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Survey: Is it possible to develop mathematical concepts and procedural accuracy at the same time?

Discussion in 'Mathematics' started by Danio, Dec 26, 2010.

  1. Danio

    Danio New commenter

    Procedural accuracy leads to a conceptual understanding. simply put, if you are getting the procedure wrong, then you dont really understand the concept. Therefore my answer is no.
    You should read some books and papers on it, as lots of research by practicing teachers has been done on this.
  2. Mandy, with all due respect this sounds like a "can you do my assignment for me?"
    What are your thoughts and what examples would you give to people replying in terms of your undestanding/research/experience?
    Perhaps whoever set the question thinks the current way of teaching is not gettting us anywhere and I dread to hear one (or more responses) you will get to this.
    I personally think, for what its worth is that the powers that be are scraed of discipline, political correctness and have turned education in edutainment and refuse to spend time hammering numeracy and mathematical CONTENT..they dress it up to avoid hard work and having kids sit in seat and learn.
    Problem is they never get the basics sorted as they are spedning time 'exploring' with no foundations.
    One can be built with the other but no amount of fannying around will get close to rote learning basic operations.
    The irony I find is that the exam system never tests any of this wishy washy exploring stuff and hammers basic maths.
    The only reason kids dont sit down in rows, shut up, get a book and learn is because the sad PC/SEN*/Inclusion ethos our education allows for it.,
    Go to Asia, Eastern Europe etc etc and you will see people learning,
    Pupils should have to pass numeracy tests which are internationally recognised and externally moderated before they are taught maths IMO..those not reaching those levels keep going round the process until a 'basic skills' route is given whilst the MAJORITY move on to maths. Still wading through 6/7/8 times tables in mid set year 10s in mainstream is painful
    Ps my * refers to some sections of SEN which are abused and I am fully supportive of true SEN
  3. 1. Do you think it is possible?

    >> Depends what you mean by 'at the same time'. Do you mean 'same instant', within the same exercise, within the same lesson, term...? Students need to develop numerical skills first because, as Betamale notes, they won't get anywhere with concepts alone.
    2. Do you think it is necessary to cover both? or is one of them sufficeint?

    >> See above. But numerical/procedural accuracy first. Not much point understanding how Pythagoras "works" and what the answer "means" if you don't have the first clue how to multiply a number by itself.
    3. Is time a major constraint in covering both?

    >> It ought not to be, but sadly students spend so long 'finding themselves' that the accuracy gets in the way of the 'real maths'.
    4. Other than time, is there other major obstacle?

    >> Students' knowledge/abilities at the start of your teaching them.
    5. Ideally, how would you develop mathematical concepts in KS3/4?
    >> I would never claim to have the ideal lesson for teaching any concept. One should always reflect on each lesson - there's usually some way it can be improved. There certainly isn't a one-size-fits-all answer to teaching mathematical concepts to teenagers. That's why we get paid to do it.
    6. Does developing procedural accuracy always equate to text book practice?
    Of course not - worksheets are good too [​IMG]
  4. To clarify - I mean their lack of numerical accuracy,
  5. Seriously, in answer to 6, there are a lot of ICT activities purely focussed on accuracy.
  6. "Mandy, with all due respect this sounds like a "can you do my assignment for me?""
    I'm sorry if it sounds that way (it really does, doesn't it? [​IMG]. I just wanted to go the extra mile to see which opinion wins out. I know this sampling method is absolute nonsense, but I am geniunely interested to widen out and hear what others have to say.
    I do apologise for not making it clear though. [​IMG]
  7. "Go to Asia, Eastern Europe etc etc and you will see people learning," that is so true! I'm a product of such system and it worked miracles! Even the dummest kid in our system know their tables well and can apply with no problem at all! The ones who can't are genuine SENS and you don;t need a doctor to tell you, you know they have a problem and you make allowances for them.
    Very ineretsting observation on trying to build on a lack of foundation too. In fact, one of the teachers have described this as trying to build on loose sand. How interesting. Do I assume you are teaching secondary maths?
    Anyone out there teaching primary maths and hold similar views?
  8. Whilst I'm a firm advocate of having different activities in lessons, I can but concur with much of what Betamale says. Last year I was forced to sit through a DfE presentation about 'Shift Happens' and how education had to be all about 'transferable skills'. At the end, I was sorely tempted to ask if we had copied our competitors in the Far East!

    A few years back I was fortunate to visit a school in Singapore. There they taught science to a class of over 70 in a lecture theatre. The teacher was going extremely quickly but the pupils I spoke to felt it was up to them to go away and learn/find out about the material. It was a real eye opener.

    A major problem in maths is that so many other subjects are now almost content free and pupils simply don't see why they should rote learn/memorise anything. Anyone without the basic foundations isn't going to get very far in maths.

