USA: Throwing it all away, by Paddington

 In many ways, the years 1945-1965 were some of the best ever for the United States.

With the massive funds of the British Empire, obtained through the Lend Lease program, the war machine was converted to civilian products (as well as weapons production), fueled by huge US oil reserves.

There was virtually no competition, given that the British, French, German and Japanese empires were destroyed, and most of Russia and China were at least a century behind us.

The government invested in infrastructure (rural electrification, the interstate system), education (especially the public universities), people (Medicare and Medicaid) and scientific research (both very pure and applied). We were the leaders in electronics, computers and nuclear energy.

The middle class grew and thrived, with good jobs with benefits, which included pensions.

At some point, the public was persuaded that pensions were bad, as were unions, and science. People were encouraged and divided over envy.

I don't think that the country as a whole was helped by the latter, and things do not seem to be going in a good direction.

I just watched an interview with a Chinese industrialist who was educated at Stanford University, who noted that the infrastructure in the US amazed him when he came in the early 1970's, and now appears to be inferior to much of China's.

In a nutshell: postwar history, by Paddington

My summary of US and UK culture from World War II onwards.

Returning soldiers decided that they deserved better from their government and country, and the rebuilding began, with strong, active and violent unions. This process was much slower in Britain, which had given all of its money to the US during the course of the war.

Deciding that things had 'gone too far', we elected Thatcher and Reagan, who destroyed the unions (and with it any hope for the working class), and handed much of the money and power to the rich and multi-national corporations.

Blair and Clinton carried on these policies with false promises of the 'Information Age', while the corporations used their power to crush the middle class, including the education system, and small businesses.

Bush and Blair gave us the distraction of the 'War on Terror', which distracted us with collective fear, and prevented us from really noticing that most of the benefits of increased productivity were flowing to the top 1% or so.

Obama tried not to rock the boat, and trod a very thin line, while being assailed for everything, including wanting the 'wrong' mustard, and wearing a tan suit.

With seemingly no hope in either direction, the US turned to an idiot demagogue (Trump, just to be clear) and the UK to a blithering idiot (Johnson)* to save us from ourselves.

* (preceded by Brown - unelected heir to Blair / Cameron - old school upper class twit / May - Thatcher wannabe)

EDUCATION: The true cost of grade inflation, by Paddington

I started teaching Mathematics in the US higher education system in 1978, and retired in 2017. Throughout my career, I spent a lot of time reading about the latest trends in Mathematics Education, including participating in several grants.

The basic problem has not changed since Euclid. To understand Science, you must speak its language, which appears to be Mathematics. And it isn't just the hard Sciences. Every study on college success indicates that grades in Mathematics courses are the most robust predictor of graduation.

Despite multiple major revisions of technique and content of teaching, the success levels have not changed since I started teaching. My personal observation is that the overall mastery has declined, as the system now forces students through who would otherwise not succeed. In turn, this grade inflation means that the upper tier of students are often not challenged to work very hard, and so arrive at higher education with an inflated sense of their capacities, and an inability to rectify their deficiencies.

This slight gain through grade inflation, of course, does not satisfy administrators in education, and politicians. They know that the relatively high level of Mathematics failure is because the subject is “too abstract” (ignoring the evidence that this is precisely why it makes people think more precisely), and that Mathematics teachers are universally incompetent.

There have been several efforts of reform in this particular direction, including the English GCSE system, starting in about 1980. The entire curriculum was changed to make it project- and problem-based, using all available technology, starting with extensive calculator use (as opposed to the slide rules and log tables that we had), and moving into computer Algebra systems.

After 20 years, the results came in. Universities reported that students arrived unprepared for coursework that had previously been standard, and even had to emulate US institutions in including remediation. Companies that had hired people with A-levels in the subject reported that they did not have enough skills to learn what was needed for their jobs.

It was a disaster, but as always, no-one would admit that and simply move back to the 'old way' of doing things. Consequently, they had to introduce huge curriculum revisions and claim that they were 'new' ideas.

“The more things change, ...”

The self-destroying economy, by Paddington

One of my old friends once told me how an accident saved his life. He slipped in his driveway, and the subsequent CAT scan uncovered a growth on his kidney. That discovery gave him a number of extra years of life.

In a similar way, the pandemic has made issues with our country readily apparent, rather than causing them: access to health care, lack of sick leave, a weak safety net, and the imbalance in the economy.

Forty years ago, a person could work really hard at a union job, and support a family. I read this morning how some celebrity's first job was sweeping up in an Iowa factory, at $12 per hour. Today, that same job would probably earn about the same, even though the total inflation since that time has been something like 400%

Starting in about 1980, a large proportion of GDP has been the banking sector, now reaching 40% Realize that banking, while necessary, is essentially parasitic. Not coincidentally, 40% of the gains of the economy go to 1% of the population, most of whom are in banking and investment. If one looks at gains in the stock market, 92% go to the 10% of the richest.

We have created an unsustainable economy, and not in the way that conservatives would have us believe. In the past 250 years, the Scientific, Industrial and Agricultural Revolutions brought plenty to the wealthy nations, and that plenty has now been sequestered by a handful of largely non-productive individuals.

At some point, the average people will earn too little to keep the system running. If too few people have good health insurance, then the medical system will not do research or treatment, because there won't be enough money in the system. Likewise for energy, information, and all other industries.

Debate: Does inequality matter? - by Sackerson and Paddington

Sackerson:

Today sees the inauguration of the 46th President of the US, Joe Biden. Bien-pensant media crapheads are rejoicing: a piece by Tom Leonard and Daniel Bates in the print edition of todays' Daily Mail begins 'Donald Trump will leave office today as officially the worst US President in history.' Already nonsense in the first sentence: there is no such official ranking. Elsewhere, in the online edition, Leonard is much more nuanced. 

The satirical Private Eye magazine's cover this week shows a still from the post-apocalyptic sci-fi film Planet Of The Apes, the Statue of Liberty mostly submerged in sand and speech-bubbling 'You can take over now, Mr Biden.' 

Oh, how we laughed. They know so much better, our media mavens and Press pundits.

As a foreign observer with no dog in the fight, it seems to me that the last four years have been little better than a bullfight, Trump being ragged by the Democrats but also very selectively supported by the Republicans that one would expect to be on his side. Some of the things Trump tried to get done, such as the Wall, couldn't be completed even though in 2016 he had Party majorities in both House and Senate; other things, especially tax cuts for the rich, have been Republican themes for decades.

The unpleasant atmosphere at the end of Trump's term in office seems to me the natural result of a prolonged bipartisan campaign to make America unworkable, at least as far as the long-term interests of the majority are concerned. British politics often echoes the American and the professional representatives on both sides, Left and Right, have appeared content to preside over the hollowing of the economy and the consequent.destabilisation of society. Perhaps over there, as here, they really believe that the system cannot be broken, no matter how much they jump up and down on the bed.

Trump's hick-brash, unapologetic personality has been a gift to his enemies and frenemies; focusing on the man ('Isn't he awful?') is a great way to bury what is really going on, and has been going on for a generation or two. The postwar crossparty consensus has broken down, as income inequality has soared back to pre-Wall Street Crash levels:

Source

The Democrat Party is, of course, definitively good - or is it? Some of the voters they have taken for granted have started to see things differently: for example poc's like Professor Thomas Sowell, or Candace Owens (initially anti-Trump) whose recent book 'Blackout' is a call for black people to detach themselves from the Democrats. There is a perception on both sides of the Atlantic that just as the Right is cold and mercenary, the official Left is happy to buy its own supporters with modest financial and service benefits without ever letting them free of their dependency.

