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  1. #81
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    Quote Originally Posted by BlueGray View Post
    In terms of practical applications I think it goes Linear Algebra > Calculus > General Algebra as the most useful.
    Most useful irrespective of context or application?

    This person's `use' is apparently gainful employment as a tutor.
    Thus, the most useful math IS the kind someone wants to remunerate her for tutoring, mentoring, facilitating, etc.

    So for her I might want to know the age range of her students/tutees and what they are willing to pay her to learn.

    Unless I missed my mark and she is tutoring for the love of that form of interaction irrespective of remuneration or the well-polished apples they may be bringing her.

  2. #82
    Senior Member BlueGray's Avatar
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    By most useful I meant in terms of widespread practical applications.
    Ne > Ti > Si >> Te > Se >> Fe > Fi > Ni
    5 so/sp
    Chaotic Neutral/Evil

  3. #83
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    Default Applied mathematics -- Applying math towards maximizing profits for NF math tutors

    Quote Originally Posted by BlueGray View Post
    By most useful I meant in terms of widespread practical applications.
    Yes, I got that.
    I was trying to re-steer your problem-solving mind in the direction of helping her exploit the information embedded in the opinion you expressed.

    Do you suppose that if she placed each type of math she is considering adding to her repertoire of tutoring skills in a set, bin, knapsack, vector, array, or list that some math could be applied towards optimizing for targeting which math skills to acquire pursuant to maximizing her income from tutoring?

    Do you suppose a minimax algorithm could be developed to help her exploit math in ways other than tutoring others?
    Minimax - Wikipedia, the free encyclopedia

  4. #84
    Reptilian Snuggletron's Avatar
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    Quote Originally Posted by MagnificentMind View Post
    This.
    That.

    An ENTP I know struggled as hard as me in geometry, which is pretty bad. He's a decent writer though. The most INFP ENTP I know.

  5. #85
    Energizer Bunny Resonance's Avatar
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    I love math! But... I am not as good at calculus as I was at the easy stuff like (high school) algebra and arithmetic.

    All the NTs I know irl are better at math than me

  6. #86
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    Default Re-thinking and reframing math qua `math'

    Quote Originally Posted by Blairvoyant View Post
    I love math! But... I am not as good at calculus as I was at the easy stuff like (high school) algebra and arithmetic.

    All the NTs I know irl are better at math than me
    Have you ever considered re-framing so that your word-based cognitive processes can be better used to `do' calculus and math in general?
    Reframing - Wikipedia, the free encyclopedia

    Or how about extending what you learned in `the easy stuff' algebra into algebraic -- word substitution -- algorithms which might be evolved into those capable of doing calculus?

    Here's an algorithm I composed and presented to another group:
    Algorithm - Wikipedia, the free encyclopedia

    (string-append
    "Does "
    "this "
    "qualify "
    "as "
    "a "
    "sentence "
    "in "
    "the "
    "language "
    "of "
    "the "
    "English"
    "?"
    )


    This can be tested without installing an app by inserting them into the web app called TryScheme: Try Scheme

    To verify that this works as advertised all one has to do is insert the symbolic expression of interest into the text box located at the lower left corner then click on the `scm' button. note: the symbolic expression starts with the `(' and ends with the `)' above

    I suppose the point I am attempting to make is that non-NTs can do better if they re-frame mathematical problems into forms their minds process better than conventional notations -- mere surface structures, actually --used by mathematicians.

    Transformational grammar - Wikipedia, the free encyclopedia

    As an iNtuitive I'd expect you to be better able to wrap your mind around the core semantic relations of a sentence than the squiggles (mis)used by mathematicians.
    Math too is about semantics -- meaning -- and relationships.
    If you make it about what your mind finds interesting and significant then said mind will serve you better towards the ends of `doing' or using math, IMO ... FWIW

  7. #87
    Senior Member paradox fox's Avatar
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    Feelin' mathy

    I'm trying to make a career out of tutoring, but I'm not just in it for the money. I thoroughly love it. Interacting, making it fun, finding the strengths of my students and watching them grow. Showing how wonderful learning is... it's very fulfilling work.

    My age ranges right now are 6th-10th grade, so 12-16 years old. It's mostly been remedial work, haven't yet worked with students who want a special challenge. That would be fun, have them do lots of great projects.

    I'd do SAT tutoring, I'm good at test-taking, but I haven't taken the SAT so I'm in no position to tutor for it. Lol. No idea what's on the test.

