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Here Is How You Teach Maths!

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

  1. mmmmmaths

    mmmmmaths New commenter

    Post 186

    "You can't say teachers are responsible for their resulst and then tell them the way they must teach. If they are forced into it ............... then it is not their responsibility if the pupils fail. It is yours."

    I think that most posters here, even those who don't agree with many of your comments, will agree with this.

    I have seen change 'forced' upon staff and no, it does not work.
    I have also seen good leaders encourage and support continued professionl development for the benefit of both the teacher and the learners.

    Just one question from me to help me to put all of your comments into context. What is the ability level at your school in terms of 5 A* to C, and the Maths department A* to C?

     
  2. alycatrow

    alycatrow New commenter

    He who knows not and knows not that he knows not, he is a fool - shun him!

    He who knows not and knows that he knows not, he is teachable, teach him!

    He who knows, and knows not that he knows, he is asleep, wake him!

    He who knows and knows that he knows, he is wise, follow him!


    I should be taught, many on here should be followed.

    JB should be......
     

  3. School 75%, Maths Department 80%

     
  4. maths126

    maths126 New commenter

    That's interesting. By the use of AfL throughout the Maths Department we were able to beat the school average by 15% (55%, 70%).
    I don't think we've been as low as FFT D for years...
     
  5. mmmmmaths

    mmmmmaths New commenter

    Thanks for your reply Granny but it was JB's school that I was interested in.
     
  6. weggster

    weggster New commenter

    I've loved reading this!

    I go for the understanding bit first, then use some method maths for students who are really not getting there near to there dreaded GCSE.

    I've got to admit they do tend to say "Why didn't you just tell us that way before?"

    Students today prefer just to "do the method" it fits in with the population's view that everything should be easy (whether it means getting qualifications, a job, fame, fortune, "respect" etc).

    By sticking to teaching the "trick" first it encourages less thought. You can either teach Pythagoras through some gorgeous maths (practically, geometrically, investigatively, algebraically etc) or just teach it the way I've done on the D grade help video

    http://one.revver.com/watch/197515

    Students, with no wish to think, will choose the video. As teachers we should be aiming for more than this.

    Think Plutarch:

    "The mind is not a vessel to be filled, but a fire to be kindled."

    I think that this should be displayed in all classrooms.

    Joesph Bloggs: I would hate you to teach any of my students! (and by the way my results have been excellent for 13 years, by teaching understanding)
     
  7. Weggster - a thoughtful post. The problem that teachers like JB have is an unawareness of the types of knowlegde taht are required as a teacher. You demonstrate this clearly in your posting.

    Although JB may well have deep subject knowledge, perhaps even evidenced by his first - who knows - who cares? - what he is unable to articulate is how he can use this knowledge and apply it and structure in teaching approaches that are useful and meaningful to students. JB - you might find the work of Lee Shulman of interest.
    The only approach that JB offers is displayed well in your video. This transmission approach is the simplest amnd least challenging for the teacher. It is also the least effective for the pupil - research has shown this.

    To engage pupils in coming to an understanding of Pythagoras through investigating algebraically or geometrically requires a different type of knowledge and far more sophisticated teaching skills than the crude transmission method method method JB recommends. JB has been unable to show that he is capable of moving beyond this primitive teaching mode.
     
  8. auntiemaisie

    auntiemaisie New commenter

    I've looked through these developing posts with interest - I've been educated too since I had not the slightest idea what AfL was! In colleges we don't seem to hear about these 'new' ideas. Happily, I find that I must be doing that OK as I write notes, suggestions etc on marked work. I'm not so sure about teaching style though as sadly I'm more of a methods person - perhaps it's an age thing? I would, however, always try to justify a method but as previously posted, students want the simplest route and if they find out that 'knowing the background or proof' is not required for an exam, then they switch off until the examples.

    One observation that I would make is that we take students from around 70 different schools and generally, year on year, we notice that they are less able to do things or have methods/ strategies to cope. If recent changes are having a positive effect, why are we not seeing them? Some seem to rely on intuition and lucky guesses to solve any equation, even the quadratic and linear type in C1 - a strategy unlikely to succeed when the answers are not integer. I like to think that I try to adopt different ideas and have used lots of suggestions from the forum but I still need convincing that solely teaching for understanding is (a) beneficial and (b) gets through the syllabus in time.

    PS. Educated at one of the first comprehensive school in the 60s!!
     
  9. Auntiemaisie, you said:
    "I still need convincing that solely teaching for understanding is (a) beneficial and (b) gets through the syllabus in time."

    In what way can ensuring that pupils are making sense of their learning not be benficial?
    Your statement suggests that it doesn't matter if pupils understand.

    Similarly your comment about the syllabus: as long as this is delivered like pints of milk obn a doorstep then you have done your job.

    You have answered your own question when you said that students rely on 'lucky guesses and intuition'. If pupils are reliant on a single fixed method (method method) and then forget a single step in the procedure they are up a gumtree. They have no back up strategy or ability to investigate mathematically. This is what you are currently encountering. Read Weggster's post again, he also explains this.

     
  10. auntiemaisie

    auntiemaisie New commenter

    Ragpicker, you have misunderstood me slightly. I am being critical of incoming skills from school which rely on guesswork with no underpinning algebraic skills - an ever increasing number of students arrive from year 11 unable to solve linear equations, factorise etc etc. They don't know a method but they also don't have a strategy - my question really was that if schools are doing their best to give understanding, why are colleges not seeing an increase in students' ability to cope at AS level. I did read Weggster's post and was agreeing that students seem to prefer a method, we can't cover all the syllabus (including the missing algebra!) in the time we are allowed and in the end compromise understanding. In an ideal world I would love to explain and investigate everything but our 'customers' would rightly complain if we had not delivered all the syllabus before exams - and like it or not, we are unfortunately driven by results.
     