Given those options, why else would so many people have voted in 2016 for a non-professional like Donald Trump? Long before Trump started to run, acerbic entertainer George Carlin gave us a clue. Back in 2005 he said the political system gave only the illusion of choice, and the audience's emphatic reactions to the last part of this clip must give us some idea of the groundswell of angry disillusion that was developing, even before the Global Financial Crisis of 2008/9:

For a while, I suppose, the media will support Biden, just as they puppy-followed Blair in 1997, all the way to Downing Street and the fake People's Celebration in the gated area outside Number Ten.

I fear that the four-year-long (and continuing) Two Minutes' Hate groupthink around Trump will blind the good-hearted, right-thinking commentariat to Biden's flaws and errors for some time yet, just as we move into a very dangerous phase in international relations and the world's fracturing economic system.

But let's start by tearing our eyes away from the great orange-haired narcissist and refocusing on the kind of people who now infest the establishment Republican Party. Paddington gives below a few scraps to indicate their Scrooge-like avarice and callous mean-heartedness.

___________________________________________________________________________________

Paddington:

Mitch McConnell, then the Senate Majority leader, blocked a $2000 payment to Americans of average income during the COVID pandemic because he was “worried that someone might get the check who doesn't need it”. Meanwhile, the 2017 tax bill which he helped ram through gave a $1.3 billion tax break to the Koch family, who are worth $113 billion.

Jared Kushner, President Trump's son-in-law, was put in charge of the national distribution of PPE and other supplies. He reportedly decided that those supplies shouldn't go to the big cities, since most of the victims would be poor Democrats. When Democratic governors secured those supplies themselves at great cost, mysterious government agents often swooped in and seized them. Later reports indicate that many were then sold abroad.

Mitch McConnell also blocked support for the falling tax revenues that states and cities are experiencing, in the hope that this would cause all of the public pension systems to fail, especially in Democratic states.

Social Security is funded through a separate income tax, even though the revenues are thrown into the same pool. Up until 2018, the system brought in more money than it spent, every year. A simple increase in the ceiling of income subject to the tax, from $125,000 to $250,000 would keep it solvent for decades after the anticipated shortfall in around 2030. A couple of years ago, Mitch McConnell declared that Social Security was the cause of the huge deficits, and the Senate would look into cutting it.

Ivanka Trump and Jared Kushner refused to allow members of their Secret Service detail to use any of the 6 bathrooms in their house, requiring the government to pay $3,000 per month to rent a local house so that the agents could take a shit.

Governor Walker of Wisconsin, based on his personal record of becoming a rich businessman without a college degree, declared that education was useless. He slashed funding for all education, including the state's previously outstanding university system. He also made other changes, such as not requiring college degrees for substitute teachers, and not requiring any education certification for regular teachers.

In Virginia in 2018, faced with an incoming Democratic governor, the Republican legislature stripped the governor of most of the power of the office.

From https://www.salon.com/2017/03/20/donald-trumps-war-on-the-poor-has-historical-precedent-and-its-not-pretty/:

'The notion of "useless eaters" must be implemented within the United States' current social values and political system. Under the logic of neoliberalism (in which human worth is reduced to a person's value in terms of economic activity), American conservatives deems the poor, the unemployed, the homeless, people on Social Security, those who need help from programs such as food stamps and ultimately anyone who is not "economically self-sufficient," that is rich, to be expendable.'

___________________________________________________________________________________

For further discussion: 

Does the fact that some people are extremely rich, matter?
What is to become of the poorer element?
Can the welfare systems of the West survive a prolonged global depression?

SATURDAY ESSAY: America's choice... nurture mathematics or face poverty, by 'Paddington'

Via email interview, a retired American maths professor explains why a crisis in maths education threatens the future prosperity of the country.
___________________________________________________________________________________

1. Am I correct in saying that all college students in the USA have to do a math course? If so, how and why was this rule introduced, and what do the students have to do?

To my knowledge, at one time every US college student had to pass a Calculus course. This was gradually weakened over the years, and Mathematics became known as the 'weed-out' subject. As more universities opened up and so needed more students, the requirements were made easier. It came to a head in 1968, when failure (for male students) meant getting drafted into the Vietnam War, and administrators seriously watered down the coursework.

With the push for the STEM subjects (Science, Technology, Engineering and Mathematics) in the early 1980's, especially in Computer Science, many universities tried to increase the Mathematics requirements, only to find out that failure rates were 'unacceptably high'. When 40 years of college-level remediation efforts were shown to have failed, lots of 'experts' began pushing the idea that one should learn Statistics instead, and a watered-down version of an introductory course began to be accepted instead of an actual Mathematics course. Unfortunately, actual understanding of Statistics requires ability in Algebra, which is the very material that the students can't pass. This is all too often the problem with the Statistics in Sociology, Psychology, Education and related areas.

Some universities accept a very cursory course in Logic, doing less in 15 weeks than I used to teach in 3 weeks in Discrete Mathematics for Computer Science. Others accept a course called something like 'Math Appreciation', 'Excursions in Mathematics' or 'Math for the Liberal Arts'.

Theoretically, the standard Mathematics course requirement at many universities is something called 'College Algebra', which is an Algebra course dealing in functions, matrices, logarithms, exponentials and some minor topics. The material is the same as that usually done in high school Algebra II, at age 16-17. This is the material that I did in 3rd year of Secondary School.

Such a course would be the jumping-off point. Students headed to STEM areas would take Pre-Calculus, or Algebra with Trigonometry, and then on to at least 2 years of Calculus. Students in Business would likely take a watered-down Calculus course, and something in Statistics.

Throughout all of this, students and administrators blame the Mathematics departments for the failure rates, which haven't changed much in over 40 years. For reference, when I started teaching in 1978, the typical state university had a graduation rate of about 33% within 6 years. This was blamed on the Mathematics requirements. However, when I asked for the data on that, it did not exist. On the other hand, when we looked at predictors for college success, it turned out that grades in Mathematics courses and standardized tests were the best ones available.

2(a). The start date still isn't clear. Would it have anything to do with JFK and the response to the realization that Russia was pulling ahead in the Space Race? (Over here in the UK, I recall that at least Oxford and Cambridge made a pass in 'O' level maths an entry requirement; a friend who got a scholarship to Cambridge in History tried and failed in maths four times and the college let him through anyhow.)

I honestly don't know when. Certainly, these was a great 'crisis' in 1957 when the USSR launched Sputnik, and leaders recognized that we were behind in ICBM technology. Then, as now, we temporarily fixed the problem with immigrants, at that time from post-War Europe.

2(b). Do you think a universal maths course is still a good idea?

After years of frustration and watching failure, I would abandon the Mathematics requirement. BUT success in all of the 'good' areas (read entry-level salaries) requires Mathematics, from Accounting and Finance to Nursing to Engineering and Actuarial Science. So, we have the do-gooders saying that it isn't 'fair', and watering down all degrees.

3. You have previously told me that maybe only 15% of students are capable of higher level math. Is that because of natural ability, or failures in high school teaching?

When I started in 1978, about 15% of high school graduates, and 20-25% of entering college students had mastered enough Algebra to pass a placement test, and take College Algebra. When I retired in 2017, after multiple rounds of reform and the inclusion of Technology, those numbers were the same. The only difference was that the top 10% of students had weaker skills than their predecessors. I attribute the latter to the overuse of calculators and related software.

