Mr Hejný, a pensioner who used to be basically innumerate, was suddenly embraced as a teaching guru by lots of "progressive" teachers. He says that the children don't have to be forced to adopt any idea – every kid will rediscover everything about mathematics he or she needs (which is utterly ludicrous, of course). Formulae and identities are "evil", he says (which is a slogan denouncing the very heart of mathematics). Also, mathematics should be maximally conflated with everyday life situations (so that children's thinking becomes maximally muddy and they can't isolate ideas and concepts and separate them from each other – and mathematics critically depends on this isolation) etc. I've explained why every single "principle" of this "progressive" methodology is just the opposite of the truth. Let's hope that in the wake of Brexit, at least the British kids will be shielded from this particular disease.
But people adopting these things aren't doing any science. They are driven by laziness and by ideology. This method that became tolerated is a great way to basically kill the teaching of mathematics or at least any rigorous enough requirements. It is clearly "mathematics as imagined by those who hate the actual mathematics". The Hejný method is just a campaign with a name.
Needless to say, the Western education systems are full of similar garbage. Schools dedicate less and less time to "hard education" and an increasing amount of time to ideological brainwashing and indoctrination by the political correctness. A major example: Children are increasingly encouraged to write essays praising the European Union and believe that they're very creative and independent if they do such things – clearly the opposite of the truth.
Last night, a commenter on my Czech blog pointed out a story in the Czech media. With a 6-day delay, we learned about a plan that the British readers were informed about from outlets starting with the Daily Mail:
Half of primary schools set to teach maths Chinese-style: Children will be required to practise sums and exercises until they can prove they have mastered themThat article seems very clear and I think you don't need another one.
Minister of schools Nicolas Gibb (Conservative Party) has noticed that despite the materially modest conditions in Chinese schools, children in Shanghai are some stunning 3 years ahead of the British schoolkids when it comes to their skills in mathematics. So he announced a plan for a revolution: In the following years, one-half of the U.K. primary schools will be switched to the "Shanghai maths" style of teaching mathematics.
It's pretty much the exact opposite of the "progressive" methods – while it's not too different from what the schoolkids were exposed to before the "progressive" rituals began to spread sometime in the 1970s. All the children in a classroom are learning from the same page which contains "pure exercises" – no relationships with the everyday life situations – and they must succeed. A teacher asks a question, a selected student must answer it, and the whole class must repeat it and rhythmically applaud. Smarter kids are more likely to be the "leaders" more often and they are encouraged to deepen their understanding of the principles instead of getting ahead.
This is my summary. The story in the Daily Mail tells you much more than that. Among other things, you will learn that the intense part of the Chinese class only takes 35 minutes – one-half of the British class that is often 70 minutes long – but they still have much better results.
What do I think about "Shanghai maths"? It's surely more right than the "progressive methods". They are actually teaching something that is well-defined. And the results speak a clear lesson. The South Asian and Shanghai kids seem to be better in mathematics. So it's a reason to think that their methodology could be better than the "progressive" Western ones.
I agree with those who say that the methodology isn't necessarily the only reason. The Chinese may have a higher IQ by 10 points, much higher innate discipline combined with lower creativity, and they're just used to rote learning (just imagine how shocking it has to be to learn the Chinese letters). But in principle, European children may surely learn something comparable to the Chinese.
Also, mechanical arithmetical calculations are not exactly what I consider the bulk of mathematics. They provide you with some basics and some raw material to use in more structured, truly mathematical contexts, but one shouldn't get stuck with them. Identities, complex methodologies, theorems, proofs, more complex algebraic structures, relationships to geometry etc. have to dominate in mathematics from some moment. And the fact that we have not only calculators but computers everywhere should influence what kids learn (i.e. some change e.g. from the 1930s). However, I think that Gibb's decision is a step in the right direction especially because the "progressive" world view is so utterly misguided.
The experts' opinions about "the right ways to teach" aren't really a science. But to adopt the methods from a place that seemed much more successful than others is something that I would consider a quasi-scientific form of common sense. And Asia is ahead of Britain and ahead of "us" in many things.
Progressive Western "experts" vs Asian food
I can't resist to mention another topic where "soft science experts in the West" clash with "benefits of the Asian approach": the opinions about "healthy and unhealthy food". OK, so I learned that an overwhelming majority of my relatives in a certain part of the family consider the magazines for the most ordinary people – many of which would deserve to be called junk tabloids – to be the Holy Scripture, especially when it comes to the insights that "this food is healthy and that food is not".
You know, even in the professional research magazines with a high impact factor, it's been seen that at least 50% or so of the published articles turn out to be false. A rational person has to be careful before he trusts a random article of that kind. I find it absolutely obvious that these "piles of wisdom" written basically by ordinary people are much weaker than the professional articles in medical research journals. It's basically noise.
Obviously, I am far from understanding much of chemistry or biology etc. But I think that people must be absolutely detached from reality if they think that random physicians let alone random journalists are more likely to be correct than me (or someone like me) on some isolated scientific topic that I was (or he was) interested in and intensely studied. It just seems utterly crazy to me that some people – and it's probably most people in our countries – completely fail to get the basic point that a big portion of the "health food science" that is written in random journals (and lots of similar "soft science") is just almost complete junk.
What I find particularly crazy is that these people mindlessly buying all the "authoritative insights" in these journals aren't worried at all by the fact that they contradict each other and they are changing the conclusions all the time. If self-confident self-described food experts A,B loudly promote their exactly opposite verdicts on a food, doesn't it self-evidently imply that at least one of them must be wrong? Is it possible that someone doesn't notice or that her or his belief in the qualities of these scientists or pundits isn't affected by the inconsistencies? And if A,B have used basically the same general methodology to arrive at their outcomes, isn't it clear that the methodology isn't a scientifically trustworthy one so both A,B should be ignored even if one of them got the right answer (by chance)?
