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Sunday, March 17, 2019

No sign for improving math education soon.

America is in a dreadful state. Has been for awhile. One of the reasons for that was and is the awful state of public education.

There is a LOT of cheating in education. But not the one that comes to mind when one reads the word "cheating". I talk about school-level cheating that leads to COLLEGE students who had a passing grade for college math, and then did this (when taking a physics course).

Didn't spot any issues? Ask in a comment field at the bottom of this post and I will help. And don't forget to send a card to your math teacher(s) saying - you taught me wrong!

These example represent just a tiny sample of what I have seen in my classes for twelve years teaching two-three thousand students. I have some statistics on the matter in a different post. And at the bottom of this post you find some examples of problems every Russian high-school graduate must do.

Question - who do you think is responsible for THAT cheating? Teachers? Principals? 
Government in general?

Ignoring the quality of college education when advocating for free college for everyone is nothing but a publicity stunt.

Once, browsing the Internet, I accidentally stumbled upon a piece from 2018: “We Should Teach Math Like It's a Language”, By Jeannine Diddle Uzzi, the provost and vice president for academic affairs at the University of Southern Maine (
The author makes a case that math needs to be taught in a way similar to teaching Latin. She appeals to a 2011 article, "An Apology for Latin and Math," by high school Latin teacher Cheryl Lowe.
This is where I see the problem.
The approach to study math as a language has been known for decades.
A simple search can show books (not just articles) on the matter published more than 10 years ago.
The methods for teaching math have been known for decades.

And every math teacher who wants to be good at teaching should have read at least elements from Euclid’s “The Elements”.
They would know that mathematics starts from the basis of language, from a “dictionary”, these days a.k.a. definitions.
BTW: this approach is not limited to teaching languages or math, it is a fundamental scientific approach essential for teaching any subject, or at least any STEM one (I use it when I teach my physics courses; BTW, very successfully).
The fact that efficient math teaching strategies have been developed decades ago but math teachers at large still need to be introduced to the very idea of the approach, demonstrates how poor the teacher professional development has been and is – on all levels, K12 and above.
This is the actual issue that needs to be addressed.
But evidently, for decades, it hasn’t.
Hence, I see no indicators that things are going to be much better any soon.
There is a wast amount of research on the state of math education. People use complicated statistical methods to prove their point of view. 
It is a major waste of energy and time and funds. 
Do you want to test the quality of the work of a math teacher? Ask his or her students - why 2 + 2 = 4? I can assure you the majority will not be able to give an answer. Hence the teacher has not done a good job. Q.E.D. ◾▢
This is how districts should approach math teachers. 
1. A math teacher must be able to teach at least 4 consecutive math grades. 
2. If N is the highest grade a teacher teaches, he/she needs to know math for (N+3) grade. 
That simple. 
Don't believe it'll work? Let's bet on it. Make your bet with me, and TRY IT.
Instead of spending millions on "research", NSF needs to invest in rudimentary teacher preparation - en masse.

The first picture in this short opinion piece often comes from my students when we start learning about normal force (in physics there are many situation when we need to apply the Pythagorean theorem). All college students taking a physics course must have taken math before - as a prerequisite. I have taught at least a couple of thousand students, probably more. A huge percentage of them have had very poor math preparation, especially American-born ones.

Lately, more and more people advocate for a utilitarian approach to teaching math - "I have not used never algebra in my life, why did I spend so much on trying to learn it, I hated it, and students hate it, so let's get rid of it!".  Yes, let's teach only things students like - what's that, computer games? watching cartoons or super-hero movies? This trend is far from being new.

