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Here Is How You Teach Maths!

Discussion in 'Mathematics' started by JosephBloggs, Oct 10, 2007.

  1. Oh dear, I will forgive you for being so rude as I can only surmise that at 2.45 in the morning that either you have had nightmares and couldn't sleep or you have had far too much to drink.

    Obviously all these wise people around you are not going to change your mind, so I will do what many people have done before me and just sit back and watch your mad ranting from a distance.

    One day JB, hopefully you will grow up a bit and realise that you have not just reinvented the wheel.

    I can only sit here grateful in the knowledge that my own children are beyond school age and are never going to be 'taught' by you. Oh dear, I've just had a thought, one day my own children may have children of their own...where abouts are you in the country? I may be moving.
  2. I taught iGCSE maths to a class of last year.

    I'm not a maths teacher, I don't have a degree in maths, I don't even have an A level.

    What I do have is an ability to teach and an ability to relate to my learners.

    My learners had all but 2 taken GCSE maths and failed. Of the remaining 2 one had been told at 14 "we can't teach you any more maths" the other had been educated in a country that does not do GCSE.

    I would slip the method in at the end of the lesson after the students had understood what they were doing.

    These people had all been put off maths by being taught by the method.

    There were frequent gasps of "ah, I never knew that" for things that they should have known. One of the biggest was when I explained that in fractions the line between the top and bottom numbers meant the same as "divided by" - no one had bothered telling them.

    For some students method is the best way, and these students will probably be the ones who will do A Level and possibly degree level maths. But you can't ignore the other students. They CAN get GCSE and as a teacher you should be teaching every one in your class.

    BTW did I mention I only had 16 weeks at 2 hours a week? And a 100% pass rate?

  3. JB without any embarassment you wrote:

    Finally, you haven't answered any of my questions about how you actually ensure that the pupils you teach understand the teaching that you transmit.

    Easy - Questions in class - homework - tests!"

    You really haven't got a clue about learning. You are so remote from what good practice is that any further discussion with you is pointless.

    You don't want to do a PhD, you want to have a PhD, there's a big difference. If you ever manage to write a coherent proposal which comes to be accepted (you've pretty well convinced me that this is far beyond your capabilities) then I think you'll struggle - especially with your supervisors.

    Merchant banker - how apt!
  4. bombaysapphire

    bombaysapphire Star commenter

    I am almost in awe of the arrogance that allows someone to believe that their achievements define "success". Anyone who has excellent value-added - that is the wrong measure. A 2nd class degree from a top class university - not as good as JB's 1st. Years of experience as a teacher - wiped away by JB's 1st.

    The sad thing about this is that the students we teach are not all capable of "success the JB way." Do they all deserve to be written off as failures?
  5. Piranha

    Piranha Star commenter

    Post 203. You haven't really answered any of my questions - just continued to sound as if you don't really understand the things you are criticising. However, I'd be happy to answer your question. I really enjoyed investment for a large part of my career in it. However, the excitement of playing with large sums of money wore off eventually. I had intended to retire before the age of 50, but a few years before that, I realised that I would actually like to do something a bit more worthwhile. Investment banking is (as you say) financially rewarding and it is challenging, but I don't think I would call it worthwhile. As Maths is something I am good at and enjoy, Maths teaching was the way I decided to go. Three of my colleagues started teaching at a similar age.

    It is much easier to do a job like teaching with finances already in place. I had never been into the investment banking lifestyle, so I don't miss the money very much. It is also great to have a job where I can be home by 4.00 pm, even though I have work to do, and to be able to enjoy the long holidays with my wife and daughter.

    So, JB, if you really want to go for Investment Banking, then do it. Be warned - it is hard work, and tough to get into. I recall my company having over 1000 applicants for 3 graduate trainee positions. I was involved in interviewing the final 24, and I picked the one I thought to be the best mathematician to work in my department (Global Bonds).

    You will also find that the field develops at a rapid rate - anybody who won't look at new ideas will fall by the wayside. That is where a good mathematician has an advantage - we can analyse a situation objectively rather than being swayed by a good salesman. With a PhD, you may want to look at working in a very specialist field, such as esoteric derivative products. That (or trading) is probably the best place for somebody who finds it hard to be nice to people they don't respect.

    There is little arguement about who is doing best - money talks. I was an investment manager, and my performance was assessed by how did my funds do against their rivals and how many revenue generating clients I could win or keep.

    I'm now very happy doing what I do, with a good school, great colleagues and the satisfaction that I am helping students learn skills for life. JB, I hope that you do end up with something you can really enjoy, preferably with colleagues you can respect. Good luck.
  6. paradoxism

    paradoxism New commenter

    JB - I am interested in your method. Just wondered - if you do these classroom tests and homework etc what do you then do if they have NOT understood and have failed to apply the method correctly?
  7. weggster

    weggster New commenter

    I'm now quite certain that Joseph Bloggs is actually someone who does use sound teaching techniques. I think all his posts are meant to be "Devil's Advocate" statements. Could it be he is really just trying to stir up discussion?

    I think that he probably never uses method method method techniques!

    Come on Joseph, spill the beans!


    ps hopefully he isn't really teaching the way he describes!
  8. weggster

    weggster New commenter

    Nothing beats good, inspiring teaching.....

  9. regards end of post 226:
    As ive said, in 2 school placements, my experiences from my school days and by talking to students from other schools i have no experience of maths lessons being different from:

    lesson objective
    here is how you do it
    do 10,0000 of them for home-work
    this gives me about 30-35 teachers i know teach this way!!!

    i was told, because i was training and felt i needed to tell them everything, that students should discover how to adapt the method by doing lots of questions.

    regards the pythag video: what is wrong with that? that is a lesson ive seen given!!! Would you let them draw and measure right angle triangles and see if they see the connection ?