Feynman on pseudosciences and would-be experts. People may disagree about many particular questions – who is an expert and who is right on this or that – but I find it stunning that some people and perhaps most people haven't been capable of noticing that a significant portion of the science-like wisdom in the "media for ordinary people" doesn't hold water. But maybe it's better for the people with IQ below 100 to believe such magazines uncritically because those were written by journalists with the average IQ of 110 or so who dedicated at least some time to the issues? By the way, have you ever read the 7-page 1965 report with Feynman's opinions about the right way to teach mathematics?
OK, a particular article in a magazine I consider mostly trash has voiced random opinions about almost all foods. Almost all food is "bad", of course, while some previously criticized food was said to be "good" etc. I would agree with some 50% of the verdicts ;-) and perhaps a bit more than that but the agreement is clearly a matter of chance because I don't find their methodology justifiable. The most controversial item was the coconut oil. The article declared it a terrible food – mostly because it contains the saturated fats which cripple one's cardiovascular system.
I am convinced that this is a part of the "fat myths" that have been around for some 50 years. I am not a systematic eater of the coconut oil but I do find it obvious that even if it became a majority of the food you consume, it would be basically fine for you. Although I am not sure about all of them, this otherwise "neutral food" has lots of benefits outside the cardiovascular system. And when it comes to the cardiovascular system and saturated fats, it just seems clear to me that there exists no credible scientific literature that would imply that in the full generality, saturated fats are bad for the people at the end – that they lower the life expectancy, for example. It's silly to "completely demonize" all of cholesterol. At the end, it's an essential part of cell membranes. Human life is surely impossible without cholesterol – and our bodies are surely able to deal with it in some ways. A human body contains some 35 grams of cholesterol and has to synthetize 1 gram a day. The devil may only be in the details.
Many informed as well as quasi-informed people quickly start to talk about lots of technical details in chemistry. PUFA, omega-3/omega-6 ratio, MUFA, SAFA, MCT fats, LDL, HDL, and so on. But I think it's important to realize that these things are very complicated and to assign any of these chemical compounds with a universal positive or negative sign may be an unjustified ritual and a mistake. There are way too many statements about these compounds and their classes that are not really backed by trustworthy research or that are not being sufficiently verified – basically superstitions.
If you look at some research carefully enough, you will see that certain claims about the harmfulness of fats in general etc. are just wrong. For a great example, this 2010 survey with 799 citations has followed 347,747 people for 5-20 years and found that saturated fat (like the acids in coconut oil) increases neither CHD, CVD, nor strokes. Someone may respond with 50 less careful or less extensive surveys or tabloid magazine articles but the weight of the evidence is not the same.
Just to be sure, the paper I mentioned leaves the possibility that the replacement of saturated fats by something particular reduces the cardiovascular diseases and indeed, there exist papers claiming that the replacement of saturated acids by polyunsaturated acids (PUFAs) is "healthy" while the replacement by carbohydrates or monounsaturated acids (MUFAs) makes no difference. Before you get excited by PUFAs, you should know that they're unstable and oxidize (e.g. go rancid) at rather low temperatures, outside the body and in the body, producing free radicals which are bad for many reasons (cause inflammation which contributes to diabetes, some cancers, obesity, fatty liver, aging pigmentation etc.). When likely enough health risks of many types are added, I am pretty sure that saturated fats are better than PUFAs, especially for those who aren't obese or "permanent cardiovascular patients". Saturated fats are the most stable ones. A neutral food. You know what you eat and there aren't too many unaccounted for chemical reactions.
The American Heart Association is probably the most prestigious group of people (well, mostly an activist, not scientific, group) that tells everybody to avoid saturated fats – at most 5 or 6 percent of your daily energy intake should come from them. About 90% of the coconut oil are saturated fats. (They don't even pretend to have credible papers or evidence. Also, they are very far from discussing the PUFA vs MUFA replacements.) But the idea that a diet with more than 6 percent of the saturated fats is "dangerous" is just utterly implausible. Instead of making guesses about the chemical processes in your organism, it's probably easier to evaluate this complex task by a real-world experiment.
Asia has been making this experiment for a very long time. The nations in Southeast Asia consume a much higher fraction of the coconut oil (and even palm oil which is almost certainly less healthy) and their health seems at least as good as the health of other comparable nations. Isn't it enough to see that their diet just can't be catastrophic for human health? Why would any rational person take complete bans or almost complete bans on some types of food seriously if the world is constantly demonstrating that this fearmongering is unjustified?
It's not just about fats and their types. Take the claims about the dangerous "dirt in Chinese restaurants". How bad can those things be? The Chinese restaurants in Europe and America are almost certainly more rigorously verified than those in China which is generally poorer. But even in China where they cook and eat in the Chinese way all the time, the life expectancy is 75 years. Western countries have a higher expectancy, often slightly above 80 years, but much of it is surely due to the fancier and wealthier healthcare. If any aspect of the Chinese diet and Chinese restaurants reduces the life expectancy at all (and even the sign of this effect is unclear), the decrease is almost certainly negligible. Should you be afraid of some 10% of this decrease? I don't think so.
We the Europeans or Caucasian Americans etc. may be a little different than the Asians and I want to keep my belief that we're better in many ways. But the soft sciences and the magazine experts' lessons trying to demonize so many things that are completely standard and dominant in Asia – food and teaching methods, among others – are self-evident bogus pseudoscience and the people who trust this pseudoscience are extremely stupid at some elementary level.