First and foremost math and physics teach people HOW TO REASON, they develop intellectual abilities (among many other important things, like advancing the brain development). Currently, American policy is governed by poorly educated people - on BOTH sides! The Republicans depend on whites without college education. And so do the Democrats - they simply cannot win without  minority voters - who have a very low average level of education. Eliminating algebra only makes this worse. For thirty years with all that talk about reforming education, it was just a talk. When will policy makers understand that the low level of American mass education has become the biggest threat to the national security? And not just because of politics. Because of economy, too. Economy needs more and more highly educated professionals. Thirty years ago business leaders and politicians had to make a tough choice. Should they start making heavy investments in education? The answer was - no. That would negatively affected profits. So, they invented H-1B visa. And now America has become addicted to the foreign-born highly educated professionals. Even a slight decrease in those numbers leads to a heavy "withdrawal" - with kicking and screaming from business leaders - we need more educated foreigners! 
Why no one asks - how come that all other countries are fine with having their own native, born and grown up professionals, but America cannot survive without foreigners
And don't say "America is founded by immigrants" - that was hundreds years ago. 

Being open to immigrants and being dependent on them 
- are the two very different things!


In response to "What's the right age to quit maths?" 

Teachers are only as good as the teacher preparation system is. In the U.S. there is no system (!) for teacher preparation. The main reason for that is that education is governed by people who have no deep understanding of what teaching and learning is - politicians and businessmen who think about education only in terms of money and hire superintendents who can satisfy their political agendas. 

Some examples of math every single Russian high-school graduate must be able to do. Of course, not everyone can, but the vast majority of graduates who want to go to a college do. If those skills are expected from school students, what do you think a school teacher must be able to do? And many can, indeed. In Russia. And from those who can do that math, many also can teach how to do it (like yours truly).
Calculate the value of

Simplify this expression

Solve this equation

Find the minimum/maximum of this function

Find the anti-derivative of this function

Calculate the area of a figure limited by these lines:

Find all values of parameter a for which the inequality has no solution

And those are just some common examples. All Russian high-school graduates are expected to solve geometry, chem, and physics problems that in the U.S. correspond to AP or college level STEM knowledge. Those graduates may never use that knowledge in their life, but they sure will use their brain for designing solutions to problems they have not solved before (the main function of intelligence). Fish rots from the head down - we know that. But this is true not just in politics and management. It is a general rule for any human functioning. The more rotten a head (underdeveloped brain) is, that leads to the more degraded actions. And v.v.. Evidently, Russia and China take this rule more seriously than America. Probably, because to this day America could simply buy enough foreign-born highly educated professionals. But what if that time will come to an end? Any long-term strategic thinking on this one? Anyone?

A recent example from a student.
The student has no developed algebraic thinking, demonstrates pre-algebraic thinking, when instead of using variables and algebraic actions the student uses a verbal description of the work done. And this student studies physics at one of the top universities. And he/she is not alone (far from alone) who demonstrates this type of thinking. Graphical thinking (plotting, analyzing graphs) is at an even lower level.
One does not need to waste $$ to "study" how bad math education is, one just needs to get an honest feedback from faculty. The key word is "honest". Evidently, no one in American higher education wants to know the honest picture. But the result is clear -  severe primitivization of education.

What is Wrong With Socialism. Really.

What is Wrong With Socialism. Really.
(the picture is from the cover of a book by Thomas DiLorenzo, which I have not read, so have no idea if the book is any good)
Disclaimer: this post contains strong language.
Well, a strong word.
But used several times.

