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how does a maths degree relate to the national curriculum

Discussion in 'Mathematics' started by dkelly000, Jul 12, 2012.

  1. hi could anyone help me answer this question above, how does a degree in maths relate to the national curriculum? i have my interview next week and would like be as well prepared as possible. so far i have thought:
    maths is a core subject it can be used and be related to other subjects e.g science, geography, technology and home economics.
    it can help in everyday life from counting change in a shop to looking at train times for example.

    am i on the right lines?
    thanks
     
  2. afterdark

    afterdark Lead commenter

    Why should it?
    The national curriculum leads to GCSE level. This is preparation for A level. A degree in mathematics is a higher level of study than A level.
    <u>Having</u> a degree in mathematics <u>should</u> give you a better understanding of how interconnected topics in mathematics are actually more connected.
    Also it should help you to better understand misconceptions and how people manage to get by with faulty understanding of particular rules.
    Having studied the bootstrapping methods in which sublime mathematical ideas are built up you should be able to start this same process with the knowledge base that children arrive in school with.
    A degree in mathematics relates to school mathematics in much more profound way than the national curriculum does.
    The national curriculum is a very poor system of trying to measure pupils progress in schools. It has been subject to constant change and lacks substance.
    O yes, everything is dumped into mathematics.
    Practical mathematics skills such as basic numeracy is assumed as given when taking a mathematics degree. It is expressly taught at certain points in the schooling system.
     
  3. PaulDG

    PaulDG Occasional commenter

    I just don't know that that's true - if anything, I'd expect the opposite to be true.

    Maths graduates are people who, well, generally found school-level maths p*ss easy. Nothing they ever met at school ever gave them (us!) any issues.. OK, there might have been times in A level when they had to do some work, but concepts never bothered them.

    Does being able to prove that 1+1=2, to form and solve higher level differential equations, to prove endless trigonometric identities actually help when trying to explain fractions to a 14 year old who, after 6 years of doing them still doesn't "get" that the demonimators must be the same before fractions can be added?

    That "ab" always means "a times b" and never means "just write the numbers one after the other"?
     
  4. frustum

    frustum Star commenter

    I think that having struggled with maths at university gives me a better understanding of the problems the 14 year olds are having - and that's something A-level didn't provide! It also taught me a bit about breaking problems down to find the stumbling block, which probably helped in learning how to break down things that I never needed breaking down when learning them myself.
    I've studied a pile of OU courses over the past few years, and interestingly, the one that has proved the most use in the maths classroom so far was "Introduction to Health Sciences".
     
  5. There are teachers with good degrees who make poor teachers. There are teachers with poor degrees that make good teachers.
    I believe there is nothing wrong with striving to have both.... to both be able to put your subject matter across effectively and to understand it in a deep and meaningful way.
    Firstly, how can students be correctly prepared and taken through A Level mathematics (especially Further Maths) without a sound understanding of the principles involved and an appreciation of the wider use of mathematics?
    If we take the example of fractions, it would be nice if a teacher who fully understands the concept can get across to the student WHY the denominators have to match, rather than turning the whole of two key stages into a "memorise this algorithm to get by" approach.
    While this in itself may not need a degree in maths to understand, generally in my experience, the teachers with a better class of degree are able to explain this aspect in a more mathematical and more meaningful way.
    I myself often have to resort to the "just do it this way and trust me"...but wherever possible I would like to think that students can have access to the reasons behind the things they use, their use and application, and sometimes that takes a very broad and deep knowledge base to be able to put across.
    Why is a negative number multiplied by a negative number positive?
    Why is inverse sin written like that?
    What does sin mean anyway?
    Do quadratics always have two solutions?
    Why is division by zero not 'allowed'?
    All these and more are very common questions from maths students that, you could argue, requires a reasonable level of higher education to both understand and explain in a manner they can understand.
    (but yes,... for me I want to see the teacher teach.. how they do it.. what they say.. how the students get on... then we can worry about silly bits of paper that say what qualification you have, if any)
     
  6. Really and really?
     
  7. i think maybe you have misinterpreted the question, "how does your degree relate to the nation curriculum?" and my degree is in maths. its for a pgce interview next week.
     
  8. PaulDG

    PaulDG Occasional commenter

    I don't know (as it is clearly out of place with the way we write "sine squared"). Why is it?

    (It used to be called arc sin when I were a lad..)

    I don't know that either. It's short for sine, but what it means*? Do you have the answer?




    *As in I know what a periodic function is, OK.. I assume you're on about the origin of the word. That I don't know (but am interested to find out.. I love "history of maths").
     
  9. PaulDG

    PaulDG Occasional commenter

    No, that's not the same question.

    It sounds like it's a "standard question" - Initial Teacher Training providers have to satisfy themselves that your degree has at least 50% (I think) of its content in the National Curriculum subject that you're training to teach.

    As yours is actually a maths degree (and not, say, an engineering degree, an accountancy degree, etc.), then it really shouldn't be hard for them to convince themselves at least 50% of the content was, well, maths!
     




  10. As I understand it, it comes from several translations and a mistranslation (Wiki says Sanskrit to Arabic, and Arabic to Latin), where essentially the word for "half a chord" got lost along the way.



    At least that relates the function to a chord which can then be explored in terms of the history of maths.



    Arcsin is a very common way of expressing the "inverse" function (which is related to working out the angle of a sector or arc in radians)..



