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Move the digits or 'move the point'?

Discussion in 'Mathematics' started by DeborahCarol, Nov 18, 2011.

  1. DeborahCarol

    DeborahCarol New commenter

    At school in the 70s I learned to multiply and divide numbers by multiples of 10 by 'moving the point'.
    Later, when training in a teacher, I was taught that on no account EVER was I to talk to children about 'moving the point', as....the decimal point doesn't move. I was to teach children, using place value charts, that it's the digits that move.
    'The decimal point doesn't move' has in fact become something of a mantra repeated by children at secondary stage. The only problem is....WHY do so many of them, having been taught 'move the digits', years later, have such problems multiplying and dividing numbers by multiples of 10 where decimals are involved?
    My suggestion is that 'moving the digits', however mathematically correct, hasn't worked for students in general. 'Move the point' is so much easier. Not only did generations of schoolchildren appear to manage fine with 'move the point', but my internet research suggests that the whole of America still teaches 'move the point'!
    The bulk of my teaching over the past 15 years has been KS2 and KS3, and in recent years I've rebelled a little. KS2 I've religiously taught 'move the digits' (would get in Big Trub if did anything else!). KS3 (and a few KS4, even Higher GCSE) I will show students for whom 'move the digits' appears to have failed that 'move the point' is a great short-cut, but of course with 'you-will-remember-that-the-decimal-point-isn't-really-moving-won't-you?' to cover myself!
    What do others think?

     
  2. I move the decimal point.
     
  3. I move the decimal point
     
  4. tim hod

    tim hod New commenter

    I explain first about the numbers moving places and give examples of this using single digits ( 8 x 10, 7x100, etc). Then show that moving the point accomplishes the same thing, but makes it much easier for longer numbers.
     
  5. googolplex

    googolplex Occasional commenter

    I'm afraid I'm in the very old fashioned club...
    The moratorium on 'Moving the point' is another example of the obsession with trying multiple methods in the vain attempt to help students <u>understand</u> something, a mantra which has been taken to the extreme by the national strategy.
    I always move the point - it's what I learned to do, it's what I first taught students to do (until I was told not to), and it is what I've often resorted to advising students to do once we've discovered why it works.
    A bit like all the other things we're not supposed to say - change the side, change the sign, etc, I learned to be a much more effective mathematician by following such rules than most kids ever manage these days. Sometimes, in fact <u>many</u> times, there is more sense in teaching method first, and then thinking about <u>why</u> later...
    Most students need simple strategies for doing day-to-day maths, not necessarily a head full of reasons...
    I'm not arguing against explanations, just that there is a time and a place, and the time/place doesn't necessarily have to be at the very outset...
     
    Katherineh31 likes this.
  6. I find this thread very strange.
    I thought that, in the old days, we were always told to move the point, but that the current (and, more correct) way of thinking was to move the numbers (ie the digits increase or decrease their place value) whilst the decimal point remains in place.
    I have to battle against younger pupils having been told to "add a zero" to multiply by 10, and move the decimal point if there is a decimal when I try to get them round to thinking of moving the numbers whilst the decimal point stays still.
    But are you saying that you find the opposite - ie, they want to move the numbers but you want them to move the point?
     
  7. googolplex

    googolplex Occasional commenter

    I can't speak for others but, no, I'm not saying that at all!
    I'm concerned by the number of students who have been taught to move the numbers yet cannot answer questions involving multiplication by powers of 10. Hence, whatever strategy they currently have doesn't work. The huge advantage of moving the point rather than the numbers is that there is one thing to move - conceptually, moving a point a couple of places one way, as opposed to all the numbers the other way can be the ice-breaker in terms of whether or not they have a strategy for dealing with such a question. If so, why not use it for some students?
    Yes, I agree that the method doesn't make sense in terms of understanding since, for example, it doesn't encourage students to think about the effect on the numbers in the place value diagram. However, if it works for some, if it gives them a strategy, why not use it? It's the way I was taught, and it didn't do me any harm..... or maybe it did [​IMG]
     
  8. erm

    erm

    Why not teach them about relative motion at the same time? (I'm being facetious.)




    Why is one more 'mathematically' correct than the other? The important concept is that the decimal point doesn't move *relative to the place value columns*. Who says you can't fix the digits and move the columns? (Easily done/demonstrated with a clear plastic wallet overlay or whatever... we can change the value of the 6 by putting the point here...)




    When working with pen and paper, isn't this what we actually do anyway: write down the digits, then think about what place value we want them to have and fix the columns accordingly (by inserting the decimal point or a few zeros to the digits already written down). Isn't that effectively what we also do when we introduce standard notation too, except with a different method of assigning the place value. Isn't that how we think 30 + 40 in our heads? We look at the digits, notice 3 and 4 have the same place value and add them. It could be pencils, apples or tens that we are adding. 3 pencils add 4 pencils, 3 tens add 4 tens. We combine the 3 and 4 to make 7 then relate to whatever we were working with.




    0.00000000000000003

    0.00000000000000004



    If I add those two numbers up, I know it's going to end in 7 before I've counted up how many zeros I need to write down.
     
