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Calculators to be banned from Primary Schools?

Discussion in 'Mathematics' started by DM, Nov 29, 2011.

  1. DM

    DM New commenter

    Tomorrow afternoon there will be a debate on the use of calculators in Primary Schools. Elizabeth Truss M.P. is fronting a campaign to ensure their use is prohibted by the new National Curriculum. She is supported by Justin Tomlinson M.P. (Chair of the APPG for the Financial Education of Young People - remember his name as we are going to hear a lot more from him in the next few weeks).
  2. DM

    DM New commenter

    Tomorrow afternoon there will be a debate on the use of calculators in Primary Schools. Elizabeth Truss M.P. is fronting a campaign to ensure their use is prohibted by the new National Curriculum. She is supported by Justin Tomlinson M.P. (Chair of the APPG for the Financial Education of Young People - remember his name as we are going to hear a lot more from him in the next few weeks).
  3. Karvol

    Karvol Occasional commenter

    Six of one and half a dozen of the other, in my opinion.
    Mathematically, the aim of the primary school should be to give our children a solid foundation in mathematics - in both mental and pen and paper methods. However, they are going to be using calculators for most of their lives, so why make them start without them.
    Well they can always learn to use them once they have mastered the basics.
    But what if they never master the basics?
    Well then after a suitable period of time they can use a calculator.
    So they are back at the beginning again, using a calculator, except one year or so older?
    Ok. All children can use calculators.
    So when will they master the basics?

  4. Nazard

    Nazard New commenter

    My views on this have changed slightly over the past couple of years. Here is my current thinking:

    A degree of mental mathematics facility is important, particularly simple addition and subtraction, and the multiplication of small numbers ("times tables"). The appreciation of the reasonableness of an answer is also vital (eg, realising that 19 x 43 can't possibly be equal to 67).

    If pupils are carrying out calculations involving "easy" numbers then they should never use a calculator. Within other topic areas they can use "easy" numbers, and should not use a calculator. For example, when working out areas of rectangles, or perimeters of polygons they could work out the answers without a calc. When working out the mean of a set of numbers then these could be chosen so a calc is unnecessary and is not used.

    But, to support the appreciation of reasonableness of answers, it _does_ seem sensible, in some cases, for calculators to be used for more awkward numbers. If the sides of a trapezium-shaped school table are measured then the sensible way to work out the perimeter would probably be to use a calculator. This is where there is a grey area. Some pupils will love doing a sum that involves decimal places and will romp through it. Others will spend so much more time doing the calculation that they won't appreciate what it is they are actually working out.

    It seems to me that there are certain situations in number work where a calculator can help pupils to further their understanding of number. And then there are calculations that most pupils don't grasp and most adults never, ever use. I can't remember the last time I did long division - if I ever need to do something like this then I will use a calculator or spreadsheet. If you need to solve a problem involving division then using a calculator seems perfectly sensible to me.

    In GCSE examiners' reports I have read comments which point out that candidates who clearly have a calculator (because they used it in the trig question), didn't use it to work out a percentage and got the wrong answer because of calculation errors.

    I think the big, missing link here is the emphasis on _appropriate_ use of a calculator. Blindly typing in 2+3 (and then accepting the wrong answer it tells you because you tried to type using a pencil because that looks cool) is daft. Missing opportunities to practise sensible and useful numeracy is pointless. "Banning" calculators from primary schools is equally daft, though, because there are certain circumstance when they are helpful.

    [Disclaimer - this is what I think I currently think. It is different from other views I have held on this subject in the past. Future beliefs about this topic may vary. Etc]
  5. googolplex

    googolplex Occasional commenter

    Judging by the state of readiness of my year 10s today, a ban has been in place in secondary for years...
  6. DeborahCarol