    The notation for sine, inverse sin, sin "squared" etc. is a mish mash of historical accident and can be very confusing for a student... it mixes up exponentiation, function notation and historical "ways we used to do it" ...



    This could also (for A Level students) lead to a discussion why we call the inverse of hyperbolic sin, arsinh and not arcsinh...



    I think it is reasonable to expect a GCSE Maths teacher to be able to tease out problems with misunderstanding the notation and honest questions as to why we write things that way and so a reasonable background in the mathematics behind that could come in useful.



    From Mr Gove
    "We still send powerful signals throughout our education system that it?s somehow acceptable to give up on maths. Critically, we allow students to abandon any mathematical study after 16, in stark contrast to other developed nations."



    If we had more teachers who had studied maths at the highest level in schools perhaps they could impart some of that great enthusiasm to their students and show them a pathway forward and hint at the wonders of higher mathematics.



    And saying so in an interview and showing directly how your mathematics degree prepares you very well to teach mathematics as well as appreciate a wider view of the curriculum and development of young people cannot do you any harm surely?
     
  11. afterdark

    afterdark Lead commenter

    I don't think that this is true. Just becuase someone got a degree in mathematics I don't think that means that they didn't work or automatically [or even generally] found A level super easy.
    I take it that you didn't understand my comment about bootstrapping then?
    Your point being?
    Actually Paul you wrong here. When a and b are both function ab means functions b followed by function a on that result.
    This leads onto your comment about function notations for trig.

     
  12. afterdark

    afterdark Lead commenter

    hear! hear! quite so.
     
  13. afterdark

    afterdark Lead commenter

    sin to power neg 1 comes from function notation.
    for function f() ...f power neg 1 meansthe inverse of f()
    f power 2 is function f performed twice
    sin power 2 is index notation meaning multiply
    Superscripts can be confusing, especially to those that have not studied maths beyond A level.
     
  14. afterdark

    afterdark Lead commenter

    sorry DazzaD I think I just repeated you.
     



  15. I have been genuinely asked many times...not just from A Level students.




    Surely notation, although 'trivial', is actually key for students who wish to score well in an exam?




    Not underlining matrices or vectors? Not being careful with the order for composite functions? not correctly writing the working out for trigonometrical operations? not understanding why we write differentiation as we do with regards to say, the chain rule? not understanding the difference between an equation and an identity? etc





    Perhaps I have too much of an obsession with trying to get across the background, reasoning and 'meaning' of each topic... Of course many a GCSE student could not care less about what sin means, where it comes from, what it does, as long as they can grab the marks in the exam...





    Unfortunately I have a (potentially bad) habit of trying to make sure they understand each and every nuance (or at least a chance to ).. I would LIKE to think it is a symptom of my passion for my subject and my excitement and willingness to share that passion...maybe it is just a very effective technique for getting students to sleep





    :)
     
  16. DazzaD
    I cannot believe with all the cool things kids could ask about maths they would ask where certain notation comes from and what it means.
    They may ask how to write it in a an exam but to be interested in why? I simply cannot believe.
    Many pupils want to know if its cm or cm^2 for area lower down the chain but I doubt any will ever ask why you have a superscript 2 on the units.
    There is a difference (IMO) between kids exploring maths and being fascinated and asking questions that simply dont need to be asked. Pupils might be interested in why division by zero is undefined but not in the history of notation (IME).
     




  17. Mine do (well some of them) :)





    They also ask a million and one other questions too, dont get me wrong. They DO ask about notation a lot and so they should because when you are first learning a topic the notation can be confusing, or get in the way, or obscure the learning, or clarify what we are doing, or help to understand the links...





    I am not saying notation is the number one most important thing in the lesson but there is nothing wrong with exploring a little bit at a relevant point or when asked.





    I think a lot of it might be because of my teaching style (in maths and science). In my opinion I think it is a reasonable question to understand what the title of the chapter means when you are studying a particular topic ... so for instance, what does algebra mean? where does the word come from? what does it mean in modern maths? how does it apply to real life? I think these are reasonable questions you could expect an 'expert' on algebra to answer...





    Of course notation becomes more and more important as you delve deeper into maths.. take a high end research paper in mathematics and chances are the vast majority of people will see it as goobldegook because in the first instance the notation is inpenetrable. I just want to be wary that my students dont have that as yet another stumbling block in their education ..



     
  18. afterdark

    afterdark Lead commenter

    Never heard of a degree with a history of mathematics component?
     
  19. rich_m

    rich_m New commenter

    An understanding of maths to a degree level has proven useful at times for myself, particularly with top sets and enrichment type investigations/activities, but on the whole it isn't a great deal of use. A good A-Level knowledge and some motivation to close any gaps you have is enough.

    Due to a timetable "quirk" this year I've had a very good top set for an 80 min lesson before lunch, then for 30 mins following lunch (we have 100/110 min lessons), a peculiar time to try to utilise effectively, so on many occasions I've gone off-piste from the NC and explored some interesting (and sometimes less than useful) maths. Without a degree I wouldn't have the knowledge of these off-piste topics, and the challenge of explaining a higher level concept simply is something I really enjoy. Showing pupils where maths leads and where it is useful is something that they should have an appreciation of in my opinion.
     
  20. i'm lucky enough to work almost entirely off-piste, so the degree really does help
    b*gger all to do with the nc though
     

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