On Education

There are multiple routes for a learner starting out on the journey of getting an education in a reasonably progressive society. There is the obvious schooling and college degree system. This used to be supplemented in earlier decades by the gathering of knowledge on the curious learner’s part by means of reading books and articles, but has now mostly become a matter of passively gathering information via online sources of videos, accessed either directly or for the majority, shared on social media.

The credibility, accuracy and authenticity of information disseminated through videos shared online remains questionable, not to mention the fact that passively consuming large amounts of such content, however authentic, is bound to degrade the mental faculties of even the best minds.

Let us consider the standard schooling system. It consists of a relatively well-defined syllabus, that is refined by some committee of experts in some periodic fashion. If, as a learner, you depend on these experts to tell you what you should be studying or not, you are doing yourself a disservice. There is no way to game the system. It exists so that you get good grades that can be displayed, pass or get good scores on entrance exams and get into a good college. There, a similar setup will see you get through four years of the prime of your learning life, mostly with a credential that allows you to get employed somewhere or pursue further credentials within the system. It is a standard the world over, as far as I know, and it exists for the simple reason that human children and adolescents are thought to have widely varying abilities and special talents that must be developed from an early age, in order to provide skill specific training while cutting some slack on the core curriculum. While this is true for things like sports, music and the arts, it must be understood by both the learner and their guardians that the skills they require later in life as an adult must at some point be learned, whether from a standard school curriculum or otherwise. So how can this problem be approached?

This document is a guide to what I believe could help. Recognize that different learners have varying needs at various points in their lives. It is also a guide for the self-motivated learner who wishes to get more out of their time spent in an educational environment.

General principles

Learn how to learn

Be suspicious of any statistic

Never be overwhelmed by what you don’t yet know

Math concepts apply to every field of endeavor, whether you choose to pursue higher studies or not

Beware of unknown unknowns

The purpose of education

Most of education is about filtering out/in people who can demonstrate an ability to:

a. Perform relatively better under conditions of stress.

• Stress may be imposed by:

  • Time constraints

  • Unclear/pedantic presentation of the material

  • Unknown application of the concepts

  • Being unable to decouple the underlying concept from the methods used to solve problems

  • Unaware of the historical development of the subject and the motivations for having arrived at various conclusions

  • Being told that certain concepts / applications are reserved for higher studies which may never be realized in the ordinary course of a student. Thus, causing the person to switch off from the subject in adult life.

• Other causes of stress may be:

  • Socio economic factors

  • Education levels / mindset of immediate family including parents

  • Circumstantial owing to unique conditions in an individual student’s private life.

b. Gaining some credential that is supposed to demonstrate a basic competence in the presented subject matter.

c. Getting to the level of gaining an interview at the institution / organization where you choose to work.

d. Gaining the competencies required to make sense of the modern world and survive the onslaught of technological change, while being a valuable contributor to society.

e. Gaining the soft skills and communication skills that would enable you to participate in activities involving coordination with other people, whether that be in your job, business or in say sports.

 

Most students are naturally curious, but somewhere over the course of the first few years of education, most of that curiosity is lost in a torrent of events that occurs more or less the same in every student’s life

• Don’t see the point in learning as they are made to be aware of not having economic problems at home. This true of both households with / without access to a large amount of wealth. The student basically loses motivation for developing independent thought and a position in society thinking they will always be cared for by someone.

• Curiosity gives way to competitive learning, which is just another way of saying that one needs to get the best possible grades on every subsequent test / entrance exam or else one hasn’t / will be unable to make any significant achievement in life. Be it in the form or wealth, prestige or any other factors deemed as part of the definition of success as imposed by the immediate society surrounding the student’s private life.

• Pains of growing up, accompanied by changes in the body and mind and the social pressures that go with it, being these days heavily cross culturally influenced as a dynamic, but being poorly understood by the adults in the student’s life.

• Different speeds of learning / methods used to disseminate learning are not taken into account when students are grouped into a class mostly by age without regard to what their actual ability is (higher / lower) at the present time. This causes disconnects between not only the time spent in a classroom but also among peers.

• Different subjects may need different motivations, which may require the teacher to know more about how the development of the course over the student’s academic life and later professional / family life may affect the student’s ability to perform in various situations.

• Most students in the first 10 or 12 grades of school do not generally know about what the applications are for the content they are taught / given very rudimentary examples of applications.

• A motivating factor could be to introduce non traditional applications, borrowing from customarily parallel or seemingly entirely unrelated career paths / popular culture.

• Both tech and non tech examples. Social media, instant messaging, content creation, ai, movies, music, arts.

• The availability of say, youtube videos covering a particular tool or technology should not deter the discussion of the application area in a more nuanced technical sense, a depth that most such videos do not go into.