    Im not agreeing with jb but trying to find out how you all differ.
  10. auntiemaisie

    auntiemaisie New commenter

    Mmmmmaths. thanks for your reply - way back on page 21! Our management insist on 'open access' so the best we can say is C at higher although we try to discourage all Cs and the B intermediates. We can insist on Higher next year but again Cs as well. I still think they are worse than they were - given that we've always had the same gate keeping. I am aware of GCSE papers and boundaries as we have several retake classes and rarely recommend that they can move on to AS.

    I was reading an article in MA News today and found this "The widespread perception is that best practice in teaching and learning is mutually exclusive with optimising module results". With the emphasis on results and their impact on marketing I think I'll just have to resign myself to bad practice!
  11. JB 1st

    'F'ool 'I'ncessantly 'R'anting 'S'upercilious 'T'ripe
  12. wrt posts 211-219 btw
  13. weggster

    weggster New commenter

    Re post 226

    The problem with the video method is that it shows no understanding of what is going on.

    Think of the example where you know the hypotenuse is 10m and the other two sides are equal to each other.

    There is no way to apply the theorem to this problem.

    However if you have spent quality time perhaps using Perigal's dissection (or even cutting up the squares on the sides of the triangles into cm square pieces) the students get a fuller idea of the ideas behind Pythagoras' Theorem.

    Students can then test whether or not a triangle is right-angled. They can allow some investigative thought into what other shapes would work (e.g. would semi-circles?).

    You can also apply thoughts on proof using angles, or area and algebra (Google a few!)

    I would not be best pleased if someone from my department was just teaching Pythagoras in the manner of the video (the video is a last resort revision bodge).

    Any fool can just teach method method method, it does not prepare students to think for themselves. They may as well go and memorise pi to 10,000 places.

  14. weggster

    weggster New commenter

    Should have read:

    "Think of the example where you know the hypotenuse is 10m and the other two sides are equal to each other.

    There is no way to apply the theorem to this problem." using just the video method.
  15. mathman64

    mathman64 New commenter

  16. Colleen_Young

    Colleen_Young Occasional commenter

  17. I like showing "the Pythagorean Theorem" using semi-circles, equilateral triangles too - make pupils think (and some teachers btw)
  18. JB ? in post 184 you correctly pointed out that I had mis-recalled one of your previous posts. Apols for doing so ? I hope you can appreciate that I was trying to defend anyones right not to reply to messages that contain personal abuse.

    To make sure I haven?t mis-recalled any other info I have quoted directly from our posts (clearly I have had to edit but I hope you will agree that the edits do not change the intended points).

    In post 184 you claimed to have answered my question regarding the source of statistics you have used. I fear that in the mass of comments and questions you have received regarding your opinions that you have mis-recalled the question I asked.

    In post 73 I said: ?Currently less than half of students who sit GCSE Maths gain a grade C or above in Maths. This figure has been an increasing one for many many years.?

    In post 83 you replied: ?Don't know where you get your stats from but everyone knows that results were better the further back in time you go - and the further back you do go the more traditional the teaching is.?

    In post 83 you also said: ?Please - you are talking to someone with science letters after my name (BSc, MSc) I know how to analyse data - the new stuff is failing us - the last 10 years it was introduced and results have dropped the last 10 years.?

    In post 101 I answered your question directly: ?I get my statistics from the Qulaifactions and Curriculum Authority who have responsibility for publishing the accumulated results for all the examboards etc. for every year. They are a publically accountable body through government and parliament.?

    And in the same post 101 I directly asked the question:?I suppose I should ask, in return, where do you get your figures as it'd be interesting to compare the sources.?

    I also said, in the same post: ?It'd be great if you could provide the sources of your data so we can compare.?

    And, further, gave some examples of the data available from QCA that I had at hand to show increasing results over the last 10 years or so (I had KS3 at hand and you mentioned in post 83 that results had slipped over the last 10 years).

    With due respect I don?t think your answer in post 184 answers my question (indeed it was just your question reflected back) at all: ?I did answer this. My own eight classes of over 150 pupils in total. Also the speaking to other teachers and combining results obtained by them with my own - thus increasing my sample size.?

    Clearly we are at crossed wires on this one ? I was asking for evidence for your statement hat results were better the further back you go. I thank you for the details about how you provided but think they were replying to somebody else.

    I very much doubt that I am going to convince you that teaching should be more than about teacher shows method and students practice lots or that you will convince me that helping students understand the methods they apply is wasted time so I think I'll let that one rest.

    I do, however, look forward to you providing the source of your statistics that back up your statements. I provided the source of stats to back up mine as you requested.

  19. Colleen_Young

    Colleen_Young Occasional commenter

  20. weggster thanks for the reply. I wish we had more discussion of this at teacher training.

    In response i would say your video tells that exactly what to do, if they can make the junp to forming an equation. This jump would be needed however you taught pythag surely?
    ie. let long side =10, other two sides are equal and unknown, call them ym and ym
    then from video, which tells us how to find a short side if we know another side and the hyp


    ah, ok im seeing this could cause problems if the video was all they knew because they would be looking to root the 10^2-y^2, but surely you would give them the good old the sqaure of the hyp is the sum of the squares etc first? I assumed so, if you were meaning the video would be all you gave i agree this would not be appropriate.

    I suppose this leaves us disagreeing on how to tell them a^2=b^2+c^2. I would demonstrate this then tell them this is how all right angled triangles work.Maybe giving a proof if time permitted.

    i did try the investigative route once, for circle theorems. It looked a very dry thing to tell them so i gave them sheets for them to draw angles,chords etc depending on the theorem and asked for them to see what they noticed. The result ? I had to end up telling them, not one could be bothered to do enough work to spot what was going on (top set y10 at a grammar!)


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