  9. DeborahCarol

    DeborahCarol New commenter

    MasterMaths, the point of the thread is that the 'current' way of thinking IS to move the digits, but my contention is that, although this way may be mathematically 'correct', it is unfortunately resulting in more children having problems multiplying and dividing where decimals are involved than used to be the case when children were taught the 'old days' method.
    After starting this thread, I brought the subject up in conversation with a HoM at secondary, who agreed...
    and it's interesting to see other 'heretics' here who are (shush!) showing students to 'move the point', because...it's easier!
    MasterMaths, are you a primary teacher? I used to think 'move the digits' made 'teaching sense' in primary, until I started teaching KS3 students and realised that 'move the digits' has failed a significant number of students. If they all came out of Year 6 being able to do what, with 'move the point', used to be a fairly simple process, I wouldn't question the teaching.
    I'll add to my earlier comments by saying that nothing awful seems to have happened, ie no plummeting of mathematical understanding/whatever) to those secondary students who have strugged with 'move the digits' and I've shown 'move the point' - on the contrary, they can now convert metric measurements with ease.
    What do we want - GCSE students who can convert measurements because, shock horror, they've been taught to 'move the point', or students who, still at GCSE, struggle with multiplying and dividing by decimals by 'moving the digits', but, when offered an easier way, are very good at parroting 'but the decimal point doesn't move!'. What value for them is it being 'mathematically correct'?
    I'd also add that there are those with doctorates in maths who 'move the point' (not to mention, millions of people in the world - America, Asia) that don't seem to have been disadvantaged by this. But the poor sap who says 'move the point' to the average UK primary school teacher (who often isn't very good at maths) will be shown the error of their ways.
     
    Katherineh31 likes this.
  10. This is an interesting thread for me. I teach 11-18 maths and have a degree in maths, and I teach 'moving the point'. Of course I understand that what we're really doing is moving the digits, but to be honest, most of the kids I teach understand that what we're really doing is moving digits from their primary education, but moving the point is so much easier.
    I never gave it a second thought until I was discussing this with my sister and mother (both primary teachers) and there was an audible intake of breath at the shock that I taught moving the point. They have been taught to teach moving digits and found it shocking that I, supposedly an expert, would teach such a travesty!
     
  11. I move the point quite simply because it is so much easier to demonstrate on the board and in their books.
     
  12. Move the point - only one object to move has got to be easier!!
    As for teaching understanding, my experience so far has shown that trying to teach understanding to most students simply confuses them and wastes so much time, one has to ask is it really worthwhile?
    I was (and still am, I hope!) very good at maths when I was at school and college but understanding was not something I was ever taught.
    Trying to gain understanding and illustrate methods with pictures and diagrams, especially with younger/lower level students, can be like trying to juggle water!
    Real understanding only comes with lots of practice and experience and generally only comes to those who move to higher levels of work!!
     
  13. I move the point, after paying quick lip-service to the "it's the digits that are moving, really"
     
  14. carriecat10

    carriecat10 Established commenter Community helper

    Lost for words at some of the comments on this thread ... does this mean that you believe outcome is more important than process then?

     
  15. googolplex

    googolplex Occasional commenter

    Nooooooo. I do think emphasis on process is sometimes at the expense of progress, though. I don't need to know what goes on under that bonnet in order to drive a car. In the same way, it may well be better for some students to have strategies for performing mathematics without necesarily fully understanding why they work. I don't think the recent obsession with teasing out understanding has always nurtured more skilful mathematicians in schools.
     
  16. But the digits aren't moving when you multiply or divide by 10, and it is misleading to teach that they do.

    Take 2.34 x 10^6 and multiply it by 10^3.

    As we are multiplying by powers of 10, we obviously have to move the digits, rather than adjust the power of 10.

    Which is the wrong answer...

    What is there to understand about multiplying by powers of 10?

    If you multiply 2000 by 1000, you will end up with something in the millions.

    If they understand roughly what size of number they should expect, who cares what algorithm they use to get there?


     
  17. lunarita

    lunarita Lead commenter

    I hope your post is sarcastic, or that I have misunderstood it.


    Yes of course, the outcome is more important than the process, if the outcome is an understanding and an ability to multiply and divide by powers of 10, and the process is a correct but unhelpful approach which leaves the children struggling.

    Surely you're not suggesting we should stick dogmatically to the process of moving the digits even if this fails to achieve the outcome being able to multiply?
     
  18. bombaysapphire

    bombaysapphire Star commenter

    I agree that outcome is more important than process but I think teaching that the digits move is easy to achieve.
    My lower ability groups all have a slider made with a piece of laminated paper pushed through a piece of card with a place value grid on it. When we start multiplying and dividing by powers of then they all use these initially. They write the number on the laminated strip in white board marker and then slide it to find the answer. They are then weaned off them at various paces as they understand the process.
    With slightly more able groups there is always a slider to hand for demonstration purposes. Students end up moving the point but they fully understand why.
     
    samsteele likes this.
  19. erm

    erm

    This was what I was trying to say, but bombaysapphire said it so much better.



    Her visual aid works the same whether you move the laminated paper with the numbers on *or* the card with the place value grid (and presumably decimal point) on. It's the same process.



    Given that what we all end up doing anyway is 'moving the point' as it's both physically the easier of the two on paper and also the easiest to imagine in our heads, I can understand how children can find it confusing to be told that this is wrong and subsequently still struggle to multiply and divide by powers of ten. Using bombay's visual aid, what's the difference?
     
  20. In computing we use the term "floating point arithmetic".



     

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