I have argued with my colleagues, administrators and all over the internet for decades that the problem appears to be something in the brain, while others argue that it is defective teaching. My argument is that, while the latter most certainly takes place, it would have to be almost uniform across the US to get such consistent results. This is probabilistically unlikely. My argument is aided by some research in brain development, showing that difficulties in learning Mathematics seem to be connected with either immaturity of the hypothalamus, or of the myelin sheaths in the brain, the latter being connected to the ability to move from concrete thought processes to abstract ones.

It is worth noting that the historical pass rates for the standard first-semester Calculus course are the same in Sweden as in the US.

4. You refer us to a paper on the cross-currents in mathematical education from the eighteenth century on:

http://jwilson.coe.uga.edu/EMAT7050/HistoryWeggener.html

What would be your answers to these questions, which seem to be the core issues:

4(a). What mathematics should all people learn, useful to them in their future work and daily lives?

Before I attempt to answer these questions directly, let me note a further problem. Not only does it appear that every person has a natural level of Mathematics attainment (my experience suggests 95% can learn Arithmetic, 85% can learn Algebra, perhaps 5% can learn Calculus, and much less than 1% can learn higher-level Mathematics), but there appears to be a 'window of opportunity' for that learning, as there is for languages. Hence, if we allow large portions of the population to opt out of the subject, they can never get back on track.

Useful math: in a modern world, every functioning person should have an idea of weights and measures, percentages, and basic probabilities. Most do not, and are not even close. That's why many people make such terrible financial decisions.

4(b). What should be taught to all, for the sake of national military security and economic prosperity?

We need as much of the population as possible ready to learn in the STEM areas. As more jobs are automated, the need for technical repair people goes up exponentially.

4(c). What mathematical learning should be reserved for an elite naturally qualified for the study? How, and how early, can such people be identified?

See the answer above, and add the need for experienced Mathematical modelers in all fields of study and research. The National Academy of Sciences in their report on the year 2025, suggested a scheme of collaborative research including an Applied Mathematician in just about every discipline, including the Social Sciences. Much of the issue with research in the fuzzier subjects is that it is Statistical in nature. That means that it is descriptive of what is (if you are lucky and people aren't lying). It is very rare to take the next step, and model the phenomena. Instead, people express opinions as to why things are the way that they are. In short, it is much easier to explain the past than predict the future. In the current climate, it is also more financially and socially valued, but totally stagnant. The science and SF writer Isaac Asimov noted this in his first ‘Foundation’ novel.

5. I was heading for this one and you have anticipated me. 

5(a). When would you say the 'window of opportunity' closes? 

Our hypothesis was that the window was around the typical age to move to formal operational thinking, at age 12-14 or so.

5(b). Does this mean there should be a wide-spectrum maths education up to that age?

In short, yes.

5(c). Is there a good way to assess aptitude for higher math?

Sadly, the only way seems to be for the student to try, although you can clearly see the tendencies in very young children - counting and sorting.

5(d). Does this also raise the issue of having sufficiently skilled math teaching in school?

Of course. In the US, most Mathematics teachers have far less than an undergraduate degree in the subject. A lot is taught by people who only had cursory education in the field, due to teacher shortages and seniority rules. Most of the most talented Math Ed students that I taught ended up not going into education at all, since the opportunities in areas like Finance were more lucrative and less stressful.

6(a). Continuing with secondary age math education, you have previously told me that your college freshmen come to you thinking they know material when they don’t. There appears to be more behind this than the school-teachers' lack of expertise - can you tell us what goes on in school to allow their students to maintain that illusion of knowledge? How are students assessed in American schools?

I would say that it's partly the Dunning-Kruger effect (https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect), and largely the difference in views on schooling between the US and Europe. Here in the US, there is zero respect for most teachers, unless they give good grades to the little darlings. Politicians and parents claim that 'good' teachers can teach anyone to mastery. People have tracked high school graduation rates (and tout them) as they rise over time. College grade averages and graduation rates go up every year. At the place where I worked, the rate went from about 31% over 6 years to 50% or more, with a discernible lowering of standards. It's one of the many reasons for these degrees in Media Studies and the like.

As for testing, we have the ACT and SAT, but lots of parents and administrators don't like them, because they show the actual weaknesses, so they claim that 'tests don't measure students'. We did a study on 7,400 of our students, looking at the ACT Math sub-score versus whether they graduated in 6 years or less, and found almost perfect correlation. When we presented this to administrators, they were less than impressed.

Our problems are compounded by the rules by which the state legislature supports the public universities. It used to be based on total numbers. Then, someone thought that we were wasting money by flunking out so many students, and changed the system to reward grades and graduation rates. Surprise, surprise, both went up immediately. By the way, the same legislature artificially increased the requirements (especially in Mathematics) to graduate high school, and then made it harder for the state universities to refuse students. The private schools and colleges had no such issue. Some remained highly selective, others just pretended, as there is no national exit exam in most disciplines.

Over the years, Ohio generated various competency tests for graduation, to be taken by sophomores (5th year students). The ones that I saw could be passed easily by a decent 6th grade student (age 12 or so), but they had to set the pass bar at 42%, and still many students failed it repeatedly.

Then, an impressively well-meaning and totally inept set of reforms changed the minimum Mathematics to graduate high school from Algebra I plus one more year, including numeracy courses, to 4 years, including Algebra I, Geometry and Algebra II, courses only previously taken by the top 30% or so. Because the less-talented students were thrown into the classes, and failure is failure by and of the teacher, students who would previously have obtained C's in courses were suddenly A students, which reinforces their illusion of mastery (a phrase which I coined when I was chair of our department). One of the reforms consisted of having State-wide end-of-year exams in those three courses. When they piloted the one in Algebra I, only 35% of students passed, even though the bar was set fairly low. The 'experts' at the State Board of Education tried to cover their tracks by changing the threshold, only to be admonished by the Federal officials. That test appears to have vanished into limbo. Interestingly, that 35% rate pretty much coincides with the historical 20-25% of incoming freshmen ready for college-level Mathematics. No-one that I ever talked to wanted to hear that either.

6(b). Leaving aside (for a moment) the teacher's own subject expertise limitations, do schools need better texts to guide the students, and better tests to check their progress?

There is certainly an issue with the quality of teachers, since they need to know the material. As the great Mathematician Polya said, "One cannot teach what one does not know". However, that same 15% of 12th-grade students who know enough to take a college-level Mathematics course becomes the 5% or less that can make it through two full years of Calculus and beyond. From that number comes all of our hard scientists (Computer Science, Geology, Chemistry, Physics, Mathematics, Statistics), and a lot of Biologists, plus all of the Medical Doctors and Engineers, the top Finance and Accounting people, Actuaries, and most technicians. That doesn't leave many people to go and teach. In the UK they offered scholarships and signing bonuses for Mathematics teachers, and got very few takers. We worked with a Foundation to take Math majors and get them the Education credentials that they needed. For obvious reasons, they were weak students, or they would not have taken this route. Getting them to pass Education courses was a doddle. Not so much to pass the Math certification exam. We gave them one such, then coached them for 8 weeks, and administered the identical multiple-choice test. Not one student changed their score substantially.

