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Massive insult to primary teachers

Discussion in 'Education news' started by moscowbore, Feb 14, 2018.

  1. Mrsmumbles

    Mrsmumbles Star commenter

    Cripes, what is an inverse? I’m already in over my head. My idea of achievement is bagging the last animated ‘write on, wipe off times table tracker’ board, available at The Works and other fine retailers for a sensational £0.99p. My students love it.
  2. Vince_Ulam

    Vince_Ulam Star commenter

    If I seemed abrupt then I apologise but I understood what you said. A new topic cannot be understood in itself except by some method. Now, that method is itself built upon prior understanding gained through prior method, all the way down until eventually we arrive at axiom, accepted but not understood.

    Explanations at this level of representation are unnecessary for children, and in fact can make confusing something that we all learned without this jargon. Much received Primary mathematics pedagogy overthinks the basics.

    Ordinality is easy to teach for Primary purposes, it's the naming of positions. There is no more to understand, the trickiest part for pupils is remembering the names themselves.

    "Only" procedural knowledge?

    Rudimentary subitising. No representation therefore no understanding.
  3. Stiltskin

    Stiltskin Star commenter

    I guess that depends of your viewpoint. I'm guessing you are a positivist?

    In the constraints of what I'd said yes. Do you think it's possible for someone to learn a mathematical method without understanding what is happening?
  4. Vince_Ulam

    Vince_Ulam Star commenter

    Nothing could be further from the truth. Why would you think this?

    It's relative. Understanding is only representation and there are different levels of representation. Primary pupils do not need any arithemtic representation deeper than method & tables.
    Scintillant likes this.
  5. Stiltskin

    Stiltskin Star commenter

    Your comments made me think it, so out of interest what philosophy do you align with?

    I am not sure I understand fully your last comment. Could you give me an example of what you mean.
  6. Vince_Ulam

    Vince_Ulam Star commenter

    Positivism is only one objection to social constructivism but it's just as extreme and wrong. Are you sure you regard mathematics as socially constructivist?

    It depends what I'm doing.

    Direct a pupil to write on the board a complete expression for the sum one plus one. Which of the following won't you accept as evidence that the pupil understands what they are asked?

    1 + 1 = 2​

    one plus one equals two​

    nervousned likes this.
  7. Stiltskin

    Stiltskin Star commenter

    Mathematics as socially constructivist, I don't know. Gut feeling is not, is it a human construction?

    I was really only considering more about the learning of mathematics and the transmission of its knowledge.

    Thank you for your example. So either could be considered correct, but the later requires a different level of understanding (and lots more pages). You can't just jump from one to the other.
  8. Vince_Ulam

    Vince_Ulam Star commenter

    No. We are not that clever.

    If it is transmitted & learnt then it is not socially constructed by learners with their teachers.

    The same fact is represented three times at different levels of resolution. The representations are equivalent but Primary pupils do not need to express all three to understand the fact they represent. By this example Primary pupils do not need any arithmetic understanding deeper than method & tables.
    monicabilongame and Scintillant like this.
  9. Stiltskin

    Stiltskin Star commenter

    I agree

    I disagree, I think that learning is a collaborative process. But I can understand that you may not.

    I agree.
    I'm not sure we're talking from the same position. Going back to teach method and understanding will follow. If we had two pupils and we teach them a method for calculating area of a rectangle, multiply the lengths of two adjacent sides. if pupil A doesn't understand what area is but knew the times tables it is possible that they could follow the method but it doesn't follow that they will then understand what is happening, or necessarily relate the answer to the space inside the shape. Such that given a parallelogram they would probably multiply adjacent side lengths to get the area. So my point was that just teaching a method doesn't mean understanding will follow.
  10. Vince_Ulam

    Vince_Ulam Star commenter

    Yet the subject is not constructed during that process.

    If someone were introducing area without explaining its meaning and regardless expecting pupils to guess different ways of finding it for any plane figure then I'd have a word in their constructivist ear. I'd also be quite chatty if someone were not teaching the properties of plane figures, then that rectangles are a special type of parallelogram such that non-rectangular parallelograms & rectangles have different properties ostensibly necessitating different area formulae. Formulae encapsulate properties, to understand the parts of a formula relative to one another is sufficient understanding for all practical purposes.
  11. palmtree100

    palmtree100 Lead commenter

    The test could be an incentive for more parents to practise the times tables with their children at home. As long as there is good communication between school and home (some schools are better than others at this) and parents have plenty of advance warning, I think most would want their children to do well in this test, and this is something that most parents understand the importance of, having had them drilled into them during their own school days. Also something that doesn't require much academic ability, to practise times tables with your child.
    This is an area where parents can really help and take some of the burden away from teachers, who have to cater for a class of 30 different levels.
  12. Stiltskin

    Stiltskin Star commenter

    I think I'll call this a day. I have tried to understand your thinking, but I find that you're unable to explain in a way that is clear to me. Your answers appear more to try and obfuscate. For example your second paragraph is well written, but for the most part is unnecessary, and I can't see how it disagrees with what I said.

