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? :hi
Do not all of these appear figural vis-a-vis a grounding frame of cognition, emotion, (re)action?
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.
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
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?
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
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.