Textbooks are a whole other ball of wax. They are big business here, and written by professional writers who usually know no Mathematics or Education. What they try to do, very badly, is to give a script to a teacher who does not know what they are doing. The good news is that there are loads of free resources out there, such as Khan Academy and quora.com, which can help students. The bad news is that these sites are used instead of brainpower, so that the skills are decaying even further. It doesn't help that so many rely on calculators (many with Algebra and Calculus features built in), to the point that they might get the right answer by accident, but can't correctly transcribe the results, or understand them.

Personally, I would do what Singapore and many Asian countries still do, and that is to not require Mathematics beyond age 14 or so. This cuts you off from the Sciences, but not the Arts and Humanities. I would go further and have licensure (the old O-levels and A-levels would be fine) at several stages. I would not use the new GCSE stuff, as political pressure has degraded their quality as well. I would use those certificates to limit what people were permitted to do in the Sciences.

7(a). There is also (is there not?) an issue (in the UK as well as the USA) of social pressure on academically-inclined students, ranging from under-trying in order to be tolerated by their 'cool' peers, through to outright bullying of the nerd or 'swot'. 

There has actually been a lot less of that in the past 20 or more years, now that computers and computer games have become ubiquitous. However, there was also the movement that 'we need more women in STEM, other than Biology'. That meant open encouragement and nurturing, which is largely a good thing. It contrasted with the common experience of older female friends, who have told me about being told that, "Girls can't do Mathematics" (by contrast, in my years as an undergraduate at Exeter, 60% of the Mathematics students were female). This nurturing also meant that many students got great grades thanks to the miracle of 'extra credit', in spite of failing tests. I believe in tests in Mathematics. I will repeat something that I said years ago: In my 39 years of teaching Mathematics, perhaps 5,000 students, I had exactly two who failed tests repeatedly, yet could pass the equivalent of an oral exam. Both had burned their brains with street drugs as teenagers. One went on to work for NASA.

In the binary mode of thinking which is so common in the US, nurturing female students meant elevating them above the males. My eldest son, no slouch in the brains department, told me that the parade of girls getting the high school awards each year were often carefully manipulating their teachers. We had many such operators (both male and female) arrive as undergraduates, to find out that they actually had to perform, and fold under the pressure.

7(b). You have said how hard it is to recruit able math graduates to school teaching. May I suggest that not everyone is motivated solely by money and that such graduates might be more likely to apply for posts in schools where pupils were selected for their academic talent and commitment to learning?

No, it isn't just money. In fact, there are even public-school systems in rich towns and suburbs where typical teachers earn double what public college professors do. This comes at the price of very 'involved' parents, including those who bring lawyers to parent-teacher conferences. Again, a lot of the US is Lake Woebegone, "Where every child is above average".

8. In conclusion, and looking at what you have said here, please summarise why mathematics matters for the USA. What detailed program of action would you recommend for the reform of mathematical education to meet the nation's needs?

The US has always got a lot of innovation from immigrants. First in the 1800's, with many peasants displaced from Russia and Germany by farm industrialization, then by refugees from Europe after WWII, then by emigres from the Soviet Union, India and China in the 1990's. Government policies and racism have discouraged such immigration, although we still get quite a few from Vietnam, Bhutan and Nepal. Many of the other nations have encouraged the educated to return home. Our officials, of both parties, seem blind to this, as they tout 'American ingenuity' and destroy the quality of the education system.

If they realize in time, and make investment in the STEM areas, it will have to be done against the vacuous idea of 'equality'. If my experience and observations are correct, no amount of coaching will help the untalented. What would help would be to create the equivalent of grammar schools in the STEM areas, perhaps one per county, and move students there in grade 6 or so. Such selection would be brutal by tests, and data suggests that it would be called racist. Not to mention the children of the richer parents, who would cause the real stink.

The cost, if we do not do something correctly, will be to sink into Third World status. The coin of a vibrant economy is innovation and technology, and always has been.

Given the large numbers of very loud groups who insist that the Earth is Young and/or Flat, that vaccines are worse than the diseases that they prevent, that twisting people's necks can cure all ailments, and similar stupidity, I do not hold out a lot of hope!

Roboteacher? That's not how people learn... by Paddington

In my 39 years of professional teaching and even longer coaching the martial arts, I experienced several 'innovations' in teaching, and observed many different styles of teaching, leading to some of the following thoughts:

There is such a thing as talent, whether or not it matches intelligence in academia. You cannot coach talent into someone.

https://www.slideshare.net/esrbk/supervision-and-technology (Slide 9)

Ideas such as 'bug-in-ear' teaching (working from a script and pre-set collection of responses), or the 'flipped classroom' (watching videos at home, then coming to school to work with a teacher on problems) will never beat actual interactive teaching, which is a very human process.

There is a reason why we put the teacher at the front of the room, with the students facing them. They are, relatively speaking, the experts, and do know better. We are also a pecking-order species and respond to authority.

“Those who can't do, teach” is a crass way of expressing a small truth. Very often, those to whom a subject or skill comes naturally very often have no way to communicate that skill to others, because they have not struggled with learning it.

Many of the people that I worked with spent far more time in preparation for lectures than I did, presenting polished material in a clear way. I developed and scribbled on the board, making mistakes as I went. My students often did much better, and I was certainly faster, often completing the full semester of material a couple of week early. Many of my colleagues kept trying to have every student catch up, and ended up boring the accomplished ones, and still not educating the others.

Most of what is taught in Colleges of Education is pedagogy, with the concept that a well-trained teacher can teach anything, including material that they don't know. This is plainly ludicrous.

See also: https://www.teachwire.net/news/scripted-lessons-are-creating-zombie-teachers

If math education is threatened, so is our technological society, by Paddington

As the late Physicist Richard Feynman pointed out, Mathematics is the language necessary to understand the Universe. That is, to do Science. He lamented that so few people seemed able to learn the material.

In the US (and evidence suggests that this is true in most countries), only about 15% of 12th grade students have mastered Algebra I enough to take the first college-level Math course, often called College Algebra. This has been the case since I began teaching.

With Herculean efforts and massive amounts of money spent on college-level remediation for the 75% who arrive at higher education below that level, we have achieved about the same success rates as drug addition therapy, or poverty relief.

In other words, it appears that we need that 15%+ of students for all of the jobs which require at least some higher-level Mathematics (or the associated analytical skills), including: Actuaries, Chemists, Computer Engineers, Computer Scientists, Computer Technicians, Dentists, Doctors, Electricians, Engineers of all types, Financial analysts, Geologists, Mathematicians, Neuro-Scientists (the newest tool for them is systems of partial differential equations), Optometrists, Physicists, Pilots, Statisticians and so much more, and the teachers and professors of these subjects.

And how do many of our leaders respond? By claiming that we can replace all of these things by Artificial Intelligence, and by defunding the STEM areas at universities because they "aren't popular enough".

Forcing STEM initiatives through the Education meat grinder, by Paddington

A couple of decades ago, it finally dawned on the Powers That Be that society was becoming increasingly technological, and that we needed more people trained in the STEM areas (Science, Technology, Engineering and Mathematics), especially given the reduction in immigration of such experts.

This charge immediately caused many problems, even though the government didn't actually do much to help, and instead gave money to groups of Education faculty, who themselves didn't like or understand the necessary areas. All the latter could do was to try to force Mathematics departments at universities to go easier on students, which led to a generation of students unable to pass the higher-level Science and Engineering courses which require deep understanding of Mathematics to even discuss.