 

 

Example

Introduction to Math at a high school level

As a student starts out, they are taught to recognize different numbers and operations like addition and subtraction. These are generally presented in two ways in a particular order:

• 1+1=2 (Using numeric representation and symbolic manipulation, presented as an equation)

• I have one apple which I give to you, and then I give you another apple. How many apples do you have? (Using words to abstract out the symbols and let the student come to a conclusion based on the intuition of everyday experience)

• Initially, the second wordy presentation seems better, and most students would have no difficulty with it.

• In later years, these same wordy problems become a source of anxiety for the student even though they thought they knew what it was all about.

• The math teacher is dependent on the language teacher having done their job well.

• The problems posed in most tests / exams do not have an analogue to a real world application.

• Math can be motivated by a more nuanced study of everyday language

• The disconnect that someone feels as they go from lower classes to higher classes, say to high school, could be mitigated by introducing various concepts that reinforce what has already been supposed to have been learned, but in entirely new ways of looking at it.

• Say, in this case, we look at the elementary school problem of apples presented above.

  • In the wordy description, does it matter if I were handing out apples or oranges or chocolates?

  • Is the language ambiguous / clear ?

What if the student already had an apple, say in their lunch bag on that day?

• What do you mean when you say one apple? Is it an entire apple / can it be in slices? Or multiples? How about multiple slices?

• When I give you the stated apple, what happens to the quantity of apples that you have in your possession? Does it increase / decrease?

• Say, it increases. So, what is the operation that you need to perform to arrive at a solution to the problem?

• Say addition. Why not multiplication? What do you do in multiplication? Understand multiplication as repeated addition

• We use the symbol 1 to represent a quantity of something. Generally, a whole quantity as opposed to a fractional quantity, which here would be a slice of the apple.

• When we translate from words into mathematical symbols, we must take care to identify the quantities being given, the operation to be performed and figure out what is to be deduced.

• This usually results in setting up an equation which is just a fancy term for saying that some quantity on the left-hand side is equal in measure to some quantity on the right-hand side of the equals sign.

• In this case, the rhs is unknown.

• Label the unknown by another symbol, say x.

• Math has an enormous number of areas which are actively pursued by research even today. Different branches of math, even different books on the same subject may use a different way of denoting the same concept, but most are generally agreed upon. There are no rules, except that you must be able to convince others in your field of your approach to solving a particular problem or presenting some new result. This is generally done best when you stick to the common conventions used in that field for communicating your ideas to your academic peers. You may invent your own notation, if you are working on some new aspect that has no other analogies in the particular field.

• So, we have now modelled our word problem into a mathematical equation that can be solved using some widely known rules. In this case, the rule is that of performing an addition operation on two quantities, both of which are whole numbers, or rather positive integers. We get the answer as 2, which we substitute as the value of the unknown x in the equation above and thus the identity is realized.

• Note that 2 is also a whole number and a positive integer. Can it be something else. Fractional, definitely, you say, but what about negative numbers? If I were to rephrase this equation, say to 1 - 2 = -1

• It makes sense mathematically, but could you, without much elaboration, translate it back into words?

• I give you one apple, then I take two apples away from you. How many apples do you have?

• Again, avoid the point about the student already in possession of an apple in their lunch bag.

• Here, although the symbolic representation makes perfect sense, a translation into words doesn’t make any sense. How can I take two apples from you when I’ve given you just one? If the student somehow gets past that, then we are left with the student owning a negative quantity of apples, negative one in this case.

• This could make some sense, so is the student now short one apple? Does the student owe the teacher an apple?

 

 

Example

The student entering college has been through, say, 12 years of a school education. Within a STEM degree, the student typically takes dozens of courses over a 4-year period. A motivation can be provided for each in the following templated way.

There seem to be two approaches that can be taken: top down and bottom up

a. Top down would provide a scenario that is reasonably understandable to the student’s everyday experience. And then break it down into smaller and smaller concepts until we reach those leaves the student is already quite familiar with.

b. Bottom up would involve stating up front a goal to achieve, and an upfront declaration of the concepts that will be used to achieve that goal. The focus would be on the process of integrating various ideas and seeing the end result as the achievement of stated goal.

 

Lifelong Learning

• The STEM courses are independent fields of study that individuals spend their entire adult careers and life studying, researching and applying.

• It is good to know what the various fields of human endeavor are, how they are structured and taught, and especially to gain an understanding of the interplay between various disciplines as they seem to apply to an event, from your unique perspective on the world, which is bound to keep changing if you get into the habit of becoming a lifelong learner.