    I have taught a number of primary children who could use some method in maths but didn't have an understanding of it. They just mimicked the procedure and couldn't apply it in different contexts. So they couldn't move on from this until we had gone back to the where they did understand and filled in the missing gaps of their knowledge.

    For the first sentence, as I said I can understand that you have a different view of how people learn maths. If you have a link to a paper/book that is a good introduction to your philosophy I'll happily have a read, and who iknpws I may change my viewpoint.
    chelsea2 and Pomza like this.
  13. peter12171

    peter12171 Star commenter

    The problem is the parents who think that education is the preserve of schools and that they don’t need to do anything at home.
  14. palmtree100

    palmtree100 Lead commenter

    It's about working together. If parents are well informed by the school, it helps.
    I remember before I started working in primary and was a full-time mum, I proudly told my daughter's teacher that I had bought a revision guide to help prepare her for the KS1 SATs. "Oh they've already done them" she said. "We don't like to make a big deal of it." At another meeting 2 years later for my next child, the teachers told the parents "There is no need to do any extra preparation at home. Everything is covered at school." It was as if they'd had problems with parents putting too much stress on children to get results. Yet this is a school in a very deprived area with low results.
    Another time, however, when I casually asked how my daughter was doing, her teacher said she needed to read more at home. I was ashamed that I hadn't been reading with her as much as I did with my eldest. So I started doing it more. Sometimes, with our busy lives, we just assume everything is going well at school when we don't hear otherwise.
    My point is that when schools communicate often and in depth, parents know where their help is needed and can work as a team with the teacher. I think communication is a whole-school issue, rather than the sole responsibility of individual teachers. Good schools (in my opinion) send out frequent letters/texts/emails and often invite parents into school for social as well as academic events.
  15. lulu57

    lulu57 Lead commenter

    It's just a tables test.
    I can't imagine the children will give two hoots about it, they get so many.
    The results will probably be used as a stick to beat teachers with, but what's new?
    It's nothing to do with pedagogy or mathematical theory.
    Somebody in the DfE is trying to make his/her mark, that's all.
  16. Vince_Ulam

    Vince_Ulam Star commenter

    You seemed to be suggesting that your example represented a misconception in response to good practice. Good practice would anticipate that misconception.

    This is because understanding, the recognition of the structure of a problem, follows the method encapsulating it as an abstract representation. The method must be practised to understand the structure and sometimes only the more intelligent & dedicated pupils arrive at understanding but in the meantime they and their peers should be led through as many different example solutions using this representation as is practical, not many different representations for the same handful of examples.

    Which is a problem to be anticipated. Good teaching for the example you gave would have described properties and related these to formulae, so it goes. Pupils can't be expected to know what their teachers omit from their lessons.

    My views on mathematical pedagogy are variously informed but founded in my experience. I've not met any mathematician who would argue that mathematics can be understood except through its practice.
  17. Vince_Ulam

    Vince_Ulam Star commenter

    When the issue of these tests was raised on last week's Question Time, a deputy head in the audience bemoaned the fact that the application of skills tested is not rising alongside test scores. I would ask in response why these children's teachers are not showing them how to apply these skills. She also, interestingly enough, thinks it "frankly insulting to have to bring in a test to do a job that we're already capable of doing". I wonder if she has, at least, been reading this thread.
  18. chelsea2

    chelsea2 Star commenter

    So, teachers teach tables, pupils practise them, teachers test them - that's normal primary practise.
    Some pupils can recall them all with ease, some recall quite a lot and can get the rest with some thought, some struggle to retain most.
    Teachers know exactly where each pupil is on this continuum. Teachers support & provide further practise for those pupils who cannot recall with ease, and keep the rest ticking over. Again normal primary practise.

    What will an external test tell us that we don't already know?
    What will happen following the test?
    Will the government say any child who has 'failed' (whatever that will mean) will be retested at the end of Y5? Y6?
    What if they 'fail' again?
    Will pupils be given special lessons in learning their tables?
    What will happen to the results? Will they be published in another league table?

    What is the real purpose of this?
    PGCE_tutor and peter12171 like this.

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