Earlier this term, I sat next to Simon*, a Year 9 student, while he worked on a non-calculator GCSE foundation paper.
My job was to make an initial assessment on his attainment, and I was impressed with his positive attitude, logical reasoning and general competence in answering most of the questions.
I was, however, struck by the fact that he was unable to recall multiplication tables.
One question asked him to calculate the area of a rectangle with a width of 6 centimetres and a length of 8 centimetres. He knew what he needed to do, but after a few minutes of struggling to calculate it mentally, he made use of pen and paper. He wrote 6+6+6+6+6+6+6+6 in a column and then proceeded to add the numbers.
Eventually, he tentatively produced the correct answer of 48. Later on, I asked Simon if his classmates knew their multiplication tables. He said around half didn’t.
Although I’d seen students of various ages and abilities struggle to multiply numbers without a calculator in the past, I’d never given much thought about how common this is in our secondary classrooms until then.
Wondering how widespread the issue was, I turned to education research. While there’s very little on secondary students, in particular, there is some data available about parents.
The results of a YouGov survey into parents’ recall of number facts revealed that 52 per cent of parents and guardians of school-aged children (under 18 years old) across Britain don’t know their times tables “perfectly”.
The culture shift in primary maths
Why is this? It’s hard to say for sure, but I think it can be traced back to a gradual shift in culture that began with the introduction of the national numeracy strategy (NNS) in 1999.
A central emphasis of NNS was to improve mental maths, and a crucial element of this was the introduction of the “daily mathematics lesson” (DML) with its mandatory requirement for every maths lesson to open with a 10-15 minute mental maths starter.
A mental maths paper was incorporated into national tests, giving teachers a further incentive to improve pupils’ mental maths.
And then, in 2011, everything changed. The NNS was abandoned, the DML ditched. In 2015, the mental maths paper was withdrawn.
Today, knowing tables up to 12 x 12 is included in the national curriculum, but the teaching of mental maths hardly features at all.
There is much that primary maths teachers have to prioritise and evidence, so it’s hardly surprising that multiplication tables have slipped down the list without firm direction from the government.
And yet, I’d argue that number recall is absolutely imperative if we want key stage 3 and key stage 4 students to be confident mathematicians, and go on to be successful in their exams.
More teaching and learning:
Questions that ask students to calculate things such as income from wages rely on number fact recall, as do short and long multiplication questions, finding the lowest common multiple or highest common factor of a number and, to a lesser extent, questions involving area and volume.
If students respond to such questions with the use of repeated addition, they pay a heavy price both in terms of risk of error, and inefficient use of time.
Time to plug the gaps in knowledge
Secondary teachers, then, do need to make time to plug these gaps in knowledge. So, how can we do this?
To begin with, we need to assess the number-fact recall of the students. The students who regularly use the “counting-on” method in their written work should already have been identified by the teacher. An assessment of each member of the class can also be achieved by asking oral questions involving multiplication tables. The students who do not have rapid number-fact recall would then be identified.
Then, we need to devise a teaching programme to address the needs of the students that had been identified.
At the outset, the students could be encouraged to memorise tables up to 10 x 10. A particular table could be set for homework, with the initial questions exclusively from that table being posed at the next mental maths session.
Additionally, you could spend a few minutes at the start of each lesson asking students to find the product of two single-digit numbers without having to resort to the cumbersome counting-on strategy.
This could commence with asking the students to retain a single number fact, for example, that 7 x 7 = 49. As this is near the middle of the table, knowledge of this fact would facilitate answering questions such as 7 x 6 and 7 x 8 by counting back or forward from 49.
Another device involves the 9 times table: students could multiply by 10, by placing a zero after the last digit, and then subtract the original number.
For example: 9 x 7: 10 x 7 = 70; 70 - 7 = 63.
Mark Pepper is a retired maths teacher and lecturer. He is a regular contributor to the Mathematical Association publication Equals On-Line
