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Nation of One

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How the ego interferes with learning
« on: May 02, 2017, 01:37:14 pm »
If you follow me along this humble path, I would suggest keeping your interests as private as possible to avoid being mocked by blockheads who have no understanding of what compels you to study what you do in the first place.  Also, there are times when this approach can make you wish you were dead, if for no other reason than there is certainly no reward to motivate you to stick with it.   

I may be between a rock and a hard place, since this kind of obsessive studying may be the only thing motivating me to continue to abstain from imbibing alcohol, and on the other hand, there are moments I would not mind if the earth were struck by a giant asteroid.

A certain degree of privacy allows you to individualize your personal re-education in a manner outside the metrics of society and academia.  It is difficult for me to articulate the psychological complications involved that may serve as an obstacle to learning and self-study.   

The ego may be more gratified struggling with something more advanced, whereas the ego may suffer when it is forced to witness "the brain" having to equally exert itself to think about problems the ego demands "should come easy."

I will document this process.  The biggest challenge is overcoming the despair that might settle in should we come to seriously doubt our mental capacity.

In what post was it mentioned that the more we are able to courageously face "the feeling of stupidity", the more we will be able to truly learn?  If we cannot bear to face our "ignorance" or "the reluctance of our brains to engage in the act of thinking hard about something", then we will not attempt to remedy our ignorance out of this fear of seeing ourselves as "not so smart".

Not to brag, but I consider what I am doing to be a remarkable defiance of the tendency for "education" to make someone willfully ignorant.  Look at education geared to specialization.   Very often I suspect that formal education might give the graduate a false sense of mastery over a subject, and there is that intellectual snobbery which we witness, not just from others, but from within our very own brains when we restrict what we will study to "more advanced" subjects, and thereby depriving ourselves of any opportunity to revisit the subjects of our earlier school days.

Some of those subjects are fundamental. 

I won't go on and on about it, but please know that I do not feel any shame about revisiting the fundamentals.  In fact, my biggest struggle is with the ego, that is, facing the reality that most exercises require me to pay attention and to ... think ... and thinking is difficult, right?  Thinking becomes especially difficult if we live with the delusion that certain things ought to come easy to us, or that we are exempt from having to think too carefully since we have something called a "diploma".   Such diplomas do not exempt the holder from having to think about a mathematics problem just because that problem is in a high school text book.

In fact, some of the exercises at the end of the sections in certain high school text books may be more challenging than many of the exercises in certain college level text books, so, here again, Nothing that is so, is so.

I want to say right here and now that it may be Holden's radical honesty which has inspired me to revisit the fundamentals, and to learn how to relax with what Schopenhauer called the "difficulties of arithmetic".

I hate to use such contradictory language, but I think the key to nurturing the spirit of lifelong learning might involve allowing myself to feel more stupid.

I am not after any degrees or certificates.  What I crave now, more than ever, is understanding - and not only understanding, but the ability to exert however much mental energy as I have to in order to stretch this brain out of complacency.

Again I say that this may have more to do with psychology than mathematics itself.  I think I may be just trying to activate my brain, to let it know that it does not have to study a physics textbook in order to be challenged.  Maybe this is a psychological experiment to see if I can work through these texts without feeling that this is some kind of reflection on my aptitude.  It's a complicated experiment that is difficult to explain.  I suspect there are many who are in positions of authority, even academic authority who might be surprised how frustrating it is to try to learn something you're not interested in.   I am curious to see if I can muster interest.

And, you know, there are times when I feel guilty for even worrying about "self-education" when there are those begging for a fistful of flour.   I suppose it is a privilege and a blessing to be concerned with self-education.

Without the grocery stores and "money" for food, without a place to rest my head, I suppose this world is a nightmare.  And so, I do count my blessings and try not to complain too much about my so-called "struggles".
« Last Edit: May 05, 2017, 11:01:31 am by Raskolnikov »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

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Nation of One

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The Mortification of the Ego
« Reply #1 on: May 05, 2017, 09:41:23 am »
Holden,

Do you think that maybe this experiment in forcing myself to revisit what I supposedly studied in high school might be a kind of cleansing or mortification of the mind?

