my previous "don't make your child read" injunction, because fewer parents enjoy mathematics themselves than enjoy reading, but if you are maths-averse yourself think of this as an opportunity to learn something new alongside your children.

And perhaps this is easy for me to say, with a child who likes to amuse herself by drawing complete multipartite graphs or counting in base four. But what matters is not what she's doing, but that she's doing it for enjoyment, spontaneously. My primary goal in doing any mathematics with Helen is to have fun with her, and to communicate how exciting explorations of pattern and structure can be. (I've also avoided doing anything with her that will be covered in school, partly because they'll treat that ad nauseam, but also because there's so much exciting stuff that she won't ever encounter in school. So I doubt her "times tables" are any better than her peers'.)

But to return to the school. The mathematics instruction at Helen's school seems solid enough, but not nearly as inspiring as its literacy instruction. Mathematics is the only subject the school doesn't incorporate into its storytelling curriculum, and there's a clear contrast with literacy. While the literacy instruction includes skills such as phonics and handwriting, it also involves storytelling and writing and a lot of creativity. I'm not seeing the equivalent of those in the mathematics teaching, which seems almost entirely focused on the nuts and bolts.

I don't want to single out Helen's school here, as I suspect this is a general problem with primary teaching. Most primary schools have some teachers who are passionate about children's literature and many who read for pleasure themselves, but far fewer who have any kind of active involvement with mathematics, or a passion for it. As with literacy, schools are constrained by the national curriculum, and by a mathematics testing regime that only covers a narrow range of procedural skills. As well as the Key Stage 2 SATs in Year 6, Helen's year is facing a new Year 4 times tables speed test. (I'm not arguing that the curriculum material doesn't matter, but, as with literacy, teaching that shouldn't preclude attempting to inspire the children as well, or giving them a broader view of the subject. For more on this, see my reviews of Craig Barton's How I Wish I'd Taught Maths and Tom Garry's Mastery in Primary Mathematics)

So, what do I recommend? I wrote a bit about this three and a half years ago, but here's an update on that.

Games and Puzzles

These don't necessarily have to be directly mathematical: almost any game involves some kind of logic — at least an implicit "game theory" of some kind — and many involve spatial intuition, memory, and so forth.

Helen plays a broad range of board and card games with us at home, has a range of puzzles of various kinds, and has a tablet with a variety of mathematical games and puzzles on it. Many of her friends are similarly resourced, but not all children are, so access to these kinds of games and puzzles is something schools could help provide. (I wonder if we can get the folks from Thirsty Meeples to run a school workshop?)

See my post "apps and games" for some specific suggestions.

Explore different areas of mathematics and tell stories about them

It could be argued that the arithmetic done in primary schools isn't actually mathematics at all, but it's certainly only a tiny part of it. Explore topology, number theory, geometry, combinatorics and graph theory as well. Kids love big numbers, so try explaining Graham's Number to them, or the countability of the rationals and Cantor diagonalisation.

Talk about the history of the discipline and about famous mathematicians. Give them some historical background on the arithmetic they're learning. Tell them how Archimedes died, Cantor went mad, and Russell and Whitehead took an entire volume of Principia Mathematica to show that 1+1=2. Get them to try imagining living out of a suitcase like Erdős and wanting to do mathematics every waking moment, or to wonder at how mathematics brought Ramanujan and Hardy together. And everyone knows about Marie Curie and Rosalind Franklin, but what about Emmy Noether and Maryam Mirzakhani?

Introduce some famous problems and results; make it clear that mathematics is a live subject, with plenty of unsolved problems. Can six year olds understand the four-colour theorem? Sure. Can ten year olds understand the Goldbach Conjecture? Show them things like that! No one finishes primary school thinking there are no stories left to tell or books to write, or nothing new about the natural world to discover, but I suspect a good number of eleven year olds think mathematics is a done deal.

All of this is hard for adults without a mathematics background to do, and while there are plenty of popular maths books aimed at adults or older children, there's not much for younger children (certainly far fewer than there are for biology). So this is something primary schools should cover, though they too might have to rely on specialist support. Helen's school has a writer as a "reading patron" — perhaps they could find a mathematician to be a "mathematics patron".

Books and Videos

This is a fairly random selection, just a few things I've read or watched and enjoyed. I actually don't know much about this myself, as I hardly ever watch videos and mostly find stuff for Helen by excerpting or simplifying my own reading.

Books for teachers or parents:

• A Mathematician's Lament (Paul Lockhart) - the book has some extra material, but the key bit is an essay available online
• Arithmetic (Paul Lockhart) - this covers similar material to the primary school curriculum, but from the perspective of a mathematician and with the goal of having fun
• Maths Recess (Sunil Singh + Christopher Brownell) - a plea for a different way of doing things

Books for children:

• Which One Doesn't Belong? (Christopher Danielson) - along with his How Many?, this is usable with children from almost any age
• The Number Devil (Hans Magnus Enzensberger) - Helen hasn't done all the mathematics in this, but she's reading it for the third time now
• This Is Not A Maths Book (Anna Weltman) - an maths art activity book

Videos:

• the Numberphile channel on YouTube has a wealth of stuff. Some of it is too advanced for primary age children, but try The Scientific Way to Cut a Cake for an easy start
• Vi Hart has some great videos, including the Hexaflexagon ones
• the Global Math Project has a collection of "Random Acts of Mathematical Delight"
• Wild Maths - online games as well as videos

With both books and videos, I would avoid anything that describes itself as "supporting Key Stage N" mathematics (or even mentions the national curriculum) - it's likely to be just covering the same stuff school is already doing (the equivalent of graded readers for literacy.)