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Can children teach each other mathematics?

Discussion in 'Mathematics' started by only_me86, Jun 11, 2012.

  1. only_me86

    only_me86 New commenter

    I am currently on the maths specialist teacher programme (MAST) at university and am writing my first year essay with the title:
    'Can children teach each other mathematics?'
    The essay will discuss talk within the maths lesson, children addressing each others misconceptions, the use of mixed ability pairing, the amount of teacher input needed within a maths lesson.
    Does anyone have any thoughts on this topic?
    Or indeed any links to articles related?
     
  2. PaulDG

    PaulDG Occasional commenter

    Loads!

    In general, no, they can't.

    As a student once told me, "it's not my job to explain that to her - that's what you're paid for!

    She was right, wasn't she?

    Addressing each other's misconceptions? Well, sounds very good, but is only of use if it doesn't introduce new misconceptions!

    Mixed ability pairing? Doesn't that mean one of two things? Either the brighter of the kids is being held back because of the need to continually explain something they already understand to someone who doesn't instead of developing their own knowledge? And where it doesn't mean that, doesn't it mean "the bright kid does the work and the less bright one copies it"?

    Maths is not a team sport.
     
  3. Well said, Paul, spot on!
     
  4. Of course they can and every classroom is better for it when they do. It is the job of the teacher to guide this task and ensure the problems raised by previous replies do not occur.Social constructivism rules!
    (at least I think that is what we all decided!)
     
  5. only_me86

    only_me86 New commenter

    Surely the idea that people learn what they have taught others is definately something to consider and implement in the classroom?
     
  6. frustum

    frustum Star commenter

    Is there a distinction to be made between teaching and helping each other to learn?
    I'm studying currently (well, actually, at this precise moment, I'm avoiding studying). If I talk about my work with fellow students, I'm getting their help with learning, but if I want to be taught, I ask my tutor, who is rather more guaranteed to know what's what.
     
  7. only_me86

    only_me86 New commenter

    We Learn . . .
    10% of what we read
    20% of what we hear
    30% of what we see
    50% of what we see and hear
    70% of what we discuss
    80% of what we experience
    95% of what we teach others.
    William Glasser
     
  8. mehmetdan

    mehmetdan New commenter

    I am currently paying a 17 year old £20 an hour to tutor my teenager maths. He is doing better with the 17 year old than with his school maths teacher so I would say yes to your question.
     
  9. mehmetdan

    mehmetdan New commenter

    Yes the 17 year old has done his A Level maths a year early.
     
  10. mehmetdan

    mehmetdan New commenter

    Well it would be possible if I hadn't hired him to teach the stuff the teacher hasn't taught so the answer there would be no.
     
  11. PaulDG

    PaulDG Occasional commenter

    In the old days when children sat in rows in individual desks (which they still do in the USA if their TV output is anything to go by), it was easy for the teacher to recognise who was having difficulties.

    Now, with the focus on "group work" (or is it really that the number of kids in the room is too high so an excuse has to be found for them sitting too close to each other to work individually?), it's much harder for the teacher to work out who needs that help as it's quite easy for a moderately well-behaved class to give the impression of "good" peer-support, etc. going on when what's actually happening is several kids haven't got a clue and are getting by by copying.

    Obviously, eventually, a teacher will find out which - but that "eventually" could be a very long time in a system that discourages "end of topic" tests (most schemes of work flit from topic to topic every fortnight or less - we can't spend on lesson in six giving a test!) - kids could carry their lack of knowledge and misconceptions for a very long time before being detected.

    And, of course, obviously the expert classroom practitioner will pick up these problems early and will address them "1-2-1", but again, we're in an environment (in the state system) where NQTs are valued over experienced staff because they're cheaper, where supply staff are often unqualified in the subject and don't have English as a first language (the more experienced supply staff being forced out of the role because it's impossible to earn anything like enough doing supply these days) - oh, and the fact they're seeing over 200 kids a week and have to spend most of their waking hours at the photocopier or phoning parents burns them out in 5 years anyway.

    Group work is not encouraged in successful independent schools because they recognise it for the waste it is - and it certainly isn't evident on that Finnish video either.
     
  12. My daughter revised and worked really hard for her Maths GCSE. The day before the exam a few friends who were studying for foundation were saying they didn't understand Pythagoras, so she taught them. It worked, they understood and it came up in the exam!
    So, yes, I believe it can work. If nothing else in this case the children were very switched on to wanting to engage, which helps. If Gove is reading - no, I don't think it's a good idea as a replacement for Teachers.
     
  13. Not only can children teach other children maths, individual children can be self-taught in maths. Learning is not limited to one person teaching the other - otherwise we would not progress.
    Of course, children or others learning by themselves will need guidance at times - that is one of the roles of someone more learned (often maths specialists can fulfil this role).
    As for becoming more adept in a subject by teaching it - I agree.
    People and children often learn from reading and trying to understand books.
     
  14. only_me86

    only_me86 New commenter

    What do people think about the idea that the child who is acting as the 'teacher' understands the concept more after imparting their knowledge onto others? They almost rethink their understanding.
     
