Please, no more rubbish about times tables!

The human adult spine has 33 vertebrae, the bones that support the rest of the body.  The lumbar vertebrae, in the lower back, bear the weight of the upper body and are very flexible.  If you have lower back problems, it’s often your lumbar vertebrae that are struggling under the weight they have to bear.

Multiplication is a lumbar vertebra in the spinal column of mathematics.  Multiplication supports the weight of, amongst other things:

• place value (in any number system, any base, hugely important for computing, for instance)
• prime numbers (which are the building blocks of the entire set of natural numbers and therefore form the basis of internet security)
• fractions (so that’s all the rational numbers included now, terminating and recurring decimals)
• percentages (there’s where the uninitiated think the “useful” mathematics is)
• leading from the one above, all of proportionality and proportional relationships (that’s a huge amount of maths right there, a sort of blanket banner for the majority of school-level mathematics)
• area, perimeter and length (from the most basic, through Pythagoras’ Theorem and beyond)
• angles (from degrees in a full turn through trigonometry and other systems of angle measurement)
• pretty much all statistical analysis (I don’t really want to list it all, you can look up a snapshot in the National Curriculum or any other curriculum document if you don’t know the extent of this area)
• algebraic manipulation and the application of algebra to any of the above (hence leading into most advanced mathematics)

So, if your life takes you into any line of work or play where mathematics study is a prerequisite, then more than a good grasp of multiplication is kind of, well, essential.  Without it, a student cannot bear the weight of all the other maths and there will be a lot of pain!

Now we all understand that multiplication is really, really important to mathematics, let’s take a look at the issue people seem to take with multiplication.  Namely, the times tables.  My post is prompted by this today in the TES, but the same arguments do the rounds regularly.

Times tables don’t make students understand multiplication

This is not false.  It would be possible (yet rather bizarre) to simply learn a list of numbers in isolation with no understanding of what you were doing.  Fortunately, any good teacher will teach their students what multiplication is, what it means, its commutativity (2 x 3 = 3 x 2) and its inverse.  So, if a group of students doesn’t know that 5 x 7 and 7 x 5 have the same answer, then the teacher hasn’t spent enough time teaching that and needs to do it properly.  If a group of students doesn’t know that multiplication is repeated addition, or can be represented by a rectangular array,  or its relationship to division, then the teacher hasn’t spent enough time teaching that and needs to do it properly.

A Venn diagram (which itself is part of a whole area of maths that uses multiplication) to show that times tables and understanding of multiplication are not mutually exclusive.  Doing both is called maths teaching.

“I never learnt them by rote and I’m very successful in my xyz [mathematical] career”

There may well be a splattering of successful people who got where they did (mathematically) without knowing their tables, but I can assure you there are plenty, plenty more who knew them.  Even those who say they don’t know them do really.  Perhaps not at breakneck recall speed, but they do know them.  Knowing the tables frees brainpower to think about other things, like what to do with the factorised algebraic expression or why the two fractions are equivalent.

Here’s a novel idea, let’s no longer require any children to learn their times tables.  Let’s get them all to work out that 2 x 3 = 6 by adding, then doubling that (only by adding, remember) to find that 4 x 3 = 12, then tripling that (again only by adding) to find that 4 x 9 = 36.  That should work.  That won’t overload their brains when trying to simplify a fraction at all.

Or they could just learn that 4 x 9 = 36 and get on with thinking about the maths.

Learning the tables causes maths anxiety

It may well do, if done poorly and left to the varying efforts of students outside of school.  Alternatively, teachers can devote lesson time to it, regularly, and ensure that the knowledge of the tables becomes as second nature as other essential areas of learning, such as the alphabet, or decoding words.  This can be done through games, chants, songs, quizzing, online practice and drill, but it must be done.

I would contend that maths anxiety, where it may exist, is a complex thing, not least enhanced and perpetuated by the “I could never do maths” culture prevalent and almost fashionable amongst even the most successful of adults in this country.

The times tables are pointless outside school

I know, phones have calculators.  You probably won’t ever use your times tables while you’re shopping.  Most jobs don’t have an active knowledge of the tables as a daily requirement.  This is all true.  But maths isn’t about shopping any more than English is about texting.  If you’ve got this far and still have this objection, please go back and read my first few paragraphs.  If you don’t want to do that, here’s a summary of why times tables are important:

Times tables (+ understanding of multiplication) = Fluency in multiplication
⇒ Proper access to shedloads of really cool maths
⇒ Loads of brilliant maths knowledge accrued
⇒ Good maths qualifications gained
⇒ Proper access to shedloads of really cool jobs

Learn your times tables, kids.  It’s not a bad thing.