Unlike the study of advanced calculus, linear algebra, and physics, which might encourage delusions of grandeur, these studies are proving to be mortifying to my ego.

The level of difficulty is not the issue.  I only make myself do the more challenging exercises or else my ever so sensitive ego will start crying about how I am just wasting time.  I catch my brain saying, "Do I really have to take this seriously?"

It's as though my brain finds the thinking involved annoying.   And yet, there are those exercises which it finds challenging, and then "we" work together harmoniously, congratulating "ourselves" on having come up with the great experiment, which we call "The Great Revisiting" or "The Great Rebooting."

I think that there is some kind of internal battle going on inside my brain, where one part of the brain wants to mortify the other.  And what purpose would this serve?   Maybe a certain amount of inner harmony, where the ego is neutralized so that the brain can just get down to the business of thinking without any interference from the Social Ego.

Am I making any sense?

I suspect that very few people would be willing to (or even able to) do what I am doing.  I am not just talking about most people having other responsibilities, and therefore not having the time to embark on a complete revisiting of their high school math curriculum.   That goes without saying.   There are plenty who would advise me to "get a life," or, at the very least, "get a job!"

What I am saying is that I seriously doubt that once a "student" has reached a certain level in the academic/mathematical hierarchy, they rarely voluntarily return to material they were exposed to so many years ago.   They may find the material is not challenging enough, or that they lack the patience.

I must be some kind of freakin' weirdo!

What the fuuck is wrong with me, Holden?  Why would I put myself through this mortification of the ego?   Maybe I am banking on there being some kind of unexpected psychological breakthrough.

I feel like I am searching for the keys to my own brain, and that my humility will be rewarded with a deeper level of intimacy with how this brain works, as though I believe I will discover a state of mind that is not convoluted with notions of academic hierarchies or social status, but can learn to contemplate with a neutralized ego.

The point is that a certain amount of effort is required.  Why should this painful to the ego?  I underestimated the amount of humility I would have to muster for this experiment!  In order to continue I have to block out my own ego.  It gets in the way.  It prevents me from appreciating what the brain is up to.

My wish is to get along better with my own brain, to trust that it knows what it is up to, and not to fight its current obsession.  For whatever reason, it wants my ego to acknowledge the care and attention that is required even for less advanced mathematics.

Of course, if exercises are simple drills, I allow myself to skip them if they are too simple for me.  Why is this?  Again, the ego puts its foot down saying, "enough is enough, I have to draw the line somewhere."

There is a strong possibility that I am not right in the head.

My brain has told me that it is doing this because it is retraining itself. 

The brain is reconstituting.

Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

Nation of One

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Forum:  Why Mathematics?
Topic:  How the ego interferes with learning

Sub-title:  Revisiting High School Algebra and Geometry as a Psychological Experiment

I have noticed something about me when I look at the less complicated exercises in a high school algebra book.   I find that this somehow threatens my ego.  I initially solve the problem in some sloppy brute force manner, and more often than I like to admit, this sloppy "thinking on my feet" approach" leads to a wrong result.   The error is usually something stupid.

Then I give the exercise my attention, make use of a pencil and notebook, keeping track the thought processes in an organized, step by step manner, and the exercise becomes more interesting.  The power of algebra is better appreciated when I honor the exercise as worthy of my care and attention as opposed to behaving as some pretentious school boy who only does "big boy math".

Suddenly I realize that this experiment, "The Great Rebooting", or "High School Revisited", while it is related to my personal journey toward mathematical maturity, its central theme may have more to do with the psychology of learning and self-education.

I notice people who are enthusiastic about self-education when it comes to web design or programming "apps".  I suspect this is because it makes the learner feel they our gaining some kind of marketable skill.  In other words, web design, to them, just feels "sexier" than revisiting algebra, geometry, trigonometry ... or, god help us, "introductory analysis".

I'll keep you posted.  Maybe I can schizophrenicize this process by imagining the "overseer part of the brain" as Frankenstein or Doctor Faustus, and the "part of the brain that has to work through exercises and eat eggs" as "the creature".