The good thing is this discussion about “socialism-smoshiolism” v. “capitalism-smashiolism” eventually will help some people get a better understanding of how economy works.
The bad thing is people in both camps have no idea what they are talking about, and even worse, they have no idea how to carry a meaningful debate.
Well, that’s not really my problem (here is a specific ideology my mentors taught me to follow), but I can offer my two cents.
First, give a definition of the most important terms you use in the debate.
Don’t try to make it as exact as possible, find one core feature and state it as clear as possible.
The initial definition is never perfect, but if it is good enough, it can always get improved in the future.
And nowadays one does not even have to go to any school to learn stuff, just Google whatever you want to learn about.
Simple like that.
“Universal Basic Income” (some rich people favor, as described in "Basic Income: from an ideology to a working mechanism") has nothing to do with socialism, as well as “Medicare For All” (well, that would depend on its actual realization), as well as many other “socialistic”-like features American socialists and capitalists constantly debate about.
The debate “capitalism” v. socialism” is a debate about the form of ownership:
private (i.e. capitalism) v. communal (i.e. socialism).
And the latter is exactly what American socialists promote.
This is what I “stole” from the Twitter (thanks to @MestizoBobbyHil, the original is at @OfficialSPGB)
So, what I want to say right now, is that those idiots, and this time I really really mean it, don't understand that when property “belongs to everyone” there are always specific individuals who manage that property, and there are always specific individuals who choose those managers. In the end, it means that property that “belongs to everyone” in reality truly belongs to few people who select some few other people to manage it.
Plain and simple.
Every society is ruled by its elite, the only difference is how do people get to that status (more on this in The Degradation of The White Male American Elite).
All socialist reformers always forget that their ideas are going to be brought into practice by flesh-and-blood people. Every "socialist" in reality is a utopia-ist - a person who believes in a utopia, in fact, in a specific utopia - a society where everyone is smart, educated and absolutely honest. In that utopia, as long as people discussed and adopted (agreed on) a rule or a law - immediately EVERYONE begins to follow that rule or law to a letter. It means one simple fact - socialists or other
utopia-ists have no idea about human psychology governing the actual current society with its jails, police, etc.. 
Not everyone can become the President ("The Biggest Lie Of Humanity"); not everyone wants that, but everyone wants to have some bread and to watch some circus. People behave according to the Maslow hierarchy, not according to the Golden Rule. Ignore this fact and you will destroy a country or
create a dictatorship.
Socialism makes a few people essentially be the owners of the “property of the people”. How blind one needs to be NOT to see that?
 Socialism, in its classical sense, is just kind of a corrupt capitalism.
But, that is not the end of the story, of course.
As many people would agree, capitalism, at least in its current form, does not really work anymore for vast majority of citizens everywhere (not just in America) – and there are objective reasons for that ("The Era Of Dictatorships: Explained").
If that would not be a case, we would not be having this discussion right now; no one would even remembered this word, “socialism” – in America, at least.
However, people who framed this whole discussion as a dichotomy “only private property” versus “only common property” are just inherently stupid.
No one has ever said that a hybrid economy cannot exist.
The economic structure of a society does not have to depend on its ideology.
People (yeah, yeah, who are smart enough, educated enough, strong enough and, hopefully, honest-ish) can design whatever economic system they want.
Thousands of years of human history offer a solid proof for that (there are no pharaohs anymore anywhere, aren’t they?).
The structure of the economic relationships has been evolving with the evolution of human society.
The structure of the economic relationships, in the end, essentially depends on what outcomes and for whom that economy delivers the most.
For any economic structure the first question to ask is who extracts the most benefits from that economy.
When the distribution of economic outcomes reaches a large disbalance – in a way that depends on historic circumstances – people change it – one way or another.
That is exactly what we all are observing right now.
The change in the economic structure of American society.
At its very very beginning.
It will take years, maybe even decades, to finish this transition.
No one can predict today what the new structure be look like.
But the old, meaning the current, economic models do not work anymore; economic “experts” are constantly wrong in their predictions.
Of course, I would never called people who are much more often wrong then right “experts”, but the point is, politicians need new economic models, and those models yet don’t exist, and the whole society is being shaken because of that.
Progressive politicians like Bernie Sanders, Elizabeth Warren, or Alexandra Ocasio-Cortez are not offering anything new; their “model” is just old-fashioned “take from the rich and give to the poor” ("Knowledge is NOT a Power, at least in Politics").
The goal, the mission, the reason for existence of new politicians like Alexandra Ocasio-Cortez is to shake the system.
Nothing more, nothing less; just to make its structure loose.
The current progressives are not reformers; they are people who pave the path for the reformers who will come later.
The can't even sell their own ideas. For example, to promote the idea of basic income they say to people: "You are useless - for our economy, but we do not want you to starve to death, so we will give you some money just because" (figuratively speaking, using some exaggeration, but true in its essence).
Unfortunately, until new economic models will be developed the economic well-being of the Country as a whole will keep degrading.
But the true reformers will eventually come.
Some of the young politicians may even slowly evolve into those actual reformers.
But people, the Country, are simply not ready yet to accept them and their ideas (whatever those ideas will be).
The task of restructuring the whole economic system is not an ordinary task; it is an extraordinary task and demeans extraordinary people.
Ordinary people cannot create a solution to an extraordinary problem.
“Progressive” solutions which are currently propelled by progressives are not extraordinary. But until those solutions will be tested and fail, no one will be even searching for new, extraordinary solutions.
And the fact that a person has reached the top level of business or politics does not make that person extraordinary.
Successful people are divided into two categories; those who have been working hard and got lucky; and those who just got lucky.
But working hard is a natural, genetically built in into every healthy person, condition. Laziness, procrastination is an illness, a disease, often psychological, sometimes cultural, and sometimes is a result of a chemical imbalance in a brain. All normal, healthy humans want and can work hard.
Note: “conservatives have a different take on it; they believe that most people are lazy and stupid and incapable of creativity, and require a strong and guidance from the few smart and innovative.
The economic “model” of “conservatives is this:
Conservative 1. “I want it all, and I want it now!”
Conservative 2. “No, I want it all, and I want it now!”
Conservative 1. “OK, let’s negotiate
Conservative 2. “OK, but what about all those people?
Conservative 1. “Screw them, they are lazy and stupid, they’ll eat up anything we’ll tell them”
Conservative 2. “OK, but let’s pretend we care about them. They can vote
End of note.

