I became a favorite source of quotes for the journalists who write about the constructivist methods to teach mathematics – although they sometimes fail to mention my name. But when they address a critic who thinks that the exercises in those classes are analogous to Sudoku; and that some kids like those classes simply because they're more similar to gyms than mathematics, you can be sure it's about me.
The Euro, a Czech weekly currently belonging under The Youth Front (and therefore owned by PM Babiš through a trust), has published two new texts promoting the Hejný method. One of them is an interview with Milan Hejný, the son of the "inventor" of the method. The title reads
A detail I find remarkable is the religious language. We, the critics of the method, often describe their meetings as religious events. The prophet Mr Hejný has found some miraculous method at schools and everyone has to worship Him – and the method. They must either be ignorant that this is a widespread criticism, or they must deliberately embrace it. For one of these reasons, they don't hesitate to call their misguided rules "commandments".
It's wrong to approach the teaching of mathematics in a religious way. And by the way, it is illegal to impose religion on schoolkids. Once the "first commandments" really start to resemble those in existing religions – and I think it's the case – they're violating the law in the same way as a church that is turning a school into a branch of its religious structures.
Aside from some basics of the method and facts about his family, this old guy says a lot of arrogant and crazy things. The accumulation of the knowledge is only the fourth most important thing at school, we hear. The education of decent people is at the top. By decent people, he clearly means arrogant SJWs such as himself and the crooked individuals who worship him. Pretending that people become "more decent" by supporting his utterly misguided methods and philosophy is immensely immoral.
The knowledge isn't the most important thing. But the more important things cannot be taught at schools – either because it's impossible due to the laws of biology or because it's incompatible with democracy. It may be better to make kids talented and independent in various ways so that they don't need the classes at all and they learn it by themselves – except that the main personality traits are determined by Mother Nature, not schools, and it's usually very unnatural to expect a kid to study by itself. And it could be more effective to change the political and otherwise important views of the kids in some good way – except that in democracy, no political force should have the power to dictate what the "good way" actually is.
He describes their family as some victims of the totalitarian regimes – which is demonstrably deceptive. And then he insists on eliminating the multiplication table from the schools. When was the last time that you used it, he asks the journalist? Holy cow, I use it dozens of times a day. It's about the damn multiplication. A thinking member of a civilized society can't live without multiplication.
Hejný also wants to eliminate variables. Like the variable in the equation \(2x+3 = 15\). Sensible teachers may debate what is the ideal moment when variables should be presented. The answers are in between the fourth graders and seventh graders. There are some subtleties. The variables involve some social conventions – such as the usage of letters, especially \(x,y\). You could use some totally different letters – or even multi-letter names or symbols instead.
(I think that many of you will have similar memories from the childhood: I was always interested in mathematics-related things but not so much in social conventions. So although I used the "methods of equation solving" as a fifth grader, I didn't use the standardized symbols and routine operations – and perhaps not even things like \(x,y\) – in most of my scribbled notes. As far as I remember, I really learned the "drill" of solving the equations and sets of equations in the standard way at school. It obviously replaced my informal methods that had the same purpose. There's nothing wrong about learning a standardized methodology at school.)
But there's no good reason for kids not to learn these immensely useful constructs in the most conventional way – so that it becomes very easy for them to communicate with everyone else (even with adults, professionals, and foreigners). What's often difficult about the equations is the meaning of the equal sign, some folks mention. That's right. A small kid thinks that the equal sign always means "here you have the uncalculated thing on the left hand side, calculate or simplify it and write it on the right hand side".
However, that's not how equations may be framed. Both sides of the equation (which are separated by the equal sign) may be equally "calculated or uncalculated" and "simplified or unsimplified". The point is that the equation with the equal sign is a proposition and the proposition may be manipulated as a whole (for example, you may add an expression to both sides). That's something slightly different than just calculating the value of an expression such as \(2+3\).
At any rate, Mr Hejný says that the abstraction may appear in his books but it mustn't be mandatory. There are textbooks A,B,C,D,E,F,G in his setup, we hear. F is for the eighth graders (reorganized as "fourth graders in the Latin-style middle schools") but only G has the variables and it's for the top notch mathematicians among the schoolkids. He wants some 2% of the kids to learn variables.
It's just insane and it could disrupt most high schools if the Hejný method becomes really common. At high schools, the students simply need to be able to understand the variables. It's needed not only in mathematics, it's needed in physics, chemistry, and even some subjects outside natural sciences. They should already be using them and manipulating with them in many ways. A kid that finds out that variables or equations are just too difficult may be lost throughout the high school. In effect, Hejný wants to bring the elementary schools to the situation in which the variables are understood by basically nobody.
It would mean to slow down the education of mathematics by 2-5 years – because the high schools obviously need to make sure that the kids understand the variables. Is it really fine to turn high schools into de facto elementary schools? And elementary schools into de facto kindergartens? And he clearly doesn't want to stop there. By placing the self-confidence of the schoolkid at the top, he gradually wants to turn graduate schools into de facto kindergartens.
