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Improve primary maths by appointing specialist maths teachers

Discussion in 'Mathematics' started by PaulDG, Nov 13, 2012.

  1. Guish

    Guish New commenter

    I teach A levels/IB HL and Additional Mathematics mainly. Hence, I can relate to secondary education only. An example would be as follows.
    Consider the solving of quadratic equations.
    Phase 1 (Knowledge): Make students learn how to factorise and solve for X. Lots of practice.
    Phase 2 (Comprehension): Interpret the solutions on a graph. Show them they were finding the x intercepts.
    Phase 3 (Analysis): If a student solves and gets the root of a negative number, that means no real root and therefore no x intercept.A bit of exploration by the student is expected to reach that phase.

    As one goes down the phases, there's an evolution as a learner as the learner is interpreting the results and just not doing. However, the foundation of a good Mathematician is good solving first. That's why I prefer that A level students or Addtitional Mathematics students already have a good Algebra foundation when they join the courses of that level.

     
  2. hairdo

    hairdo Occasional commenter

    Think all of this is more straightforwards with older students. The challenge is getting a firm foundation with the building blocks of maths that produce good mathematicians in the longterm. I do think some attention should be paid to understanding when children are first learning maths but I can also see the value of teaching methods which are just really playing around with numbers, and lots of practice where kids get the opportunity to get things right.

     
  3. paul - would you really be happy with kids who could do long multiplication with abolutely no understanding of the place value behind it - or even subtraction using borrow-and-payback rather than decomposition with little or no understanding of why they were doing what they were doing, but with an ability to get the correct answer all the time?

     
  4. hairdo

    hairdo Occasional commenter

    I bet if you practise it often you will be able to do it just as fast as a column method
     
  5. PaulDG

    PaulDG Occasional commenter

    I'd see that as a better place to start to build that understanding than a "level" that claims "understanding" when what I see in front of me is someone who not only can't do with pen and paper but can't do with a calculator either.

    The place to start is the doing. Then work on the understanding.
     
  6. PaulDG

    PaulDG Occasional commenter

    There's more to write. Much more. So given two people equally proficient in each method, long multiplication must be faster.
     
  7. hairdo

    hairdo Occasional commenter

    I would expect someone proficient in the grid method to move onto long mulltiplication fairly quickly. I agree it is quicker and therefore more efficient but only if you are clear about what you are doing. The grid method is a good stepping stone to long multiplication so ideally both methods would be understood.
     
  8. so - all you other secondary school teachers - should we let them get on with it - are you happy to work on understanding with 11 year olds who 'put a 1 there' or 'put that number over here' 'because my mother (or i suppose it would be 'because my teacher) said so' ?
    i am interested if you would, but i am genuinely surprised

     
  9. Actually I think my results this afternoon were wrong. I just downloaded a stopwatch and did it properly.

    Traditional........Grid
    14...correct.......22 correct
    38.. correct.......87 correct
    74...correct......199 incorrect
    130 correct......couldn't be bothered, sorry.
    Times in seconds. Details of calculations withheld. :)

    Anyone else care to contribute data?

    I always thought the traditional method was better. Now that I've done what I consider to be a fair (enough) test I am sure that it is.
    But I have nothing against the grid method at certain point in a child's education.
     
  10. PaulDG

    PaulDG Occasional commenter

    Do they need to "understand"

    I remember a short-lived TV series, it may even have been a one off, from when I was a kid. Some school kid was communicating with aliens and had learnt "advanced" mathematics from them. The kid wrote his maths using a notation where every number in the next column was worth double the previous column. This was, of course, binary.

    Yet how many of us who were taught binary (or used it in solving problems with computers) ever thought of binary significance as "double the previous number?

    When I do column addition, I don't remember "each of the numbers in this column is worth 10 of the numbers in the one on its right" - I don't need that.

    Do they?
     
