What is the hardest times table question??

What's your favourite times table? "Eight times eight equals sixty four." Chant it, take yourself back to that sun-bathed classroom, those hazy days before the summer holidays, warm milk from a small bottle, piercing the silver top with a straw..... That's how I learnt times tables and how in many classrooms today tradition carries on. And for me the number 64 just feels nice, rounded, well mannered. What don't I like? Nine times six equals fifty four.... that's just strange, jaggedy, unpleasant. Definitely a "sticky" one for me and one that I have to work at to remember.

What's the point of this trip down memory lane? Well if children are memorising times tables today, which ones are harder to remember? Do we *really* know what kids find hard and easy? And if we do know that, why is it? What are the actual cognitive processes taking place (in the brain, in memory) that cause this? Well, we need to know the first question before we can even proceed to a deeper level of understanding.

And at Flurrish this is something we have actually done! Working with the staff and children at Caddington Village School we logged a total of 60,000 questions across 232 children in years 5-8 using our intuitive smartphone/tablet app. Each child logged in to a centralised server using a fast graphical routine (no tricky passwords!) and played games that were batches of 20 random questions across the 12 times tables. - all the answers (and they time they took) were then returned to the server.

We took all the individual results and graphed the number of right/wrong answers for each question - shown below; the 45 degree line plotted so you can see where the multiplier and factor flip (and you might expect the error rate to be mirrored either side of the line; it doesn't and that's a project in itself!). Some interesting patterns show up, notably that 6x8 is the hardest (wrong 63% of the time); closely followed by 8x6, then 11x12, 12x8 and 8x12. The 12s are the hardest individual table - wrong over 30% of the time.

These have profound implications for what we teach children and therefore *how* we teach them.... perhaps the single most important message to take away is we don't know what our children don't know.

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