    I would take exception with Betamales SEN comment. It's usually more the parents that schools are afraid to stand up to and tell them that rather than having a problem their child is poorly behaved and lazy.
  9. I have set up lessons recently that have had tasks such as
    "By the end of the lesson I want the answer to the following question
    I would like the product of
    • (i) David Beckhams Man U shirt number
    • (ii) The area of a circle with a radius of 5cm
    • (iii) The number of the day in the month we break up for summer holidays this year
    The rules are:
    You cannot leave the room
    If working together each member of a team (no more than 3 per team) must be able to take questions I ask about their findings
    You must present all work accurate to 3 significant figures "
    Now, I have sat and watched the tumbleweed for 10-15 minutes before.
    The usual response is "Can't you just tell us?"
    The pupils have a range of text books on the class for the circle, the word product and what a significant figure is. There are so many posters up in the class Their planner will give them the term dates and I am sitting with google on my screen, tabbing between wiki and all manner of search engines.
    Very rarely can any get it together and we are talking C/D level pupils and Im not sure any of them have ever said "Sir, can you google..." followed by a very specific question.
    Many cannot handle this situation and often try to play up or go into " i dun geddit" mode. Pupils are in my experience often unable to think and need to be spoon fed, cannot research outside of lessons and very often take responsibility for their own learning.
    I have given my own books to help kids and when they return I have asked how they got on "I didnt like the book" and I respond...."So what did you do instead?, google? a different book? find me?" the answer 9/10 times "No"
    Saying that, I have some that are an utter inspiration from a range of ability levels.
    "have you got a calculator?" 30 times before a final year 11 exam is IMO a joke .....
  10. is it just me or what? I seem to come across a lot of children who do not know their tables and this is really hindering their progress. In my training so far, this seems to be the norm and I got the impression that this is just the way it is. It seems to me a silly idea not to learn the tables by rote. This idea of counting fingers work for KS2 type questions, but once you start KS3, the lack of proficiency in numerical agility really show. am I just being silly in questioning this? or is my observation somehow flawed? Is this a valid case for saying it is important to develop procedural skills more so than the so-called conceptual knowledge (such as how to proof pythargos was right, or where the sine-rule comes from etc)
  11. PaulDG

    PaulDG Occasional commenter

    I just wanted to say that I've agreed with everything Betamale has written on this thread (and every other thread I've looked at this morning). (Where were you when I was training Betamale? [​IMG] )
    And the quote above is a real gem for me - I've experienced it and it totally sums up, for me anyway, the problems we see day-to-day.
    They're taking life-changing exams and they can't be bothered to bring a calculator. They clearly don't see the importance and also, clearly, have learnt to be completely lazy.
    When I left school, the notion that it wasn't necessary to learn tables was just coming in - and it was something I supported. I couldn't see a need, given calculators were almost being given away in cerial packets why anyone needed to know "instantly" what 11x12 was (esp as we had moved to a decimal coinage system some years before and were also moving to metric measurements).
    Now though it seems such a big issue to me.
    Without a working knowledge of tables it's impossible for them to follow the simplest explanation - I've had groups that don't "get" area simply because they just can't see that 2x3 = 6 and so never associate side lengths and area being related by product.
    And that means they never remember it, can't tell the difference between area and perimeter (and I don't just mean forget what the word means) and can't get it right even with calculators.
    I think you're right and your observations match mine.
    But heck, what do I know? I'm only a teacher, I'm not an Ofsted expert....

  12. Karvol

    Karvol Occasional commenter

    Did you lend them one though?
    We have a strict policy in my school that no-one is allowed to borrow a calculator in a test or an exam. If they turn up without one, then that is their problem. If it runs out of power ( rare, I know ) then that is their problem.
    It does not completely solve the problem ( some kids are just absent minded ) but it does reduce it considerably.
    As to my initial question, in an official external exam situation, I would lend one if I had one at hand, otherwise no.
  13. PaulDG

    PaulDG Occasional commenter

    But it isn't just their problem, is it?
    Having that calcualtor might be the difference between a D and a C or an A*/A or a B and both of those will affect the school's statistics.
    So, of course, we lend calculators.
    (And then employers moan about school leavers not having "basic skills" by which they include such things as "turning up with the necessary equipment to do the job".)
  14. my daughter took 2 calculators into her mock gcse - one ran out of power and a key jammed on the other
    she took 3 into the actual gcse and my son will be doing the same [​IMG]

    betamale - do you have any more of those 'david beckham's number shirt' questions - i could really enjoy those - i mostly work either in a room with a suite of 5 computers, or in the ict suite so they wouldn't even have to bother me - pile in the maths dictionaries and a couple of other reference books - i could enjoy this
    i've pm'd you my email address , in case you have a handy word/ppt document
  15. Chirimolla

    Chirimolla New commenter

    Procedural accuracy is necessary but not sufficient for the development of mathematical concepts.

    I have encountered far too many children who have been held back by spoon-feeding and rote teaching. Some of the children I teach went to school in South Asia where they were drilled with times tables and long multiplication. Give them pens and paper and they can do those perfectly, yet they have extreme difficulty doing even simple mental calculations (eg. 20 - 11, 15 * 8 or 83 + 12) and some of them show very little understanding of what multiplication actually is, or when they might need to use it.
    For all the faults of primary maths teaching these days, the children we get coming up from UK primary schools are good at mental calculation, and almost all of them know their times tables. They often struggle with division, however, and many of them are weak when it comes to shape and space. If I had a pound for every child I've come across who thinks "calculate the area" means "multiply together every number on the page in front of you", I would be rich! I can't say for sure, but I suspect that this kind of misconception stems from teaching to the test in primary school - in a SATS exam, this strategy probably works.
    Oh, and getting year 7s to write down the question, let alone show their working out, is always a battle at the start of the year!

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