But if working hard is a natural human condition, then successful people are successful just because of their good luck ("A Curious Case Of a Risky Entrepreneur"). They were lucky to get good healthy genes. There were lucky to meet a person (at least one) who impressed them, who influenced strongly their aptitudes (maybe it was a face-to-face interaction with a parent, a friend, a teacher, maybe it was a book or a movie character, maybe it was someone from the Internet). They also were lucky to meet a person who believed in them, who trusted in their ideas and abilities. All that good luck is basically “be at the right place at the right time” and be smart enough (due to genes, culture) to recognize the opportunity and act on it.
So, a good luck, not extraordinary abilities, propel people to success.
It does not mean that extraordinary people do not exist; they always exist. But in ordinary times, under ordinary circumstances, ordinary people do not require any extraordinary actions. So, extraordinary people remain unnoticed, but may be eventually discovered, sometimes, postmortem.
When social fabric begins to crumble, at first many ordinary solutions begin to be tested. Eventually, things become so bad, that a large portion of a population notices that ordinary solutions do not work anymore. Then and only then they turn for a search of an extraordinary person who could pave the path to a new social and economic structure.
America has observed it in 2008 and 2012 when elected Mr. Obama as the President.
Mr. Obama was elected not because he was an extraordinary politician, but because he was different from other politicians.
People wanted changes, and Mr. Obama promised them that, and most importantly, he was that.
But as an ordinary person – smart, educated, polite, funny, hardworking, honest – but ordinary, he has not delivered on his promise.
And that what propelled Donald Trump.
Donald Trump is a racist, a misogynist, a bigot, and a white supremacist.
But he is an extraordinary person.
To the surprise of everyone on the left and on the right, even to himself, he became the President. And that was an extraordinary achievement (again – a BIG surprise of everyone on the left and on the right).
What progressives do not have is an extraordinary politician who has extraordinary ideas but can present them to ordinary people in an ordinary form.
“Universal Basic Income” or “Medicare For ALL” are not those extraordinary ideas because they do not address the most important question of any economy – how is wealth being produced?
All they offer is various forms of a redistribution of wealth.
But only after trying all ordinary solutions, people and politicians will come to a realization that they need to go to the root of the economic functioning – forms of wealth production.
The notion that wealth can be produced only by private  economic entities is wrong.
That is what is wrong with capitalism.
But the notion that wealth can be produced only by “communal” entities is wrong either.
And that is what is wrong with socialism.
The strongest feature of capitalism is competition. When the filed is leveled, when the competition if fair,  everybody wins. One of the problem with current capitalism - it suffocates competition: the markets are divided between super-huge corporations. To deal with this problem a country needs a strong and smart government. 
There is NO rule that would say that the government cannot compete with the private sector. The goverment has enough resources to take on any monopoly. We live in the new economic era - when few monopolies rules all the markets. In this era the goverment needs to play a new role.
The role of the government is not just making the rules/laws that a fair for all.
The goverment has to enter the "game", it needs to create economic structures that could compete with existing monopolies. 
Some on on this in
A word to Senator Sanders, and other anti-Trump warriors