Then, there was the cultural problem, given that scientists have long been presented by the popular media as either boring men in lab coats, or dangerous sociopaths (the latter is only true for Chemists, in my experience). Add to that the distorted sense of 'independence' in the US, which all too often means disdain for any kind of expertise and gaining recognition is an uphill battle.

Then, there was university politics, which at my institution meant Psychologists (who already earned more and taught less than the Scientists) arguing that they should get extra funding as well, and others who wanted STEM to become STEAM, to include the ARTS. The Education College faculty even tried to convince us that the 'E' stood for them, rather than Engineering.

As it started to become apparent that recent graduates were more likely to get good-paying jobs if they had mastered a lot of Science and Mathematics, I started seeing claims that Liberal Arts degrees were better than STEM degrees because places like Google were looking for 'creative problem-solvers', with 'critical thinking skills'.

There are so many major errors in that line of thinking. Firstly, it is demonstrable that the average STEM major knows more in the Humanities than the average Liberal Arts major knows in the STEM areas. Secondly, such arguments are a very lazy use of the Excluded Middle, since an implicit assumption is that the STEM areas are not creative, and don't require critical thinking. In my experience, STEM experts are generally not welcomed in meetings precisely because they can see through the BS. As for creativity, I cannot imagine anything more creative than the solutions presented to life's problems by Engineers. It isn't as if they are just given plans by a higher power to implement.

As necessary as this move to emphasis on the STEM areas is, my lifetime of observation suggests that it is, at best, an underdog, and I would bet against it.

Maths learning: go figure, by Paddington

In over 40 years of teaching and tutoring Mathematics, and reading lots of studies in Mathematics Education, I have become convinced of the following:

1. Almost (*) everyone can learn more Mathematics than they currently know.
2. There is a fairly clear hierarchy of difficulty in the subject: Arithmetic, Algebra, Basic Functions, Calculus, Advanced Calculus, Real Analysis and the higher level material. Almost (*) everyone has a maximum level that they can achieve, long before the top.
3. The top level for 80% of the population appears to be Basic Algebra or lower, with only about 5% able to pass a standard Engineering Calculus I course.

Understandably, these observations have met with a great deal of resistance, especially from politicians and administrators who have read the studies that performance in college-level Mathematics classes is a good predictor of overall academic success (undeniably true). This leads to the insistence that we pass more students without lowering standards.

The people who insist that this is possible tend to fall into two categories: Those who themselves do not perform well in the subject, but blame all of their experiences on a single bad teacher, and those who found the subject relatively easy.

Large scale experiments, such as the mess in the O- and A-level syllabi in England from 1980 to 2000 show that increased pass rates mean lower achievement. In the US, cases such as the impressive improvement at Georgia State a few years ago were a result of lowered standards, but the people in charge blinded themselves to the fact.

Nonetheless, a higher percentage of jobs are now tied to higher education (including many trades), and most of the degrees in demand require levels of Mathematics far higher than Basic Algebra. We have also built an Education system which treats students as consumers, and the failure rates in Mathematics are unacceptably high to the administrators and political overseers. Never mind that those rates are close to the same across countries and decades, if not centuries.

What to do?

Form the perspective of a politician or administrator, especially one trained outside of the STEM areas, the obvious answer is to increase pass rates, and pretend to be maintaining standards.

This has been happening for decades, but it is getting worse. Be prepared for the majority of college graduates to have the paper qualifications, but not the actual abilities.

They will, however, be full of confidence in those missing abilities, thanks to the Dunning-Kruger
(**) effect, which is all that really matters.

ADDITIONAL NOTE (5 July):

To follow on, I would point out that one of the loudest and all-knowing groups to criticize what we did were the Engineering and Science professors.

Some decided that they could do much better, and tried to create courses which took students with the base competence to start Precalculus, and tried to get them do do Differential Equations in a semester. That did not go well.

Another group decided that our placement process was too restrictive, and insisted that they could tutor and nurture the students with weak backgrounds. Those students simply couldn't get through.

Yet another group thought that we were just too harsh, and were not getting students through to their courses. They believed the famous 'Calculus is a weeder course' meme. They encouraged students to take their Math courses at online places, or local institutions who were known to have higher pass rates (i.e. lax standards). Those students got great grades in those courses, and then couldn't pass the higher-level Engineering courses.

In short, we Mathematicians generally know what we are doing.
__________________________________________

(*) Excluding mathematical greats such as the late Paul Erdos, Terence Tao and the like.

(**) 'The Dunning-Kruger effect is a type of cognitive bias in which people believe that they are smarter and more capable than they really are. Essentially, low ability people do not possess the skills needed to recognize their own incompetence.'
https://www.verywellmind.com/an-overview-of-the-dunning-kruger-effect-4160740

Crazy Christians in America, by Paddington

Jesus summed up the Law and the Prophets in two sentences - without dinosaurs - and yet, as Paddington shows, some American churches have added and altered until unrecognisable...

As a sequel to my piece on US evangelism last week, I offer some tidbits.

1. In the last few years, the Texas School Board has held hearings on textbooks and curricula, with a great deal of pressure from fundamentalists. This is very important, as Texas buys the books for the whole state, which in turn affects the offerings of publishers. Among the proposals was the watering down or elimination of evolution (replacing it with 'change over time') and any Science which indicates an old Earth (most of it). Then there was the rewrite of History, marking Moses as one of the most significant people ever (he is a composite of several, including Sargon), and claiming that US law was based on the Ten Commandments and Leviticus, rather than Old English Law. Then, there was the cheery description of the slave trade, describing Africans as climbing on boats to come and work in the New World (technically true, I suppose).

https://www.dallasnews.com/news/education/2018/09/14/history-curriculum-texas-remembers-alamo-forgets-hillary-clinton-helen-keller
https://www.prindlepost.org/2016/05/removing-slavery-textbooks/

2. The fundamentalists have this bizarre concept of 'interpreting the Bible literally', and the assumption that it is totally inerrant, which leads to a significant level of doublethink. So much so, that adherents are forced to ignore most of Science and much of History. It can lead to some significant absurdities, such as the Smithsonian museum survey some years ago, in which 60% of respondents replied that the Earth was less than 10,000 years old, and 60% replied that dinosaurs lived on the Earth millions of years ago.

http://religion.blogs.cnn.com/2012/01/10/survey-u-s-protestant-pastors-reject-evolution-split-on-earths-age/

3. Last week, we had the latest end-of-the-world prophecy. The 'literal' reading of the Bible, especially Revelation, makes this a fun game. I have talked with adherents who can't wait for the Rapture and End of Days.

https://sensuouscurmudgeon.wordpress.com/2019/06/19/the-world-ended-yesterday/ https://en.wikipedia.org/wiki/Rapture
https://raptureandendtimes.com/

4. This week in Alabama, the buckle of the Bible belt, Roy Moore announced that he is once again trying for a seat in the US Senate. He was narrowly defeated the last time, when it came out that as a city prosecutor in his 30's, he was banned from a local shopping mall for trying to pick up girls as young as 14, and was accused of assaulting some. He became famous for planting a 10-ton granite monument of the Ten Commandments in his court building, when he was elected as Chief Justice of the Alabama Supreme Court. He refused to remove this blatantly unconstitutional decoration, and was removed from his post. He was elected again as Chief Justice, then suspended for ignoring US Supreme Court rulings on same-sex marriage. After leaving office, he set up a religious charity, of which the primary beneficiaries appeared to be him and his wife.

https://en.wikipedia.org/wiki/Roy_Moore

5. Also in Alabama this week, we have the news that the governor has authorized one of the most racist churches in the state (quite a high bar) to have their own armed police force, with full arrest powers. And Americans worry about Sharia law!

https://www.theroot.com/alabama-quietly-passes-law-allowing-church-with-history-1835697951

Brits have ***no idea*** about US-style Christianity! - by Paddington

My observation, based on the 40 years that I have lived in the US, is that the average Briton does not grasp what religion means to so many people here.