    Anyway. Ran out of words to say.
    Just because I'm an INFP doesn't mean I'm emo!

  8. #88
    Energizer Bunny Resonance's Avatar
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    Quote Originally Posted by gps View Post
    Have you ever considered re-framing so that your word-based cognitive processes can be better used to `do' calculus and math in general?
    Reframing - Wikipedia, the free encyclopedia
    I'm not sure what you mean by this... it seems like the article is mostly about 'looking on the bright side' which...yes, I do a lot, but I don't see how it helps with math...

    Quote Originally Posted by gps View Post
    Or how about extending what you learned in `the easy stuff' algebra into algebraic -- word substitution -- algorithms which might be evolved into those capable of doing calculus?

    Here's an algorithm I composed and presented to another group:
    Algorithm - Wikipedia, the free encyclopedia

    (string-append
    "Does "
    "this "
    "qualify "
    "as "
    "a "
    "sentence "
    "in "
    "the "
    "language "
    "of "
    "the "
    "English"
    "?"
    )


    This can be tested without installing an app by inserting them into the web app called TryScheme: Try Scheme

    To verify that this works as advertised all one has to do is insert the symbolic expression of interest into the text box located at the lower left corner then click on the `scm' button. note: the symbolic expression starts with the `(' and ends with the `)' above
    Again, not sure what you mean... word substitution? Like 'Soh Cah Toa' and one d two plus two d one..? Derivatives and simple integrals I'm ok with, but when it comes to the more complicated integrals where it's not quite clear what to do, that's when I start to get stuck.

    I'm pretty familiar with computer code and syntax.

    Quote Originally Posted by gps View Post
    I suppose the point I am attempting to make is that non-NTs can do better if they re-frame mathematical problems into forms their minds process better than conventional notations -- mere surface structures, actually --used by mathematicians.

    Transformational grammar - Wikipedia, the free encyclopedia

    As an iNtuitive I'd expect you to be better able to wrap your mind around the core semantic relations of a sentence than the squiggles (mis)used by mathematicians.
    Math too is about semantics -- meaning -- and relationships.
    If you make it about what your mind finds interesting and significant then said mind will serve you better towards the ends of `doing' or using math, IMO ... FWIW
    Well.. I took a course on semantics this year and I don't think that's where my problem lies (drawing the tree structures wasn't difficult.) I'm ok with understanding the symbols and relations according to the notation, it's just a matter of knowing what to do to solve it...

    Thanks for the suggestions, anyway I'll keep looking into them.

  9. #89
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    Quote Originally Posted by Blairvoyant View Post
    I'm not sure what you mean by this... it seems like the article is mostly about 'looking on the bright side' which...yes, I do a lot, but I don't see how it helps with math...
    Okay, I'll accept your bright-side `half full' example as a starting position.
    Let's say you're an average American, capable of reducing any number of actual possibilities into a 1-bit false dichotomy:
    You can would-be `think' in terms of Democrats and Republicans, Liberals_and_Conservatives, Right_and_Wrong, Right _and_Left, Male and Female, Black and White, Good at math and not-so-good at math, Optimists and pessimists, Good AND Evil,
    Go(o)dAnDevil, map and territory, Half empty OR half full.



    Having bifurcated the infinite into two false-dichotomous `frames', your `looking on the bright side' might be tantamount to framing `the issue' as an Optimist noticing how full the proverbial glass is -- merely seems, really -- rather than a pessimist noticing how empty.


    As an enneagram 5w4, a male, A crab, someone born in the year of the monkey, blue-eyed, brown-haired, an NT good-enough-at-math-reframing, an INTP -- pick whatever set of attributes or influences you'd like to attribute this too -- I've noticed that re-framing and bisociation SEEM related -- The Act of Creation - Wikipedia, the free encyclopedia -- and that bisociation can work with those who have bifurcated the infinite into two branches ... two frames within which to frame what is figural for them vis-a-vis figure-ground cognition and figure-ground reversals:
    Gestalt psychology - Wikipedia, the free encyclopedia
    Figure-ground (perception) - Wikipedia, the free encyclopedia
    Figure-ground in map design - Wikipedia, the free encyclopedia
    Map–territory relation - Wikipedia, the free encyclopedia

    How might reframing related to math or those doing mathematical processes?
    How might a method used for enriching or context-switching-out-of one's impoverished mental model or mindset help with attitude and behavior regarding math?
    Ref: Mental models Models - Psychology Wiki

    Does math entail or require the modeling, (re)framing, or representing of `a problem' pursuant to generating one-or-more solutions?
    What about identities, relations, and relationships ... the stuff of both mathematics and the prevailing mentality of NF Flakes? (You still paying attention Elaur? )
    Do not all of these appear figural vis-a-vis a grounding frame of cognition, emotion, (re)action?