    DeborahCarol New commenter

    I will cheer if they're banned in primary schools. Sure, there might be a few situations where they're 'useful', as one poster said, but I think the small advantages of having them in primaries are outweighed by the disadvantages of some teachers handing children calculators for basic calculations. If they can't do them, then they should teach them! I speak with feeling, as a One to One tutor of struggling Year Eights, many of them basically quite able, who have left primary school with no written methods for subtraction, or division (basic - not even long!).
    In secondary, sure - occasionally, eg for trigonometry, to save looking up trig tables! For roots, etc.
    I just don't buy this argument 'well in real life you'd use a calculator for'...x and y. We're teaching children maths, not what they'd do in 'real life' if they don't want to do the maths. In real life most people might not make their own sauces or soups, as it's quicker to buy a jar or carton. Does that mean that a course in cookery shouldn't include such things?
  7. You need to teach the fundamentals, as well as the application. For instance very few people will have to implement floating point arithemetic for a commercial program. But I teach the subject, so that students can understand why their computer will often calculate 0.9 + 0.1 as slightly off unity, and as a matter of principle.
    So I think primary school children should be taught two's complement notation, how to build a logical adder, how to do integer division by bitshifting and subtraction, and the rest of the fundamentals of how their calculators work, so it's not a mystery to them.
    Should they also be taught the now obsolete denary alogrithms for pencil and paper arithemetic? I think you can argue that either way, but Id be inclined to err on the side of safety. However I wouldn't demand fluency and accuracy with them. The reason is partly that the skill is obsolete, they'll never have to do a long division without a calculator "for real", partly that they know it's obsolete. No-one going to be happy sitting for an hour truding through a page of long divisions, when they know they've a mobile phone in their pocket that can answer the sums in a few seconds. That's not human nature. But they should know how to set about doing a long divison with pencil and paper.
    The the questions set should be changed to reflect the fact that pupils have calculators. Too much is made of the magnitude estimation problem. If children were regularly set questions where the calculator is forced into scientific notation, after they've got an understanding of the four rules, of course, they'd soon get an idea of magnitude.

  8. Completely ignoring the madness of the previous post...

    The question I ask students who seem to be highly reliant on calculators is this - how do you know the output is right?

    Calculators, and computers ultimately, only do one thing - speed up the calculation process. They are only as good as the input and process defined - therefore, if a student has no sense of the correct process, then they'll have no sense of the correct answer.

    A classic example is a student trying to find an average of five numbers, say, and having a result that is not within the range of the values given.

    Obviously there is a point where the use of calculators is appropriate and necessary, but when it comes to the four basic operations, and fraction arithmetic, I don't think they're necessary.

  9. Calculators should absolutely be banned for all elementary age students. The harm that calculators do to young math students far outweigh any benefits. Where I am, there is an entire two or more generations of students now ranging from elementary age to past high school who do not know their times table, cannot do long division, cannot divide fractions or reduce/multiply/add/subtract them, cannot subtract or add with negative numbers, cannot add large numbers and so on. All of them were handed calculators in fourth or fifth grades. All of them believe I am out of my mind for thinking they should be able to do basic arithmetic without a calculator. All of them are struggling with basic algebra because they can't do basic arithmetic. All of them say, "My calculator will do everything for me, why do I need to do it?" Apparently, people don't understand that the ability to think mathematically is a developed skill and arithmetic is one early necessary way to build those pathways in the brain. No arithmetic becomes no ability.

    Has anybody seen the cartoon Wall E? These students' brains are mush. I see it every time I tutor or teach. They haven't ever had to exercise them because machines have been doing the thinking for them and their brains have turned to useless sludge. Allowing elementary age students to use calculators to do their thinking for them is as wonderful an idea as giving them all wheelchairs to do their walking and running for them. What you don't use atrophies. Their brains have atrophied. It is a sad state of affairs.
  10. PaulDG

    PaulDG Occasional commenter

    Out of interest, which students are these?

    I ask because most of the kids I teach don't have calculators, can't use the ones we give out (because they hardly ever use them) and don't have working pen-and-paper methods either.

    It would be nice to be able to say they were "highly reliant", but, reality is, they can't do it with or without calculators....
  11. DM