If the subject comes up, people might tell you that they are Catholic, Mormon, Jewish, Methodist and so on. But, if they answer with “I am a (Bible-believing) Christian”, they are almost certainly Evangelical Protestants, and very likely Southern Baptists, or the more extreme Pentecostalists, Seventh Day Adventists or one of their offshoots.

The short explanation that I can give as to the significance of these identifications is to imagine that 10% of the British population were following clones of Northern Ireland's Ian Paisley, but a little more aggressive. This is not an accidental comparison, as he was educated at the Fundamentalist Bob Jones University.

For the longer version, we need a little history.

The precursors of the Evangelicals were the Pilgrims who arrived in 1620. They had been thrown out of the liberal Netherlands for being intolerant, and encouraged to leave England, after they tried to tell King James how his church should be run. They came with beads to trade, and guns to steal with, but no skill in construction or farming. Had it not been for a few skilled sailors who landed with them, and the help of some local native tribes, they would have starved, and nearly did. A few generations later they had almost exterminated the local native tribes, and were starting to persecute and kill fellow Christians, like Quakers.

Their descendants were quite happy with the idea of slavery. So much so that the Southern Baptists were formed to support that very issue. Racism and exclusion have been a hallmark of the sect ever since. As late as 1916, there were Church picnics in Southern towns, centred around lynchings of African-Americans (https://www.cvltnation.com/nsfw-american-terrorism-lynching-postcards/).

Just as Voodoo and Santeria took African animism and combined it with Catholicism, the Southern states took Christianity and made it American. Take generous helpings of Genesis, Exodus and Leviticus, plus the nastier writings of Paul, throw in the miracles of the New Testament, but ignore the Beatitudes, and you have some of the flavour of the typical teachings, delivered with the energy of a used-car salesman in a bad hairpiece.

I did not understand the adherents and their views of a hateful God until it was explained to me that all of the vengeful ideas and proscriptions were for other people. Members of these churches believe in the idea of faith over deeds, which is expressed as “Once saved, always saved”. In theory, it is supposed to mean that followers of Jesus will be good thereafter. However, followers will tell you that once you are saved, you are going to Heaven, no matter what you do. Hell is gleefully reserved for everyone else, especially Catholics and Jews. While there are current alliances with both, the former are used to get their way with the government, the latter because Revelation describes a massive genocide of the Jews in Armageddon, and they need to be kept around for that.

In short, the whole belief system was a shock to me, having been raised nominally in the Church of England, complete with required Religious Education and church services 5 days a week.

Voter Suppression in the USA, by "Paddington"

In the good old days, the primary paths to power were generally simple. Things like birthright, marriage, assassination and conquest.

Now that most countries are democratic, at least in theory, one must claw to the top of some power structure, and then be elected.

One way to do the latter is to convince enough voters that they need you. This carries a high risk of failure.

To increase the odds, one could take the route favoured by Saddam Hussein, and famously described by Stalin, “It doesn't matter how the people vote, only who counts the votes”. While effective, this method requires a large conspiracy, which is hard to maintain.

In some places of the US, such as Chicago and Miami, Florida, a popular method used to be what is called the 'graveyard vote', having people impersonate dead voters. In New York, they just got enough street dwellers drunk and marched them to the polls.

With better modern record keeping, these methods are much less effective. In fact, despite claims by Republicans of millions of illegal aliens voting, and massive voter fraud, repeated investigation has only uncovered a handful of cases nationwide in the past two decades. Most of those were Republicans, claiming to 'test the system'.

It is the South, now primarily Republican, which has outdone itself, with the simple tactic of voter suppression.

We can begin with the founding of the Republic. The slave-holding states realized that their population was mostly slaves, and so apportionment of Congressional seats by population would leave them with little power. Hence, the allocation of two Senate seats per state, and the famous '3/5 compromise', where slaves counted as 3/5 of a regular person.

After the Civil War, the 14th and 15th amendments now allowed all former slaves to vote, so a new tactic was needed. The answer was to arrest the now-homeless freemen under vagrancy laws. Not only could they not vote while in prison, but also were generally prevented from doing so if they ever got out. An added bonus was that slavery was still allowed for people in prison, so they were a tremendous source of free labour, a system which lasts through today. This method was supplemented with poll taxes, which the African-Americans couldn't afford to pay, and literacy tests, which were strangely harder for people of colour.

Under the cover of claiming massive voter fraud, there have been major moves to require 'valid' identification to vote. This sounds reasonable enough, doesn't it? Now consider:

1. Texas accepts a state-issued Concealed-Carry Weapons permit as valid, but not a state-issued university ID card (those 'liberal' students)
2. Many older African-Americans in the South cannot get their birth certificates, as most were not born in official hospitals, and so cannot get ID.
3. In Arkansas, the single office to get a state ID (for those without a driver's license) is only open for a few hours on the fifth Wednesday of a month (not a joke).

And then there are the other clever techniques used most recently in 2018:

1. A bus in Georgia was taking a group of African-American retirees from a nursing home to the polls. The white workers at the home stopped the bus, and dragged them off.
2. In Georgia, there is automatic voter registration when a driver's license is renewed. But, it only registers the person for the national elections, not the local and state ones, keeping things like the Sheriff's position away from 'those people'.
3. A law in Arizona required voters to have a street address. Most Native Americans use rural post boxes, without one.
4. Dodge City, Kansas, closed its single polling station, and moved it a mile out of the city, miles away from any bus route.
5. The state party in charge after each census gets to decide the Congressional map for the state. In the last elections, Republicans have so gerrymandered the districts that they were awarded 12 of 16 seats in Congress for Ohio while only getting 52% of the vote.

While our leadership lectures the rest of the world on democracy, we behave more like a banana republic.

___________________________
Further reading (Ed.):

https://en.wikipedia.org/wiki/Voter_suppression_in_the_United_States

... and a recent example from Texas:

https://www.eurekastreet.com.au/article/the-frontlines-of-voter-suppression-in-the-us#

US Political Parties: Clowns to the Left, Jokers to the Right - by Paddington

I live in the US, where we have two barely-functioning political parties, the Grand Old Party (the Republicans) and the Democrats. We are unlikely to ever have a major third one, as the American culture strongly favours an A/B decision-making process, rather than recognizing that there is such a thing as a grey area.

Returning veterans of WWII, in both the US and UK, had had a taste of equality with the monied classes, and they wanted it to continue. The GI bill enabled many to get a good education and rise to the comfortable middle class.

That reality was reflected in the platform of the Eisenhower Republicans. It was pro-union, pro-Social Security, pro-conservation and largely anti-war. I would have been at home with that party.

However, in order to secure the Presidency, Nixon executed the 'Southern Strategy', which involved absorbing the racist Southern Democrats over Civil Rights issues. That was followed by Reagan absorbing the Social Conservatives over the issue of abortion and the teaching of evolution.