  11. hairdo

    hairdo Occasional commenter

    some do, some don't need to understand. The able mathematicians will pick anything up quickly in any case. Column addition is the easiest to understand ...long division, long multiplication and long division are the most confusing and many adults would not even remember how to do them (unless they are teachers, of course)


     
  12. I don't think this is always the best way forward. Someone who is good at a subject is not always the best teacher. I think back to my own experiences of secondary maths with maths teachers who clearly knew their subject, but did not know a thing about how to teach the subject. The teacher has to be competent in the curriculum they are teaching and has to be able to teach it in a way that children understand and can move on.
     
  13. Guish

    Guish New commenter

    I agree. I had some lecturers at uni like that and I possibly do the inverse of what my Mathematics teacher used to do at secondary school. However, having a subject specialist who is a good teacher as well can be a good deal.
     
  14. I was trained as a Key Stage 2 and 3 Mathematics Specialist, and I can see both sides of this argument. I am currently teaching in a Primary School where I teach the majority of subjects.
    I'm not going to add any 'arguments' to this conversation as I think it's already going around in circles and I think both opinions are valid (I love teaching Maths, I do understand percentages and, luckily, a number of other areas... However, I have also worked with my fare share of not so competent teachers, in both Primary and Secondary schools). Personally, I just think there needs to be better communication between Primary and Secondary schools - working together would be a start.
    My question to the original poster is: Do you also think we should have specialist English teachers in Primary Schools? A lot of children have terrible grammar and many are behind where they should be in reading. The difference with English is that as long as a child can write, they can still attempt a written task - even if the outcome is terrible. Maths is different and lower than expected numeracy skills can lead to a complete stop, rather than a useless but 'finished' piece.
    Hope this all makes sense... it's very late!
     
  15. I don't agree with this.
    We (or those that agree) are not talking about having a degree in maths or even still be fluent at the top end of A Level. We are talking about those who were dragged through and scraped a C at GCSE who are now teaching maths.
    They do not know how to teach maths as they had no concept at school let alone be able to flexible when it comes to slightly different ways of looking at a topic.
    I know a number of past pupils who have either become or are becoming primary teachers and thinking back to solving basic equation with one unkown was hell. (just one of many examples)
    These people simply should never be allowed near a classroom until they competent. "Is area when you add the sides?"...etc
     
  16. ShadowMan

    ShadowMan New commenter

    Hairdo: do all of your Yr 7s know their times tables back to front, at speed by the end of Yr7? If so, please tell us how you do it. If not, is it because you need to be replaced by someone with a better grasp of the subject?
     
  17. CarrieV

    CarrieV Lead commenter

    And there's a thread on here where 6th form teachers are bemoaning the fact that A level students don't know how to square simple numbers, clearly specialist maths teachers have problem students too!
     
  18. Still missing the point.
    An academic will have a range of methods to teach if they are not getting through the first time. Clueless 'teachers' will not.
    Many secondary teachers and specialists still having failing pupils. This is not up for debate. They do though have more tools to allow pupils to learn.
    You can type all you like defending uneducated 'teachers' but at the end of the day the issue is there and will only go away when the UK gets tough on said 'teachers'.
     
  19. It's not about defending teachers with poor subject knowledge. It's about the idea that subject specialists at primary level would solve the problem of having children underachieve in maths. It wouldn't. If it did, and everything would be fine by simply putting a maths specialist in front of children, everyone would be coming out of secondary school being perfectly capable in all areas of maths. This is not the case.
    "Clueless" is not just a problem when the person has an issue with subject content (this can be alleviated by further training), but having someone with an over-inflated ego and no understanding of teaching methodology and didactics teach children, is equally dangerous. Just being an "academic" doesn't make you a great teacher and it also doesn't mean that this person automatically understands how to adapt their teaching to support pupils, who struggle and find maths difficult. In the same way, being rubbish at maths and having no understanding of the subject, doesn't automatically make you a great teacher, either.
    I personally find it strange, that some people in this country, who train to become teachers, struggle to do basic written division or multiplication. However, I find it equally strange, that these people have supposedly achieved an educational level that equips them for university study in the first place. But then, I'm educationally spoilt...and wouldn't want my own children to study for GCSE or A-levels, which I find rather limited and aspirationally limiting anyway.

     
  20. what do they study? are they home-edded? (sorry - just being nosey [​IMG] )
     

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