    DM New commenter

    Liz's position:
    "When talking to local employers I often hear about candidates for job interviews who lack the basic ability to do sums. The truth is that too many young people fail to gain the mathematical skills they need to maximise their future career prospects. Many also struggle with managing their finances. Britain's performance in maths is abysmal, with the UK currently at 28th in the world in the OECD PISA tables. Whilst there are many factors that have contributed to this poor performance, I am concerned that government policy that encourages calculator use for students as young as 8 is diverting time away from mastering the basics.
    In schools I have visited calculators and computers are too often viewed as "magic boxes" by students and sometimes used as a replacement for mathematical operations. The present National Curriculum has a section on "Calculator Methods" for those at junior school (ages 8-11) while the Key Stage 2 SATs in maths have a paper where calculator use is allowed, but asks questions where a calculator is superfluous. Rather than boosting their basic arithmetic abilities we are creating a 'Sat-Nav' generation overly reliant on technology.
    According to a Trends in International Mathematics and Science Study (TIMSS) conducted in 2007, virtually all primary school students in England use a calculator, making it the country with the highest use in the world. Singapore, which came second for maths in the 2009 PISA tables, only introduces calculators to the classroom at age 11. Meanwhile the study found restricted use of calculators in primary schools in other top performing countries, such as Hong Kong and Chinese-Taipei. However, limited calculator usage was not just restricted to the Pacific Rim, the study showed lower levels of calculator usage in Germanic nations, which outperform Britain in maths.
    Calculators are more heavily used in Anglophone and Scandinavian countries such as America, Britain, New Zealand and Denmark. This is changing with concerns over the early use of calculators in school. In Massachusetts, the top-performing American state for maths education, the curriculum states that pupils should learn how to perform basic arithmetic operations independently of calculators. In Sweden, there is a non-calculator paper for 18 year olds.
    In the debate today, I will argue that the government should abandon advice encouraging calculator use for 8 to 11 year olds and make the 11 year old SATs tests calculator-free."
  12. But that, ultimately is my point. A lot of students I have taught want to use a calculator because they think it'll automatically give them the right answer, rather than having to think for themselves. As you and I both know, if you don't know what you're putting into the calculator in the first place, how do you know the answer it gives as a result is correct?
  13. DM

    DM New commenter

  14. This seems like a very poor example.
    I wouldn't like to see them banned. We should trust teachers to allow appropriate (hardly any) use.

    It's not just basics though. Working with A level students I often see them reach for their calculators and watch them work through calculations which require many keystrokes. While they mindlessly tap away I work out the answer mentally. In most cases I can get an exact answer and when I can't I can get a good estimate and in either case I will finish the calculation well ahead of them and will often be able to inform them they have the wrong answer. Sure, I show off a little but with a purpose. I tell them that if I can do it then so can they if they just stop using the calculator for every little calculation.

    People talk as though mental calculation is difficult and unpleasant.......a bit like walking when you could drive.
  15. DM

    DM New commenter

    Anyone else watching?
    I enjoyed this line from Nick Gibb: "Pupils must learn multiplication facts all the way up to 12 x 12 as there are 12 months in the year".
  16. 0.1 cannot be represented exactly in the floating point format used by most computers.

  17. DeborahCarol

    DeborahCarol New commenter

    Sure. If they needed to work out how many repayments for a car over eg 3,4,5 years they'd need to know to x12. I've always taught tables to 12x.
  18. Hmm, sorry about my other post. Looks like you know what you're talking about and I don't. Still 0.9 + 0.1 is unlikely to cause any problems, even on the cheapest of calculators so it was a strange example to use. I appreciate that even in this case the device only displays the correct answer but in fact has a slightly incorrect answer stored.

    I have tested some programs. One gives 0.1*10^6 = 99999.9999999999999674739 which I think is correct to 64 binary places. I suppose that the extra accuracy that can be achieved by using other representations is too expensive in terms of time and generally is not sufficiently useful.
  19. Floating points aren't the point here. It's the ability of a student to a) use a calculator correctly and b) to know that the results are correct (because they have the mental arithmetic skills).

    Like everything in life, the argument isn't black and white, and there has to be balance. Students will eventually use calculators, and it's our responsibility that they have the comptence to do so. Similarly it they need the mental arithmetic skills to hand to make numerical judgements and comparisons quickly. It's a question of how to strike the right balance. I don't think banning calculators in primaries is a responsible move - but then I do feel that some teachers let children use calculators too quickly when they should be challenging their mental arithmetic.

    After all, shouldn't be all working in the 'Zone of Proximal Development'?
  20. DM

    DM New commenter

    That contrived context seems a bit weak to me. I would hope they might have the wherewithal to multiply by 10 and multiply by 2 and add the partial results together.
    90% of the children I teach only know their 2s and 10s properly but even they would be alright here!

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