What has happened is that the party has become a very disparate set of interests, from anti-abortion, to isolationism/anti-immigration, to anti-feminism, anti-science, anti-education and so much more. The tactics are of fear and hatred. There is no part of the party which appears to follow the 'common good' parts of the Constitution to build anything, with the standard idea seeming to be that making the rich even richer will make everyone better off.

On the other hand, the Democrats look to be completely dissipated, trying to satisfy every marginal constituency, while also appeasing the very wealthy. If there is something positive to be said for them, it is that Democratic presidencies have resulted in smaller annual deficits than Republican ones. Where the GOP is anti-science on the subjects of evolution, an old Earth, climate change and several other topics, the Democrats appear not to believe in biological differences in genders, or innate intelligence, or the reality of alternative energy without nuclear power, or vaccines (although there are nuts on both side who are against the latter).

In short, neither party represents me, and the other parties are just out there, from the Natural Law party, to the Communists. There was even the case where a cult tried to poison a whole town in Oregon to gain political power.*

And that is why I call myself an orthogonal-American.

Representation of a 4-D cube (a tesseract) - at right angles to all 3 dimensions
https://interestingengineering.com/understanding-fourth-dimension-3d-perspective

_________________________________________________________________________________
*https://en.wikipedia.org/wiki/1984_Rajneeshee_bioterror_attack

Private vs. Public: A Closer Look, by Paddington

American conservatives like to say that private enterprise is always better than government action. They tell stories of government inefficiency, and promote the idea that competition drives all innovation.

But is it really true?

Before our society fell into the pit of “I've got mine” in the mid-1980's and started to pretend that we could have everything we wanted without paying for it, here are some of the things that the government used our tax funds to do:

- start Social Security, Medicare and Medicaid, saving a generation from dire poverty and possible civil war in the Great Depression.
- built a fantastic National Park System
- helped to save freedom in World War II, and to rebuild Germany and Japan afterwards to prevent global war from happening again
- built the Interstate highway system
- cleaned the air and water in places like Los Angeles
- started the nuclear power industry
- started the electronics industry
- started the computer age
- started the modern drug age, developing the first antibiotics, and things like the Epipen
- landed humans on the Moon

Most of these things were of no interest to the business community before they were developed, because the pay-offs were too far in the future at the time. Once the concept was proven, they swooped in and sucked up all of the profits from the taxpayer-funded research and infrastructure.

Now let's look at some of the negative parts of competitive private enterprise:

- we tried to privatize much of the Iraq and Afghanistan conflicts to avoid a draft, and ended up with gasoline delivered there by Halliburton for $15+ a gallon, and dozens of Afghanis beaten to death at Khandahar airfield by Blackwater operatives, in our name.

- even though the average private school underperforms public schools in standard measures, certain parties pushed the charter and voucher movements. The charters in Ohio are so underperforming that they are the laughing-stock of the charter movement itself.

- the state universities in the country are a bargain, producing top-quality teaching and research at 40-50% of the cost per student of private universities, yet get little but criticism and more funding cuts
- we used the overflow of convictions from the War on Drugs to fund a system of private prisons, which turned out to be at least as expensive as public ones, and totally corrupt, with many judges bribed to give longer sentences.*

- we have the most expensive per capita healthcare system in the world, with some of the worst outcomes in the developed world. Until the ACA, the majority of that spending went directly to the insurance companies, which might be a win for capitalism, but makes mockery of the 'competition' idea.

In short, except for the shuddering fear that Americans experience at the word 'socialism', we actually seem to like the concept, when we look at individual cases.
________________________________

*E.g.: https://www.forbes.com/sites/walterpavlo/2011/08/12/pennsylvania-judge-gets-life-sentence-for-prison-kickback-scheme/

Mathematics - the crumbling foundation of US wealth and security, by Paddington

Let's start with a simple syllogism:

Modern society requires cheap energy and lots of technology to function.

Technology relies on basic science.

Mathematics is the language of science.

Civilization requires large numbers of technicians to maintain our technology, engineers to solve problems and develop new technology, and scientists to do both basic and applied research to develop new ideas.

Most of the higher-paying jobs now require higher levels of both Mathematics and applied technology.

Therefore, it is good for society as a whole, and the individuals concerned, if we improve Mathematics education.

Our politicians have gotten the gist of this logic several times in my life, beginning in 1957 with the Sputnik scare. Most of the American public saw the resultant Space Race as a matter of US pride. Those able to think knew that the USSR had the one-sided capacity to launch missiles at the US. What was presented as a bold exploration venture was an exercise in self-preservation.

Today, the fear is on the vulnerability of our many computer-based systems. It is just as real a danger as nuclear war, but not quite as obvious. The attitude seems to be that, “if it breaks, somebody else will fix it.”

There is also the small matter of repeated studies showing that success in any higher education is directly correlated with performance in College-level Mathematics.

This awareness led to several rounds of attempts at Mathematics teaching reform, at least four of which happened in my career as a Mathematics professor. I was even involved in a couple of them, trying to do the right thing.

We had the 'New Math' of the late 1960's, which attempted to put the subject on a firm theoretical footing. Next was the 'lean and lively Calculus' movement in the early 1990's, to have students learn 'deeper', using more graphical methods and less Algebra. Then came project-based teaching, which had students working in groups to 'learn' Science, Mathematics and English. Most recently, we have had the push for 'flipped' classrooms, in which students watch videos to teach the lessons, then sit in the classroom while the teacher helps them solve problems.

All of these reforms shared a few features:

The instigators were energetic, enthusiastic, honest and delightful, and were absolutely convinced that they held 'the answer'.

Every such approach wanted to use technology, starting in the 90's with graphing calculators, followed by laptops. Later it was computer Algebra systems.

Every approach ignored human nature.

Each approach showed initial gains, in what is known by Psychologists as 'The Novelty Effect'
( https://en.wikipedia.org/wiki/Novelty_effect ).

Each reform had an obvious flaw built into it.

The New Math failed in large part because the teachers didn't understand what they were teaching.

The graphical/Algebra-light Calculus left students able to generate (sometimes) correct answers, with no understanding of where they came from, and no ability to interpret them. In extreme cases that I experienced with some top students, they could no longer tell the difference between subtraction and division.

In the project-based models, students rarely learn anything significant, but get the impression that they have learned everything. That makes them ready for management, not so much for productive work.

The flipped classroom model ignores human nature. We learn by mimicry, for the most part. In teaching martial arts, I have noticed that, if you give verbal instructions, and do something else with your body to demonstrate, most students will attempt to do what you did, not what you said. Except for the most talented, people learn Mathematics in that way, by watching a teacher solve a problem, then solving several just like it, with numbers changed, then having more of the concept explained.

Every single reform ended up with worse results than when we began. Even more depressing is the fact that, instead of returning to the original ideas, the system just tried the next new model. When I started teaching in 1978, students either mastered their Algebra in Calculus I, or they failed. Now, the bad Arithmetic and Algebra has penetrated as far as Differential Equations (Calculus IV in some systems), because the bad habits are just so ingrained. I once had 2/3 of a class of Honors Calculus III end up with the equation '2x=3', then write 'x=3-2', so 'x=1'. And these were the select of their year.

Meanwhile, the Asian systems are churning out Engineers, while we busily criticize their education systems as not 'inspiring creativity'. There is some justification for this, and many in Asia agree. Students there are taught by rote, and not allowed to stand out. On the other hand, the successful have actually learned something. By contrast, I have met many students who have been labeled as 'creative' who consistently generate ideas and solutions which are as practical as oars on a spaceship.

