Rote learning gets a bad press. The term is associated with good old-fashioned chalk-and-talk teaching methodologies… “Sit down and shut up! Open your books at page 359 and complete questions 1 to 59 before the bell…” But as any teacher knows, it remains the best way to learn a lot of what we need to make us good at maths.Fortunately, times have changed, and technology has opened up new ways to teach by rote. Here are some of the techniques we employ in our tuition centre, and within our app, to liven things up:

- Introduce a time constraint on a question: “You have five seconds to answer each of these questions before you get it wrong…” (useful in forcing children to guess – not always a bad thing when it comes to learning facts by heart!)
- Introduce a time constraint on an exercise: “How many of these times-tables can you do in one minute?”
- Compete – against others, either in the classroom or across the globe on tutpup.com or similar
- Compete against last week’s score. Children almost always improve their score, and this spurs them on more.
- Instant feedback. Rote learning is deathly if nothing’s marked until the end of the lesson – and then it’s all wrong. IT allows children to see instantly if they are on the right track.
- Muscle memory: remember this can play an important part in learning some tasks by rote. For example, it is vital when completing sums by column addition to always show working (this is the purpose of the overlay on these questions in DoodleMaths). The brain remembers the sequence of muscle movements as much as the principle itself.
- Set the bar at the right height: in other words, ensure the balance of success/challenge is correct for the individual.

Here are some areas of Key Stage 2 maths that lend themselves well to such techniques:

- Doubles and halves
- Number bonds to 10, 20, 100 and number facts up to 10 and 20
- Times Tables (leading to associated division facts)
- Column addition, subtraction, multiplication and division
- Naming shapes and solids
- Units for measurement
- Adding and subtracting 9, 19, 99 etc.
- Compass points
- Decimal and fractional bonds to 1
- Calculating the fraction of a quantity
- Fraction/decimal equivalents

This is the tip of the iceberg. But what are we doing when we learn these things by rote? Simple: we are committing a mathematical fact to our long-term memory. Storing facts in our long-term memory frees up our working memory to perform more complex calculations. For example, 80 – (4 x 7) becomes a lot easier if you know 4 x 7 = 28 as a fact immediately.

I’m not saying all maths needs to be learned in a rote fashion. There are equally plenty of areas of maths where a deeper conceptual understanding is required. But most of the children that we meet find maths difficult because they are frustrated by their lack of knowledge, rather than their lack of understanding.

Reblogged this on DoodleMaths.

Reblogged this on Kip McGrath Bath: Our Tutoring Blog.

I completely agree that muscle memory and practice are essential to retaining basic maths skills. In my classroom, we do times tables practice for 3 minutes a day and after 6 months the difference in recall speed is amazing (this is with year 7s and up). I give them all a rock name and play rock music while they time themselves completing 60 questions. Then at the end of the week, I take their scores and times in and turn it into a Top 40 Countdown which I put up on a website for them to see.

It’s now all online (the answering questions part) which they love, especially as it has a live multiplayer element and a place to create a rock avatar. It makes it easier for me to set different pupils different times tables to work on too.

Times Tables Rock Stars …let me know what you think.

I’m joining this one rather late, however, I have to say that the children who are weakest at maths in my class are the ones who have been pushed into rote learning before understanding. This can be seen in times tables where they simply have not been given the time to understand that multiplication is repeated addition. This leads to them learning incorrect skip counting and rote learning because there is no understanding to back up the sounds they are making. I teach years 2, 3 and 4 together and I do not start rote learning of times tables until year 3 usually. I find that the children who have worked out the skip counting patterns using beads or dienes aparatus for a year are the ones who securely and quickly learn all12 times tables in a year. The ones whose parents have forced the rote learning down their throats before they are developmentally ready are he ones who struggle and are still rote learning in y4.

Thanks for your comments, and I totally agree with everything you’ve written. It doesn’t apply just to maths, either – I frequently encounter children who get 10/10 in their spellings every week but cannot remember how to spell the same words a few days later, or apply it to their writing, because they lack a basic understanding of phonics and word structure.

To emphasise this, here’s the kind of calculation that a year 4 might encounter:

100 – (4 x 7) = __

A child who has learnt his 4x tables and bonds to 100 by heart will find this easy: they will ‘see’ 4×7 as 28, and then they will see 100-28 as 72. They’ve barely used their working memory at all, and completed the question accurately in seconds.

However, a child who is still skip counting tables will need to accurately skip-count seven 4s, holding their answer in their head, before (at best) remembering to partition 28 into 20 and 8 to do the subtraction. The strain on the working memory is considerable, particularly for a child who is already low in confidence in maths. The question takes much longer to answer, and the ‘hit’ of getting a right answer is delayed.

But as you say, there’s no point embarking on the rote learning of anything until the underlying principles, in this case of the four operations, are fully understood.