With number fact knowledge (times tables and number bonds) forming the foundation of numerically confident children, it's pertinent to know what are the hardest time's tables before we can move on to think about how to learn them.

Do we really know how often children get times tables questions wrong? And which ones they find hard? And if we do know that, why is it? And how can we adopt better teaching practices to make number fact knowledge easier to acquire?

At Flurrish this is something we have actually undertaken, working with the staff and children at Caddington Village School. Over a 2 week period a total of 60,000 questions were logged from 232 children in years 5-8 (age 7-13) using our intuitive smartphone/tablet app (none of whom had used it before). 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 the time they took) were then returned to the central server.

We took all the individual results and graphed the number of right/wrong answers for each question (see right); the 45 degree line shows where the multiplier and factor flip (and you might expect the error rate to be mirrored either side of the line; it isn't and that's a whole new project in itself!).

Some interesting points are worth noting:

  • Overall Error Rate: 20% of questions were answered incorrectly. A worring result for accessing higher level mathematics.
  • Hardest individual question: 6x8 is the hardest (wrong 63% of the time); closely followed by 8x6, then 11x12, 12x8 and 8x12.
  • Hardest table: the 12s are the hardest individual table - wrong over 30% of the time.
  • Boys and Girls: much higher error rates amongst boys (32% boys and 22% girls), although they answer the questions faster!

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 that we don't know what our children don't know. Until we have this baseline information on our pupils then it isn't difficult to target intervention and so improve learning.

What to know more about this study? Read our paper "Why is 48 so hard to remember?" in Mathematics Teaching.