There is a way to generate more people with talent in Mathematics and the subjects which rely on it: Select them at say age 12, and put them together in special schools. It reduces bullying, and their natural competition will drive them to succeed.

The Contradictions of US Education, by Paddington

What are we doing wrong in the US education system?

The short answer is: nothing.

The appropriate way to evaluate a system is based on what it is designed to do, and the education system is not designed to do anything. Rather, throughout 200 years of public education, it has been given a sequence of demands, and has responded by adapting organically.

Among other things, the system has been required to:

• prepare young men for factories and the military, and young women for marriage and domestic service;
• serve as a mechanism for upward social mobility (Dewey);
• produce an educated electorate (Jefferson);
• generate 'well-rounded' individuals;
• serve as a minor league for professional sports;
• fix major social problems (Head Start);
• provide enough science and engineering majors to keep the economy working;
• graduate most students, each immediately ready to be successful in higher education, or prepared for a job;

with no recognition that some of these goals are in direct conflict.

For example, demanding increased performance necessarily means that more students will fail to clear the bar. Alternatively, demanding increased graduation rates necessarily leads to grade inflation and lowering the bar. There is no way around this, as it is precisely the problem of Type I and Type II errors in statistical testing.

The over-emphasis on sports in some districts, and the effect on grade inflation, has been well-recorded. What is rarely noted is the effect on the other students. If unprepared student athletes, or others who seem to put no effort into their studies, still progress to the higher grades, what is the immediate incentive to work hard?

If teachers are trying to fix every social problem in their classrooms, where is the time for learning? In my experience, the more talented students tend to get less attention, because 'they will learn anyway'. This is a recipe for mediocrity.

In short, before we try yet another major overhaul of the system, we should perhaps first decide the goals to be met, and also check that those goals are actually achievable.

Forget tax changes and austerity; invest in R&D and education

From the USA, "Paddington" says: I'm trying to cause trouble again. I sent this to Michael Gerson of the Washington Post, and Paul Krugman of Princeton and the NY Times:

________________________________________________________________________________

There is a great deal of discussion on the amount of economic growth that can be generated by changes in tax or fiscal policy.

What appears to be missing in that discussion is the likely answer: none. In fact, the changes proposed are very likely to hurt the economy.

The reason is that all long-term growth can be attributed to innovation, discovery and conquest. The first two are themselves dependent on earlier basic science research. The last is one reason why the Roman Empire collapsed when its expansion stopped.

Without basic science research, open access to the results, and a lead time of 20-30 years, there is no major innovation. The technology boom which began around 1990 was built on the government-funded research of the 1940's through the 1970's, in computers and electronics. Companies do not generally invest in research until the potential profits are demonstrated. When they do so, the results are often treated as proprietary, which impedes human advancement.

The US reduced funding for basic science around 30 years ago, which is one reason that most 'innovations' that we are seeing are the offshoots of earlier work, and nothing really novel is appearing.

Added to that is the attack to trim university budgets and faculty lines. Those faculty members are the very people who generate much of that new knowledge, for the common good.

Finally, we have the escalation in the cost of higher education and the proposed elimination of tax write-offs for it, without the realization that most of the people who staff the laboratories of the country are from middle-class families. Children from wealthier families choose business, law and sometimes medicine. Why more children from poorer families do not choose the STEM paths is a matter of some discussion.

In short, we are proposing, as a country, to shut off every avenue for the very innovation that we need to thrive. Our policies are a recipe for economic disaster.

Declining by degrees

US professor "Paddington" writes: 

About 20 years ago, our political leaders finally became aware that the well-paid industrial jobs were becoming much more technical, and fewer in number. They looked at the famous statistic that college graduates earn more over a lifetime than non-college-graduates, confused correlation with causation, and pressured the education system to increase the number and percentage of graduates, and the quality of them.

The last is impossible, but it was quite easy to increase the number and percentage of graduates, simply by watering the coursework down.

However, there are disciplines where actual mastery matters, including Nursing and Engineering.

I contend that it is only a matter of time before we separate 'real' degrees from the others.

This leaves the question of how to designate the other degrees. Since B.S. is already taken, I would suggest B.E. (Bachelor's of Equality), B.F. (Bachelor's of Feelgood), or B.N.P. (Bachelor's of Nothing in Particular).

HEALTHCARE USA: a guide to "Obamacare" (the Affordable Care Act)

Sackerson has asked me to write a short piece on the effects of the Affordable Care Act, based on my 39 years of fighting insurance companies in the US.

Since this is primarily for readers in the UK, it helps to understand that many Americans do not consider healthcare to be a right, or even an issue of infrastructure. The fact that it is referred to as the 'healthcare industry' should show that the emphasis is on the money.

There are many different programs for it, including:

·         Veteran's Administration – a completely separate set of doctors, hospitals and testing facilities, paid through the Defense budget, only for those who have served in the Armed Forces. In the past two decades, its funding has been reduced by conservatives. The inevitable problems which have arisen during two wars have been used as justification that the system should be privatized.

·         Medicare – a federal program for the elderly and disabled, paid by payroll taxes. Ever since it was introduced by President Johnson in his Great Society initiative, it has been another target of conservatives.

·         Medicaid – for the poor, paid by a mixture of state funds and payroll taxes. Also introduced in the Great Society and yet another target for anti-government conservatives.

·         Group insurance through employers – lose your job, lose your coverage. Only available if you work enough hours.

·         Group insurance through unions – rapidly going away as the unions do.

·         Group insurance through small business co-ops – typically expensive.

·         Personal purchase – very expensive.

Most of these offer multiple plans, requiring specific doctors and hospitals (or a hefty financial penalty),with assorted co-pays, lifetime maximum benefits and deductibles. I have three degrees in Mathematics, and I still cannot figure out what procedures other than basic office visits will cost, as the bills dribble in, sometimes for a whole year.

That said, here are some of the changes that have taken place:

More people covered

Before: An estimated 31 million or more uninsured.

After: Over 20 million people with affordable insurance.

Insurers' profits capped

Before: Insurance companies kept up to 54% of all premiums.

After: Insurance companies restricted to 20% of premiums.

Fewer health-related bankruptcies

Before: Medical bills were the #1 reason for bankruptcy.

After: Medical bankruptcies down 90% or more.

Less misuse of emergency services

Before: People without coverage used Emergency Rooms for primary care, paid by increased hospital costs for everyone else. Hospitals are required by law to treat critical patients.

After: Much less pressure and cost for many of those hospitals. Better outcomes for those with chronic conditions.

Extended coverage for dependent children

Before: Dependent children age 18+ not in college, or 22+ in college lost coverage on their parents' policies.

After: Coverage for dependent children up to age 26.

Birth control

Before: Many policies did not cover any birth control, although most covered viagra.

After: All policies cover birth control.

Cover for pre-existing conditions

Before: People with pre-existing conditions, from arthritis to cancer and much more, could either be refused coverage for those conditions, refused any coverage, or made to pay for much higher risk and higher cost policies.

After: Pre-existing conditions covered with no penalty.

Benefit caps removed

Before: Most systems had a lifetime maximum benefit, typically around $1 million, which could be exhausted in a couple of months of intensive care.

After: No lifetime maximum.

DRAWBACK: unintended effect on work contracts

Before: Small companies (around 50 people) could offer as many hours to their workers as they wished without offering benefits.

After: Part-time workers with over 30 hours per week must be offered coverage, so many people had their hours cut back.