 "How the ego interferes with learning" could be extended to "how the ego interferes with learning and thinking in general".

Also, by "ego", I suppose I mean "false consciousness".
« Last Edit: May 05, 2017, 10:11:40 am by Raskolnikov »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

Holden

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Re: How the ego interferes with learning
« Reply #3 on: May 05, 2017, 10:44:38 am »
Herr Hentrich,

Its a great privilege for me to be able to witness you effort to tame the ego. I hope to learn from your experience.
Please do keep studying mathematics. I would try out this experiment too. I believe that I am not studying mathematics as ,maybe,subconsciously,I want all of it come to me very easily.And when it does not,then instead of admitting the limitations of my own intellect ,my ego,wants to throw it all away.
La Tristesse Durera Toujours                                  (The Sadness Lasts Forever ...)
-van Gogh.

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Re: How the ego interferes with learning
« Reply #4 on: July 05, 2017, 09:56:39 pm »
FROM NOTES:

Wed 05 Jul 2017 09:41:11 PM EDT

Major Breakthrough

The way for me to construct a formal proof in geometry is to resist the mechanical tendency to start writing down statements and reasons, and to, instead, start by reasoning back from what I would like to prove.  Think, "This conclusion will be true if __?__ is true.  This, in turn, will be true if __?__ is true ..."

Sometimes this procedure leads back to a given statement.  If so, you/I/we have found a method of proof!

Now, I am not sure how anyone else feels about jotting down extensive preliminary work showing the details of their thought processes, but since I generally write for posterity, I would at least like to leave as much detail as possible to show the reader of my "mathematical diaries" what goes into the formal proof prior to writing down the very first statement.

I would like this to become a habit, a modus operandi which marks a turning point in my life.

And I would be pleased were the notes I leave to prove helpful to anyone who comes across my notebooks, even if that someone is a future version of me!
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

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I found a book which proposes injecting more integrity into early mathematics education.  This is a collection of three excerpts from the author’s book,Rational Numbers to Linear Equations (Amer. Math. Soc., Providence, RI, 2020):

Preface(pp. 2-21)
To the Instructor(pp. 22-37)
The Bibliography(pp. 38-42)

 What can we do about our dysfunctional school mathematics curriculum?

The text itself: Rational Numbers to Linear Equations by Hung-Hsi Wu.

Hung-Hsi Wu's homepage:  https://math.berkeley.edu/~wu/
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~

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Re: How the ego interferes with learning
« Reply #6 on: December 24, 2021, 12:18:39 pm »
I want to make it clear that I also very much respect what Hung-Hsi Wu is doing.  Maybe before we croak, Holden, we might start an open-air university - and we can choose Wu's Way, which reminds me of when mathematicians were asked to write the "school mathematics textbooks" ---- Yes, that what it is, but he is going about it in a more sensible manner, teaching the teachers in this manner.


From the section "To the Instructor" in Rational Numbers to Linear Equations:

Quote from: Hung-Hsi Wu
At this point, we return to the earlier question about some of the ways both university mathematicians and educators might misunderstand and misuse these three volumes.

Potential misuse by mathematicians

First, consider the case of mathematicians. They are likely to scoff at what they perceive to be the triviality of the content in these volumes: no groups, no homomorphisms, no compact sets, no holomorphic functions, and no Gaussian curvature. They may therefore be tempted to elevate the level of the presentation, for example, by introducing the concept of a field and show that, when two fractions symbols m/n and k/l (with whole numbers m, n, k, l, and n != 0, l != 0) satisfying ml = nk are identified, and when + and × are defined by the usual formulas, the fraction symbols form a field. In this elegant manner, they can efficiently cover all the standard facts in the arithmetic of fractions in the school curriculum.  This is certainly a better way than defining fractions as points on the number line to teach teachers and educators about fractions, is it not? Likewise, mathematicians may find finite geometry to be a more exciting introduction to axiomatic systems than any proposed improvements on the high school geometry course in TSM [Textbook School Mathematics]. The list goes on. Consequently, pre-service teachers and educators may end up learning from mathematicians some interesting mathematics, but not mathematics that would help them overcome the handicap of knowing only TSM.