"My kid is already so mature. Last week, he saw snow and as soon as he saw the snow, you know what snow is, he screamed: Snow is here, snow is here. We will build shnew shnew shnewmen!" – Oh, that's cute and impressive. And how old is your baby? "He was recently 15 years old."
Hejný wants to turn the kids into retarded ones and to be sure that this becomes the societal norm, he wants to make it a blasphemy to mock such retarded children. At the end of the interview, he says that the professional mathematicians are genetically ready for abstraction (so far so good) which is why they consider classmates who haven't mastered variables (and abstraction) to be inferior (a deliberately tendentious language, he's trying to make the mathematicians unpopular) which is a "strongly asocial behavior" (and by now, that's just a brutal insult).
Just imagine the insanity of that. The man whose name is most frequently associated with the teaching of mathematics at Czech elementary schools thinks that everyone who thinks that abstraction (e.g. variables) is important should be labeled "strongly asocial". Maybe he will want to jail all mathematicians and similar people into mental asylums as if they were psychopaths.
I am sorry, Mr Hejný, but it is you who is a senile psychopath in this debate. Mathematics, mathematical abstraction, variables, multiplication tables, formulae, and mathematical algorithms that you fight against are important, and so are the people who work in various occupations that require this standard type of mathematics for adults and that build on this background in many ways. If they're a minority, they're a minority, but it doesn't make them or their skills and methods less important. On the contrary, the scarcity of such people probably makes them more precious. In the future, such people will also be needed which is why a sufficient number of kids must be prepared for such occupations. We already have a shortage of kids capable of doing technical and quantitative fields today (and employers see a shortage of potential employees in technical occupations). If you deliberately plan to reduce their numbers further, where will we end?
Even communists had quite some respect towards such "minority" things. They didn't cancel variables or multiplication tables at school although the average kid of the working class parents has always had greater problems with these things than a kid from the wealthy classes. In fact, they didn't bastardize the education of mathematics and STEM fields at all (well, almost). They didn't really cancel operas, either – despite the fact that most people can't appreciate it because their ears aren't sufficiently refined for that music and operas were connected with the "other classes". But just because most people don't have XY doesn't mean that XY isn't important – communists understood but Mr Hejný and his disciples don't.
The Euro has published another text on the topic, an opinion piece by Ms Hana Boříková (the same lady did the interview). That opinion piece had a ludicrous original title as well – one that presented Granddaddy Forrest, a character from numerous exercises (where animal species represent small integers), as a vampire that terrifies children (the purpose of that title was to mock the critics as infantile alarmists). But what seems unbelievable to me is that she is employed as a writer focusing on city halls' real estate, public transportation, and municipal waste. But in that opinion piece, she attacks our side – including some of the top notch Czech mathematicians or mathematics officials (Czech-Canadian senior mathematics professor, director of the Mathematics Institute of the Academy of Sciences, and others).
Well, the weekly doesn't find it strange to allow such an arrogant low-information "lady" to act as a top expert in mathematics and mathematics education. Analogously, two weeks ago, Mr Vidomus was treated as a top expert in climatology although he's just a student of humanities and a host of a jazz program in the public radio. He has absolutely no clue about the required science. But this spoiled brat also found it appropriate to speak as if his knowledge of climatology were superior not only relatively to the ex-president Klaus but also the researchers he has interviewed such as myself.
Now, Ms Boříková wrote that it was "crossing all the red lines" when the critics said that the kids typically like the Hejný method classes because they're closer to gyms than mathematics. I said this statement explicitly and because of other details, she was clearly reacting primarily to my assertions (she may have been present at the conference in February). (In another sentence, she reacted to Prof Dlab's assertions about the psychological harm caused by the Hejný method and he mentioned his name.) But other people from our side have said similar things and it's common sense. Just look what the Hejný method classes look like. They're playing games, they're moving a lot, it's similar to gyms. The mathematics over there isn't too much abstract than counting the score in basketball. And that's why such classes are more popular – it's just a well-known fact that gyms are more popular with most kids than mathematics.
What sort of "red lines" does it cross to point out this obvious fact that is so essential for a proper understanding of the emotions and arguments in favor and against the method? Indeed, one can make the mathematics classes more popular – but the price one pays will be that there will be less actual mathematics at schools. Do we really want to change the schools in this way? Everything may be made more popular by populist reforms. Greece has made the public sector jobs more popular because these employees get all the benefits but the employees have virtually no duties or work to do, except for drinking coffee for 8 hours a day in their office, if I exaggerate just a little bit. But populist policies like that have certain negative consequences and it's just unethical if not suicidal for the nation to overlook these consequences.
Do we want to be bullied by aggressive witches such as Ms Boříková who would love to declare all important questions and ideas to be politically incorrect and de facto banned? I won't allow it. She's an arrogant stupid bitch who has no business to talk about such matters and I will always work hard to make sure that this fact is understood by as many people as possible.