Why Technology Cannot Entirely Replace Times Tables

The other day I was listening to a high ranking technologist asking why 7-8 year old children were expected to learn times tables by rote. From what I hear most of his audience disagreed with him. His argument was that everyone carries technology now that allows them to do multiplication, so why should anyone bother to learn to do it in their head or on a piece of paper. He argued that only people who needed this skill should learn it later as young adults. Perhaps I am old fashioned, but my mobile phone nor the camera I habitually carry has the ability to multiply. However, with the majority of even 5-year old children now carrying mobiles, many of which are smartphones, one could see his point. Yet, he has utterly missed other significant elements about why it is so important to have these basic skills. Just because they can be done by a machine does not mean that they should.

I have worked in warehouses and was able to unload pallets of boxes quickly because I knew precisely how many boxes there were on a pallet. The number on pallets varied depending on the size of the box and the heaviness of the contents and if a box or two was missing. However, I would stand there as see a pallet with five boxes down each side and stacked five high and know that there were 125 on it. If the next pallet was stacked four high, it had 100 and so on.  I knew that a stack with 5 x 5 x 5 boxes had more in it that one which was 4 x 5 x 6 boxes despite how it might appear on first impressions ('but it's stacked higher!').  Of course, there was not an infinite variety and you tended to get set quantities but my mental arithmetic was there to work out if anomalies came up. I could also work out on a piece of cardboard with a pen how much I would earn if I did overtime and how much tax I would pay on that. Yes, I could have pulled out a phone and typed in the numbers, but you try operating even a large mobile phone while wearing working gloves.

Anyone who is a parent of school aged children will know that multiplication has changed. When the boy who used to live in my house started primary school his mother and anyone else in earshot was told not to help him with multiplication because we would do it 'wrongly'. Parents were pointed to a government website to show them the right way. The method now used is 'repeated adding'. In other words if you want to work out 4 x 3, you add up 3+3+3+3. This might be fine when you are doing basic sums, but once you reach 12 times something let alone 20 times something, then you begin to see its drawbacks. The said boy is now in Year 8, i.e. 12+ and has to do the square root of decimal numbers. Try doing that with the 'repeated adding' approach! I had to teach him long multiplication because the teachers had left him without the mental equipment to do the sums. At this stage he is not supposed to use a calculator, but I imagine most children do. The thing is, mathematics is compulsory for children up to Year 11, i.e. 16, so if he does not have the tools to deal with the sums in this year, how is he going to do it over the next three?

Like the speaker, you might argue, well it is no problem, the boy simply types it into the calculator. However, you need to know what to put into the calculator. The square root of a decimal number is always larger than the number itself. However, if you have no idea of the multiplication of fractions or decimals, you are going to struggle to know what to put in. Such calculations need a lot of estimation so if you cannot get into the 'ballpark' of the answer, you are going to spend a long time with guessing. The child is a quarter of my age but saddled with the repeated adding approach I can constantly beat him in how quickly I can calculate. It should be the other way around. You need some grasp of the mathematical concepts behind the calculations you want to make otherwise you cannot be certain if you are entering the correct data. How do you know what numbers to put in for calculating the area of a circle, which you may have to do when, for example, siting a toilet or a dustbin, if you do know that the formula is πr2 (i.e. r x r; I cannot show a superscript for squared on this system).
I use mental arithmetic on a daily basis, even without thinking.  Most often this is when I am driving.  Yes, I could switch on the sat nav and have it tell me my journey time, but on the daily commute this seems pointless.  Thus, constantly I am seeing my speed and working out how much time is left given the distance.  I also work out if I have time to stop for petrol - how much that will reduce my average speed and my overall journey time.  I might also consider an alternate route and how the extra distance has to balance against the speed I am doing on the current route - something too few people balance up hence speeding through 'rat runs' when they realise the 'short cuts' are not actually saving them time.  Maybe I think about my driving too much, but among the millions of motorists I cannot be alone.  I would feel pretty powerless if I did not have a grasp of time, distance and speed as I travelled along.

Thinking more broadly, the speaker may have lauded the internet for providing what everyone needs to know.  That may be the case in his subject area, however it is not in mine.  Despite common assumptions, the amount of information on the internet on many subjects is very limited and very repetitive.  I have written on numerous occasions about the boundaries of the internet when it comes to historical knowledge.  You can soon end up reading exactly the same information again and again, with nothing new being added, even if you have the ability to hop over to websites in other languages.  Wikipedia's encouragement of using translations to flesh out entries, simply adds to that as it is the source of so much material that is used by other websites.  You also run up quickly against bias whether political, racial or religious.  I have spoken about how comment on Muslim universities in Europe has been purged and the Wikipedia entry on universities spends more time in ruling Muslim and Orthodox Christian institutions out of the definition than it does actually speaking about what a university is.  Another example, everything on Mormons appears to have been edited by pro-Mormon writers, especially playing down the hostility to polygamy in the USA of the mid-19th century and especially the number of pioneers killed by Mormon forces.  This happens so much, that actually it made me more suspicious of the Mormons than I would otherwise have been.

The internet is far from perfect.  A lot of the information on it is erroneous and shaped by people with an agenda which has little to do with putting up objective facts.  It is a hostile environment.  I have spoken before how even reviews of a First World War poem attracted more ill-informed commentary that wrecked any chance of an interesting or informative discussion about it; drawing parallels to any other conflict was ruled out and it was even questioned whether it was a First World War poem given that it had been written after the war.  The danger of errors creeping into computerised teaching systems was parodied as early as 1967 in the television series 'The Prisoner' which featured such a system called Speed Learn, but which included an error about historical dates.  Too often the internet, primarily Wikipedia has become the 'right' answer even when it is actually wrong.  It would be wrong to see the internet as decreasing human knowledge, that is not at all the case, but what it does accentuate is populist views and often particular groups' agendas, over broader discovery of knowledge.  If a time comes when it cannot be countered by other sources, then there could be argued to be a decline in knowledge.

There are practical reasons why it is a mistake to promote an over-dependence on electronic devices.  As you will have witnessed yourself, many people go to pieces when they have their mobile phone stolen or lost.  They have no idea where they should be or what they should be doing; most importantly, especially for young people, they have no idea what they should be thinking.  You will see everywhere 'phubbing', i.e. two or more people sitting or walking together and yet not talking, rather all their discussions are going on with other people not present via their phones.  To deprive them of their phones is like snatching their souls away; literally you will see them with as much distress as if a favoured pet had been lost not a machine.  Despite such dependence, in recent weeks it has been highlighted how short battery life is becoming for smartphones.  With connectivity constantly on and so many apps running, the average life is a single working day, whereas a few years ago you could expect a phone to run for a week between charges.  I imagine in time battery life will increase but at present the number of things you 'have to' be doing via your phone is increasing faster than the power storage necessary to permit that.  How can you guarantee that the moment you need to do some multiplication your battery will not be dead?

The final reason why I would argue it is foolish to simply allow people to use machines to do their multiplications for them, is because the brain needs exercise.  Constantly we are advised that to avoid the onset of Alzheimer's people need to keep working at mental challenges.  As with the rest of the body, the brain can become 'flabby' if it is not exercised.  To rely on a machine to do calculations which should be typically part of every day business, certainly if simply going shopping or how many potatoes each person in your family should get or whether you need to buy toilet roll before the weekend or will run out of petrol before you get to work or will get a better deal on one mobile phone tariff compared to another.  Yes, we do have machines that can do times tables, but as with learning about personal hygiene, manners, eating well and exercise, these are things we need to instill into children otherwise they and society will suffer as a result.