  11. mmmmmaths

    mmmmmaths New commenter

    Hi Auntie.....

    What grade do they need to have at GCSE to get onto your AS course?

    Can they have achieved this at Intermediate?

    Will you let them take AS next year with a grade C from a foundation GCSE course?

    Pupils can get B grades with very little algebra.

    I have taught A level in the past so my higher groups are taught to prepare them for A level.

    I could teach them much less of the algebra content and get them to GCSE A grade standard.

    Get hold of last years exam papers and the grade boundaries then have a look what your struggling pupils could have missed out or got wrong to achieve their GCSE grade.

    I think you will realise that it isn't how it is taught at GCSE but how GCSE grades give you little information about pupils algebraic understanding.

    Our better post 16 providers are now telling our Y11's at open evenings to get an A grade in Maths if they want to take it further.
     
  12. THINGY SAID...

    Hello all, I have sneaked on here from the Primary Forum. I'm a primary teacher teaching year 6, I'm a Lead Maths Teacher in the County, I have a second class degree, I'm part of the Senior Management Team, I am also part of a team promoting Assessment for Learning in other schools.

    Ha - typical - exactly my point - losers get those kind of posts. I am beginning to think that there are so many teachers out there with low qualifications that they don't like promoting people with good qualifications to "keep it in the family" as it were or "get their own back on those they knew at university in those bad times when they couldn't compete and who they envied so much".

    Here is an example. She said I don't care about children. Are you deaf - it is you lot spouting about AFL BTL JCB KGB and god knows who don't care about anything but your career.

    I want my kids to do well in exams and get got jobs and teaching method does that. I am living proof. I COULD NOT LEARN other than method. When I had teachers like you I struggled. I could be on the DOLE right now - instead I am one of the most qualified on this whole site. THANKS TO METHOD TEACHERS.

    So I will follow that apporach - and miss - my kids will get better jobs thah yours ever will. They will have what a second class graduate lacks - EMPLOYMENT POWER!
     
  13. WHATS-HER-NAME WROTE...

    I sincerely doubt whether you'll take my advice because I only have a second class degree,

    YEA - Couldn't have put it better mysefl love.

    P.S - I have nothing against primary teachers - why would I? Do secondary think they are better or something.
     
  14. DEAR Piranha....

    You said you have had a successful career in INVESTMENT BANKING.

    Why did you leave - can I ask. It is an area that maybe once I have my PhD I may move into.

    Yes everyone - I have a tick box of what I want out of life and a PhD will come sooner rather than later if this teaching continues to go down the pan and I don't meat any inspiring teachers soon.

    But after that - hey - investment banking sounds good - sounds like money there.

    If I am talented - and wasting my time talking to brick walls in teaching - maybe I should use my abilities in something worthwhile and something challenging.

    And info would be useful. If you don't mind sharing that is.
     
  15. whats-his-name said soemthing like "prove to us you can whip Andrew thingy who proved Fermats thing.

    I never said that. I said "But I could whip a Oxford or Cambridge maths grad anyday."

    I.E - A grad with a BA - not one that has done a PhD and research silly.

    I don't have a PhD (yet) - so how can I be better than them. They are like - WOW - up there to me.

    Hope to join them soon though.
     
  16. ragpicker...

    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.

    ANSWER:

    Easy - Questions in class - homework - tests!
     
  17. a poster said.....

    He who knows and knows that he knows, he is wise, follow him!

    I wonder if that applies to me. Let's see.

    He who knows (yep - me - 1st class degree) and knows that he knows (yep - always talking about it - as you lot have said) he is wise (oh thanks) follow him!

    Cool post - thanks.

    I take it you agree with my desire to get top grades and the methods used.
     
  18. Joesph Bloggs: I would hate you to teach any of my students! (and by the way my results have been excellent for 13 years, by teaching understanding)

    yea but they could be even higher if you use methods!
    JB
     
  19. AUNTIE SAID...

    students want the simplest route and if they find out that 'knowing the background or proof' is not required for an exam, then they switch off until the examples.


    Yea - that was me at school. And I went on to get - well we all know - so therefore the methods were correct.
     
  20. THE SOLUTION THEREFORE ON HOW TO TEACH MATHS IS..........

    1. TEACH METHODS - IT GETS THROUGH THE SYLLIBUS - AND THE PUPILS HAVE A STRATEGY FOR THE IMPORTANT EXAMS.

    2. THEN TEACH "HOW MATHS IS DONE" AND ALL THE "SWITCH OFF" AFL VAK ETC STUFF NEXT IN THE TIME REMAINING. IF PUPILS SWITCH OFF NOW IT DOESN'T MATTER BECAUSE THEY ALREADY HAVE THE KNOWLEDGE. THEY CAN HAVE A BIT OF A REST NOW ANYWAY AS THEY HAVE EARNED IT.

    3. IN THE LAST WEEK OR SO GO BACK THROUGH REVISION OF THE KEY METHODS. REFERESH MEMORIES ON THE IMPORTANT THINGS YOU NEED FOR THE EXAM.

    THAT'S IT! PASS - BE HAPPY - EARN MONEY - AND RESPECT (OR DISRESPECT DEPENDING ON WHAT PEOPLE YOU DEAL WITH - BUT AT LEAST YOU WILL HAVE THE LAST LAUGH - LIKE ME!)
     

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