Follow to this page for all publications on politics.

NB: "An idiot" is not a swear word, it is being used in its clinical meaning. From The Degradation of The White Male American Elite (I advise to read this post, too, and other linked in it).
I want to stress that terms “stupid” and “idiotic” do not have any offensive meaning, but used in their clinical/original sense. “Stupidity” means an inability to think (e.g. due to biological reason). “Idiocy” means a refusal to think (usually due to psychological reason). “Idiots” are those people who due to their social status or official position are supposed to be smart, but make stupid decisions.
One may ask, why using so strong language, anyway?
Well, to stress my frustration with the actions of current politicians on both sides of the political aisle. Because the actions of the current politicians will greatly affect my own living 15-20 years from now, and most probably, in a negative way (I have another post on this matter "Ignoring sloppiness: a sign of tolerance or mismanagement?"). Plus, I write for people who can hold their emotions in check. People whose emotions override their reasoning do not matter in politics because they are easily manipulated (an old Russian saying goes "Call me a pot, if it makes you feel better, just don't put me in an oven").

P.S. Maybe America is ready to an economic state that could be called "socialism" - in certain sense (e.g. read A word to Senator Sanders, and other anti-Trump warriors.
Most Americans are NOT ready to live in a society called "socialism". that is just a fact. And calling themselves "socialists" to push for progressive agenda is simply not smart.
But not smart.

And, BTW, Donald Trump knows that very well.
A truly smart politician would not use to describe himself/herself a term which would impede his/her political agenda, because the majority of voters would not accept that term - not a politician, but the term! The fact that progressives still keep calling themselves "socialists" is a clear proof that they are not smart politicians.

This is the link to the list with more post on politics.

Appendix I: An example of an ordinary thinking.
Donald Trump is a racist, a misogynist, a bigot, and a white supremacist. But he has never really tried to hide it, hasn't he?
So the question is redundant, rhetorical, basically meaningless, because the answer is simple - that is who Donald Trump is.
So, why ask such a question?
This is how I see it.
The author, the editor, many readers, have a rather comfortable life, good job, family, friends. And the only splinter in his/her eye is Donald Trump. The President is not a nice person. If only the President of his/her Country looked good, was nice, polite and educated, if only he was a good person, the whole life would have been just peachy. There would be no more problems in the life of the author, the editor, many readers.
So, why asking difficult question, like why did Donald Trump become the President, what social and economic events have led to it, what are the political and economic perspectives for the Country, and what to do about them? 

Why thinking about political future of the country, planning political actions which must be done to ensure that the future will be at least as good as the past?
No, all the author, the editor, many readers want is not having them be reminded every day that there is something wrong with them. It is just much easier to ask - why is Donald Trump such an awful person - express your distaste, and feel good about themselves, feel involved, feel important.

 P.S. A comment on a recent attack on Chelsea Clinton.
Yep. And don't be the one.
Appendix II: Some Further Reading