    Quote Originally Posted by Blairvoyant View Post
    Again, not sure what you mean... word substitution? Like 'Soh Cah Toa' and one d two plus two d one..?
    Sure, I can mean that ... and other concepts blendable confluentially, concurrently.
    Algebra was originally done with whole words ... back in the days when there was precious little difference between
    algebra and algorithms.

    Words were substituted for `something else' ... used as symbols.
    Then algebraist started abbreviating ... reducing words down to single glyphs as symbols.
    Substitution is still part and parcel with Algebra, no?
    One does the symbol manipulations then typically substitutes numerical values in for the symbolic place holders -- so-called `variables' -- for such numbers ... such identities.

    Quote Originally Posted by Blairvoyant View Post
    Derivatives and simple integrals I'm ok with, but when it comes to the more complicated integrals where it's not quite clear what to do, that's when I start to get stuck.
    I love derivatives.
    `Ridiculous' was derived from `ridicule'.
    Ignorance was derived from `ignore'
    `Stupid' results from stupefaction and seems functionally-equivalent-to or
    one-to-one-and-onto with `stupefied'.


    And `trapped in a metaphor' results-from -- is derived from -- the (mis)use of metaphor ... of a cognitive framing which one's brain automagically `stays between the lines', stays framed, bounded, straight jacketed, hobbled, and/or hand cuffed.

    I love integrals and integration too.
    Joseph Campbell's
    Joseph Campbell's 3rd and final phase of his Heroes Journey entails `integration' ... becoming whole, at-one, atoned ... `integrated', if you will.
    Monomyth - Wikipedia, the free encyclopedia

    Quote Originally Posted by Blairvoyant View Post
    I'm pretty familiar with computer code and syntax.
    Oh ... which computer codes?
    Machine codes ... represented in binary, octal, or hexadecimal?
    Assembly language codes and mnemonics?
    Medium level programming language codes such as those of C or Forth?
    Higher level PL codes such as APL or a dialect of Lisp, such as Logo or Scheme?
    How about the nested parentheses employed by both Algebra and Scheme ... can you evaluate innermost parenthesized expressions before using the results in the next outer-scoped parenthetical context of evaluation?

    Quote Originally Posted by Blairvoyant View Post
    Well.. I took a course on semantics this year and I don't think that's where my problem lies (drawing the tree structures wasn't difficult.)
    I'm ok with understanding the symbols and relations according to the notation, it's just a matter of knowing what to do to solve it...
    Right ... what to do to solve it.
    If the problem posed IS that the glass IS half empty the person grading the solution you present on a test may not accept the answer of `half full' as the solution.
    Such a would-be `solution' would constitute a simple reframing of the problem which would be tantamount to a tautology.
    Tautology - Wikipedia, the free encyclopedia

    Thus reframing might help if it helps get one unstuck from a mental model which doesn't get the metaphorical problem-solving squirrel in one's cranium to the bird feeder.
    Lateral thinking - Wikipedia, the free encyclopedia

    Quote Originally Posted by Blairvoyant View Post
    Thanks for the suggestions, anyway I'll keep looking into them.
    You're very welcome ... well-received, well (re)framed.
    I have plenty more suggestions at the ready.
    Feel free to interact with me via thread, visitor message, or private message ... as the spirit moves you.

  10. #90
    videodrones; questions Verfremdungseffekt's Avatar
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    The system is simple enough. It's the details that trip me up, every time.

    I'm fine with the theory of math; I'm useless at the mechanics of calculation and memorization. It's that I simply do not multitask. As soon as I switch from one thought to another, the first thought might as well never have existed beyond a vague sense of emptiness that it leaves in its wake. Which makes any kind of rote processing kind of a hell for me.

    Say we're multiplying six by nine. Okay, great. Multiplication. Of nine. By... what, again? Nine by what? Oh, six. What about six? What are we doing with it? Dividing it by nine? Nine... wait. We're multiplying, right? Or... which problem am I on?

    Though curiously enough, I'm fine when we take away all the numbers and it turns into pure reasoning. Give me an alphabet soup, and the logic may just be broad enough that I can provide you an answer.

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