  15. mature_maths_trainee

    mature_maths_trainee New commenter

    How incredibly disappointing that we're still at the stage of not being in clear agreement on this issue.
    I believe the discussion is severely hampered by over-generalisations (e.g. 'you only learn 10% of what you read,...,...', that may in some sense be generally true, but may or may not be true in Maths, or particular topics within Maths) and very different understandings of what's meant by 'teaching' and 'learning'!
    Whilst the classroom teacher is pre-eminent is communicating the new knowledge to students (and deciding precisely when to do so), surely there are very good reasons to believe that other students ('group work') might be able to play a hugely important part in helping to embed and apply that tentative new knowledge to a broader range of contexts, and embedding it within their broader set of knowledge? That too is certainly part of 'learning', and (depending upon your definition) probably part of 'teaching'.

    So to answer the original question, I think it has been clearly established beyond any reasonable doubt that other students ('peers') have the *potential* to play a strong role in certain aspects of other students' learning. [and so, could reasonably be said to be playing (part of) the 'teaching' role].
    I feel that the big danger though is that its potential (in Maths) is often very, very difficult to realise in practice (in the UK, at least) and the reasons are rarely acknowledged. ['Group work' was promoted above all else in my Initial teacher training course, and any critique discouraged].
    So it's not good enough that there's 'benefit' from group work. For it to be used, you must judge that there's *more* benefit from it than from any other activities you could pursue at that time. And I'm not sure that calculation is often even considered.
    MMT
     
  16. Of course pupils can teach other pupils, in fact in a lot of cases it is prefereable for a pupil to teach another pupil, it frees up the teacher to do more useful things, like pushing the stronger students and supporting the SEN students.

    I guess I can put my views into this - 'the teaching of mathematics should be about understanding and interconnectedness of ideas and if you understand something you can explain it, if you can explain it, you can teach it. So if you teach well, and the understanding is there, then the pupils whom understand it best can teach those pupils whom understand it least'.
     
  17. I'm probably at my most cynical having spent two hours after school with 62 exam papers to mark listening to an "expert consultant" telling me children should be teaching each other maths however here goes.
    If all children can teach each other is there any purpose having a teacher? Surely if I'm not teaching I don't mean dictating or standing at the front of the class but moving in the classroon clarifying ideas, debating points with children I wasted my time at university and training to be a teacher because my job could be done by anyone.
    If by children teaching each other you mean i set up the new learning whether an activity, investigation or consolidation then they work together on problems helping each other out then yes they do teach each other but I don't really think that is the same as my role.
    I think my skill as a teacher is to look at a child's work and be able to say if they have a misconception, what that is and how to put that right - can a child really do that if so i've wasted 25 years of my life and thanks to Mr Gove's plans for no retirement I have another 20 to go.
     
  18. Doitforfree

    Doitforfree Star commenter

    I was at primary school in the 1970s when pupils teaching each other was all the rage. Our school was compleely open plan and the idea was that the more able and older children would help the younger and less able. By third year our teacher was so appalled that we knew nothing at all, in spite of having to 'do' some Maths every day before we could play, that he taught us fractions and percentages every day for an hour. I've no idea how he got away with it as that sort of thing was really frowned upon, but we all left his class very proficient in fractions and percentages.I daresay children can teach each other but in my experience they don't want to!
    My own children were often put with less able ones to help them which they found deeply frustrating as they wanted to leanr new things. The teacher tried peddling the idea that by helping the others they would understand the Maths better but the Maths was already so easy for them that there was no chance they didn't understand it, and appropriate maths for the bright ones would have been way beyond the less able whoever was teaching it. And they're not just arrogant little so and sos. They've all grown up to be excellent, natural educators. But when they were at school they wanted to learn, not be surrogate teachers!
     
  19. frustum

    frustum Star commenter

    I do remember learning one thing when I was helping my classmates. You see, my mum had taught me to subtract by borrowing and paying back, and all my teachers were wise enough to let me carry on, even though everyone else was decomposing. But since other kids would keep asking me for help, I got one of the other abler ones to show me how to do it their way. (But note, I had the sense to ask one of the other bright ones.) It has come in useful since (although I still borrow and pay back when nobody's watching).
     
  20. GrahamLawler

    GrahamLawler New commenter

    I think there is a conflation here. There are 2 areas:
    1 introducing a topic/concept for the first time and
    2 consolidating that experience. Children are often good at the latter but not the former. Group work is part of the mix and is a good thing. Anyone who thinks education should be an isolated activity has a lot of personal reflection as a teacher to engage in.
    I have literally just come back from an industry based training meeting and there was a feeling that young people do not possess the group work skills and some were arguing that schools need to do more groupwork not less. In industry, working in groups is called teamwork, in schools some call it cheating.
    We need to prepare children for the 21st century and that means being emotionally stable, self resilient, critical thinking problem solvers. That is why maths is so important in a child's development and why we need to develop language/communication and a love of our subject in all children.
     

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