Why Math is considered more difficult that it is.

Discussion in 'Physics & Math' started by Dinosaur, Aug 30, 2017.

  1. Dinosaur Rational Skeptic Valued Senior Member

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    If you miss out or do not understand early math courses, you are very unlikely to catch up.

    The above is unlike many other subjects. Flunk an early course in ancient history due to immaturity or failure to pay attention & it will not keep you from passing a later course in European or American history. similarly for various other disciplines.

    Flunk an early mathematics course & you will probably flunk or have serious problems with later math courses.​

    Learning mathematics is a bit like building a pyramid or a house. Mess up the bottom layer or foundation & the building will probably collapse or be at best be an unreliable structure.

    Many intelligent folks fail to pay attention to early courses & never learn much beyond early algebra & perhaps never cope with early algebra at a level consistent with their overall intelligence.

    If you are capable of paying attention & are smarter than a high grade moron, you can learn mathematics thru at least the second year of college mathematics, assuming that you pay attention to the early courses.
     
    Confused2 likes this.
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  3. Geon Registered Member

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    Math is difficult though, not sure math is considered more difficult than it really is - I think the consensus of any ordinary math class at high school level will rate it as one of the most difficult subjects to keep up with unless you are pre-disposed to understand this stuff better than the average Joe.
     
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  5. spidergoat Valued Senior Member

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    Nope. I tried really hard to understand math and it didn't work. I got personal tutoring from a math professor.
     
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  7. exchemist Valued Senior Member

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    Yes, I think it comes a lot more naturally to some than to others. My son, seemingly quite bright and very interested in history, struggles still with algebra, at 14 yrs old. I hope he starts "getting it" soon......

    But I think too that mathematics requires a level of thinking in abstracts that some children cannot do until mid teens. I certainly found maths suddenly got a lot easier in the 6th form, even thought the topics were more demanding, because it suddenly started to make sense. I had grown able to think in the required abstractions, so things like complex numbers and conic sections made sense to me.

    And then I hit my mathematical ceiling at university, with the magnetic properties of molecules. Combining group theory, QM operators, Dirac notation and vector calculus all at once proved a bridge too far. But it was a hell of a ride while it lasted.
     
  8. iceaura Valued Senior Member

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    Some math is more difficult for some people at some times. It's not a unified, undifferentiated field of intellectual endeavor, even at fairly high levels.
    Example: The math tutors of my experience generally agree that comprehension of the formal concept of a limit requires, in some and probably most children, a stage of "physical" development of the brain/mind - that attempting to teach "real" calculus before that development has occurred is at best an inefficient use of time, and potentially even damaging.

    But the flip side of that is the development - it's not inevitable. Like the ability to throw objects, sing, dance, navigate, etc, childrearing matters. Human beings do not automatically develop.
    Factors:
    1) method of instruction - there are several different approaches, and results vary dramatically by child. One common neglect is physical manipulation - doing things by hand can make a significant difference.
    2) field - topology, geometry, combinatorics, graph theory, formal logic (approached as rhetoric?) can be taken a fair ways while what most high schools focus on as "algebra" waits for the stars to align. Can the kid play cards - physically, not on a screen?
    (And then Satan said: "Let's put the alphabet into arithmetic")
    3) background - a surprising (to me) fraction of children are saddled with holes, even crippling errors, in their basic elementary arithmetic. Check comprehension of simpler arithmetic - negative numbers, division, the ability to handle fractions; are you sure his early teachers could multiply and divide fractions themselves? Many cannot. This can matter, years down the road.

    Inexplicable difficulties with abstraction often stem from a hidden deficiency in the material from which abstraction is expected. People can't think unless they have something to think with.

    Just saying - what I've run into, over the years.
     
  9. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Imagine Newton thinking: Wait, wait, wait... I can explain this shit with math!
     
  10. sweetpea Registered Senior Member

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    And when he had worked it out, he stuck it in the drawer. It was only later when Halley ask Newton a question about orbits did Newton take it from the drawer.
    I think even Einstein had someone direct him to Riemannian geometry for his General Relativity.
     
  11. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Einstein was thinking more of James Clerk Maxwell, IMO.
     
  12. iceaura Valued Senior Member

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    One mathematician is no mathematicians.
     
  13. sweetpea Registered Senior Member

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    Perhaps, but he was at a loss to find a geometry to express his thinking, until directed to Riemannian geometry.
     
  14. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Maxwell united electricity and magnetism, yet he needed the speed of light to be constant for his equations to work.

    The constant was more my point.
     
    Last edited: Aug 30, 2017
  15. Confused2 Registered Senior Member

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    443
    My copy of Mathematical Methods in the Physical Sciences by Mary L. Boas (or the title at the time) went AWOL about 40 years ago - with hindsight one of my biggest mistakes in life was failing to replace it immediately. To this day I don't have a proper maths book. When involved in engineering my approach was to take maths from the shelf and put it back when I'd finished with it. This approach has left me with a whole mountain of maths to climb before I can even start to understand modern physics. I was kind'a hoping rpenner would write the maths book - but for me I fear it will come too late.
     
  16. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Know what you need: calculus, linear algebra...? Take a math course?
     
  17. Michael 345 Valued Senior Member

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    I recall some years ago the Quisener sticks were all the rage for young kids. I think the idea was to teach kids concepts of mathematics early
    Never hear of them now
    Kids apparently don't pick up concepts until a certain age by which time they don't need sticks
    The spelling of the name may not be correct

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  18. exchemist Valued Senior Member

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    Yes a lot of truth in the last part. My son somehow missed the bit in which one learns simple arithmetical additions and subtractions, e.g. knowing that 8 + 6 = 14 without counting on your fingers. He caught up eventually, but it was a surprising struggle. He's good at geometry, including trig, and fine at probability and arithmetical problems, but with algebra he's a rabbit in the headlights, unless you give him simple procedures to apply, which he can then execute. He has no feel yet for how it works.

    He is also cursed with appalling carelessness: silly mistakes all over the place. I hope that is a puberty thing and will go away, but I'm having to read him the riot act about it, because it is starting to matter.
     
  19. QuarkHead Remedial Math Student Valued Senior Member

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    exchemist - if your 14 year-old son is anything like I was at that age, his main interest will be in calculating how to get inside a girl's pants (or girls' pants, if you see the grammatical difference)

    One strategy which is sure to fail is "I am a whizz at maths, so get your kit off"

    But seriously; mathematics is, in my opinion, generally poorly taught in schools and universities. For example, I came to category theory (which is the attempt to find a common "language" for all branches of mathematics) very late in life. If I were to teach an introductory course in mathematics, that is where I would start, (and I know of no professional mathematician who shares this view.) But this requires a certain logical maturity, .

    Not to mention a certain detachment from the inside of girls' pants
     
  20. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Just make math fun.

    :EDIT:

    I feel I should've posted "have" than "make".

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    Last edited: Aug 31, 2017
  21. Walter L. Wagner Cosmic Truth Seeker Valued Senior Member

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    The only sticks we had were slip-sticks, which no one uses anymore.
     
  22. exchemist Valued Senior Member

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    Er well we haven't really got into all that too much just yet. He's more preoccupied with Roman war games on the computer. The girls will have to wait another year for his full attention, I think.
     
  23. Geon Registered Member

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    190
    The battle between mathematics and reality, is matter of evolution and cruel game of thrones

     

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