• In science, there are multiple ways to analyze a scenario. Multiple ways in which data more or less agrees with some theory. It is useful to have multiple theories because one can never be sure which one is absolutely true. But a good theory makes useful predictions that can be measured by current or some potential future technology, thus validating itself to rank higher in the grand scheme of things. Also, sometimes, a shift of perspective can highlight certain other details which are unknowable by the current theories or the generally accepted one. The frontier of research in every field is filled with debates and speculative ideas that have yet to be proven. Your job as a learner, is to navigate the system that is designed mainly to make you employable in some role in some industry. It could even be research if you are so keen, bur that will require you to get more advanced credentials than the ones traditionally students stop at, to move on with general life and make money. If you are coming from a background of lifelong learning, and wish to see the world from new perspectives based on your experience of an adult career, you have now at your disposal, access to most of the resources that a student would have. What is required is the mindset to change views, and biased opinions. Learn fundamentals if you have forgotten it, it helps to review stuff you thought you knew, but from different sources. You will be able to make much more inter disciplinary connections than an inexperienced school or college person ever could.

• As an adult who is already into a career, there are multiple reasons why you may want to learn something new or take a fresh look at the core of your field or any field, for that matter:

  • You need to keep up with changing technology and would like to earn some credential that you think provides an employability benefit.

  • You need to earn a credential as it is mandated by your employer

  • You have realized that opportunities to gain wealth or success may come across by having insight into what other people in other fields are actually doing

  • You may have entrepreneurial ambitions, leading to having to learn various things both technical and non-technical in a short period of time.

  • You may realize that you do assimilate information better than most people around you, so you may want to hone your skills further in a more directed manner, so as to break new ground with some insight that allows you to either make money directly or by means of seeking out employers who would value the insight that you bring.

  • You have already earned a lot / do not care about money so much, but have a nagging desire to put the rest of your life in service of those who cannot help themselves

  • You have that long cherished dream of having wanting to do something entirely different as a child, but somehow ended up in your present career. You feel that the least you can do now is to give the dream a try, even if it doesn’t turn into something as viable as a career.

Learning how to learn

A layered approach to understand anything

• Everything has layers

• Everyone has a biased view, which varies from person to person

• A definite event that takes place anywhere in the Universe can be viewed and analyzed from multiple points of view.

• An understanding of varied phenomena at the present time is only a general consensus on what is believed to be true.

• The ultimate nature of human understanding is philosophical, but it is better to take a more pragmatic approach when dealing with issues that affect living beings.

• Much of basic human motivations have not changed significantly over the last several thousand years

• There are two main motivating factors for continued inequality and conflict in the world:

  • The desire of some group of people to impose their way of thinking and life upon other people in the same or other parts of the world.

  • The desire of some group of people to accumulate as many resources as possible for themselves.

These may play out independently or collectively, as they are not mutually exclusive.

• Your brain works in two modes, focused and diffuse, focused is when you are intently studying something for a short burst of time. Diffuse is when you let your mind wander and are not doing too much processing, say, taking a stroll. This is when your brain organizes its internal structures with all the stuff you crammed into it. Both are necessary for effective learning.

• Another way to look at it is in terms of system one and system two, with the former being the quick responder to any given situation. You may jump to a conclusion based on the information that has just been made available to you, but if you give it some thought, system two, which has access to your past database of results and unique perspectives, will kick in and either corroborate or refute the results of system one, thus, effectively making you take a different action than the one you would initially have taken.

Examples of layers

• From your body and mind to anything accessible to your senses

• Every technology ever invented

• Every prose or poem written

• Every game or tournament ever played

• Every piece of music ever composed

• Every work of art that has ever been created

• Every tool you’ve ever used

• Every plant, tree, animal, bird and microorganism that has ever existed

• Every social structure that has existed

• Every political structure that has existed

• Every nation

• Every community

• Every family

• Your interactions with anyone or anything that is external to you happen in a myriad of layers

• Now, the effect of an interaction may or may not be noticeable at first glance. But may be noted in some other form.

• Economics is layered

• Science is layered

• Religion is layered

• At any given moment in time, there are an infinite number of interactions taking place in the world, and you have access to information on certain events only. This information that you receive from various sources have no independent means of being verified by you. If you need to take an action based on the information available to you, remember that there are layers to this too:

  • If you trust the sources, then you need to realize that you are basing an action not on the information actually presented to you, but on your perception of that information as it is currently represented in your brain, which would have altered state based on the incoming data, possibly leading to fallacies such as confirmation bias.

  • If you do not trust the sources, then you will resist the temptation to fall prey to confirmation bias, but, since an action must be taken, given you have chosen to ignore the incoming data, your decision will be based solely on the current state of your brain, which has not been altered by these untrustworthy sources.

In both these cases, we note that the reality of the event under consideration has very little effect on the decision maker who has already formed an opinion about the event. At various points in life, you will trust and lose trust in various people and other entities which will seek to gain your attention for whatever purposes. To maintain sanity in such a situation, it is important to understand some basic things about human psychology, which is also layered.