Mathematicians may also engage in another popular approach to the professional development of teachers and educators: teaching the solution of hard problems. Because mathematicians tend to take their own mastery of fundamental skills and concepts for granted, many do not realize that it is nearly impossible for teachers who have been immersed in thirteen years or more of TSM to acquire, on their own, a mastery of a mathematically correct version of the basic skills and concepts.

Mathematicians are therefore likely to consider their major goal in the professional development of teachers and educators to be teaching them how to solve hard problems. Surely, so the belief goes, if teachers can handle the "hard stuff", they will be able to handle the "easy stuff" in K–12. Since this belief is entirely in line with one of the current slogans in school mathematics education about the critical importance of problem solving, many teachers may be all too eager to teach their students the extracurricular skills of solving challenging problems in addition to
teaching them TSM day in and day out. In any case, the relatively unglamorous content of these three volumes (this volume, [Wu2020b], and [Wu2020c]) — designed to replace TSM—will get shunted aside into supplementary reading assignments.

At the risk of belaboring the point, the focus of these three volumes is on showing how to replace teachers’ and educators’ knowledge of TSM in grades 9–12 with mathematics that respects the fundamental principles of mathematics. Therefore, reformulating the mathematics of grades 9–12 from an advanced mathematical standpoint to obtain a more elegant presentation is not the point. Introducing novel elementary topics (such as Pick’s theorem or the 4-point affine plane) into the mathematics education of teachers and educators is also not the point. Rather, the point in year 2020 is to do the essential spadework of revisiting the standard 9–12 curriculum—topic by topic, along the lines laid out in these three volumes — showing teachers and educators how the TSM in each case can be supplanted by mathematics that makes sense to them and to their students.

This sounds similar to what the so-called "New Math" movement was attempting.  Maybe it was my anger and frustration as a teenage student which make me sympathize with this attitude - or maybe I will live long enough to be in some Detention Camp where I might teach a "Mathematics for Jailbirds" course!   

Quote from: Hung-Hsi Wu
Coherence.

Another reason why Textbook School Mathematics is less than learnable is its incoherence. Skills in TSM are framed as part of a long laundry list, and the lack of definitions for concepts ensures that skills and their underlying concepts remain forever disconnected. Mathematics, on the other hand, unfolds from a few central ideas, and concepts and skills are developed along the way to meet the needs that emerge in the process of unfolding. An acceptable exposition of mathematics therefore tells a coherent story that makes mathematics memorable. For example, consider the fact that TSM makes the four standard algorithms for whole numbers four separate rote-learning skills. Thus TSM hides from students the overriding theme that the Hindu-Arabic numeral system is universally adopted because it makes possible a simple, algorithmic procedure for computations; namely, if we can carry out an operation (+, −, ×, or ÷) for single-digit numbers, then we can carry out this operation for all whole numbers no matter how many digits they have (see Chapter 3 of [Wu2011a]). The standard algorithms are the vehicles that bridge operations with single-digit numbers and operations on all whole numbers.   

Moreover, the standard algorithms can be simply explained by a straightforward application of the associative, commutative, and distributive laws. From this perspective, a teacher can explain to students, convincingly, why the multiplication table is very much worth learning; this would ease one of the main pedagogical bottlenecks in elementary school.

 Moreover, a teacher can also make sense of the associative, commutative, and distributive laws to elementary students and help them see that these are vital tools for doing mathematics rather than dinosaurs in an outdated school curriculum. If these facts had been widely known during the 1990s, the senseless debate on whether the standard algorithms should be taught might not have arisen and the Math Wars might not have taken place at all.

« Last Edit: December 24, 2021, 04:21:40 pm by Half-Crazy Nobody »
Things They Will Never Tell YouArthur Schopenhauer has been the most radical and defiant of all troublemakers.

Gorticide @ Nothing that is so, is so DOT edu

~ Tabak und Kaffee Süchtigen ~