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When dumb humanities trainees deform education

In the morning, Europeans learned that the number of dead and cured Covid-19 coronavirus patients grew to 361 and 475 or so, respectively. The second, "recovered", figure starts to clearly dominate. It may become even rosier in coming days when the HIV+flu drugs improve the treatment of the patients.

The London attacker was an ISIS fanatic who wanted his GF to behead her parents, who has done some planning of terror attacks in the past, who was arrested, who shouldn't have been freed again, but who was freed prematurely instead (deja vu). Within days, he went to stab the people. What a surprise. In a society that encourages murderous scum, the murderous scum feels encouraged (Sky News called the terrorist a Gentleman, cool).

In a Quora digest, the following question stimulated my interests and raised my adrenaline level even more, however:

Why do so many Americans insist that “anyone can learn mathematics” when the available evidence strongly suggests otherwise?
A fair enough question. The answer is that these Americans are either stupid and misunderstand mathematics themselves – and they actually say that everyone has enough brain power to misunderstand mathematics as much as they do – or they do understand mathematics but they are politically correct liars who build their well-being on similar "everyone can do everything" lies.

Among the 50 answers, the most successful one is the answer by Jean Rafenski Reynolds. It has some 200k views and 2k upvotes and it's annoying, indeed.

She is a teacher of English who has posted 10k answers to Quora but only four are comparably successful to this one. She's been allowed to teach mathematics courses somewhere and she clearly believes that this fact makes her informed if not a mathematician. In reality, she is completely clueless about mathematics education, mathematics itself, and what the discipline even means.

First of all, she completely ignored the question and answered a different one: How can I teach mathematics to everyone. Fine, how does she do it? She gives them this problem:
Grandma tells her two grandsons: There is a pie in the fridge. Do you know what a pie is? Such a yummy thing you may insert into your mouths. There are two thirds of a pie in the fridge. Do you know what a third is? It's when you cut the pie to three equal pieces, like the Mercedes logo. Take one-half of what is there, i.e. one-third of a pie, and share it (1/6 for each of you), so that the other one-half of what is there, i.e. one-third of a pie, is left. Now, the problem is: How much of a pie is left?
So she tells us that she knows people – obviously totally retarded people – who cannot solve this "mathematics" problem. Nevertheless, defying all logic, she uses this fact as an argument to claim that "everyone can learn mathematics". And her moronic answer ends up at the top of a long list.

Tiberiu Tesileanu, a Romanian physicist who's been doing string theory (and I know most of his co-authors) and who switched to astrophysics and/or neuroscience reacts appropriately. There are two problems with the answer. (1) The pie problem is so low-brow task in basic arithmetics that it shouldn't be called mathematics at all. Discussions about
the complete innumeracy that is widespread in the population is something else than the discussion about the mathematics education. (2) Abstraction is really the very point of mathematics. Mathematics has to generalize and create the abstract essence of concepts. This isn't a vice of mathematics, it's a virtue and the very purpose of mathematics. People trained to do things with particular objects and situations often end up being unable to solve isomorphic tasks in other situations – and this is the clearest manifestation of the fact that they haven't understood or embraced mathematical thinking.

On top of that, the particular situations are full of distracting noise. So Reynolds says that it has to be a grandmother, a pie, during a Thanksgiving, and she even tells you how warm the pizza must be when you're teaching mathematics to someone and he eats it to feel good while "learning" things. I am sorry, the right verb for her proposed activity is "to feed", not "to teach".

Tesileanu is totally right, of course. I've said similar things when we were fighting against the degenerative "Hejný method" to teach mathematics and its anti-mathematical philosophy. Note that it's probably no full-blown coincidence that the author of the most sensible reaction is Romanian. Romania is teaching real mathematics to the kids and that's also why it is doing very well in the International Mathematical Olympiad and arguably in research, too. In IMO, Romania has won about 4 times (#1 in the world). In recent years, it dropped to some 20th place in average but it's still better than the 40th or so place of Czechia and Slovakia. I've known several brilliant Romanian string theorists.

The real problem is a social construct here. Someone who clearly doesn't understand what mathematics is – assuming that one may recognize "one-third of a pie" as a unit, her problem is about the subtraction of integers up to 2 or 3 ;-) – has been made very self-confident and is shaping the education of mathematics to the kids today, either locally at the place where she lives, or by her Quora answer that is pushing the public perception somewhere. It's just bad. The fact that she was allowed to frame herself as a mathematics teacher is a mistake, not something that may change the truth.

Her illogical mind – the typical kind of illogical thinking that is arguably promoted among the humanities trainees intentionally – manifests itself in many other answers. For example, someone asked how professors wrestle with plagiarism by the students. And she answers that she doesn't have to wrestle because her problems are designed so that plagiarism is impossible. To do so, (1) she encourages critical thinking, (2) invents the skeleton of the paper that the student must respect, (3) invents fresh papers that the student must include, and so on.

If your CPU is in a good shape, unlike hers, you immediately see that this answer is self-contradictory gibberish. If the student is forced to follow a skeleton ordered by someone else, and told which papers must be worshiped, then she is clearly prevented from applying the methods of critical thinking. So if the operational rules (pre-planning) hold, the claim that she is supporting critical thinking is unquestionably a lie. Instead, she is growing mindless obedient sheep.

Her more general claim that "plagiarism becomes impossible when the tasks are designed well" is logically impossible, too. One may make plagiariasm impossible or near impossible by making the task very special, contrived, restricted by many conditions. Then the mean number of usable papers that may be copied from other sources may really drop below 1. But it has additional consequences: such a special assignment will be interesting for a tiny number of readers, too. It will simply be about too special or contrived a topic. Also, much of the paper – the conditions – would be invented by the instructors, as I explained above. A greater number of people are only interested in topics that are sufficiently important, answering sufficiently simple and obviously consequential questions, and when it's so, there have already been other people who tried to answer the question in a similar way, too. Up to some fluctuations that are rather small, the number of relevant papers that could be copied is pretty much proportional to the importance and meaningfulness of the project!

These two – "good" and "bad" – traits come together. When you want to assign an interesting project that others will be interested in which will also stimulate the student to write it, you are also assigning a project that other students may be getting (or may have gotten), and therefore there is an unavoidable risk that some plagiarism could be used by your student. There is really no simple yet universal way out. Teachers simply must microscopically check that the students aren't plagiarizing or otherwise cheating and if teachers ignore this part of their job, it is clear that they are not doing their work quite well. Learning as well as teaching include "hard work" which is often unpleasant for some students or some instructors and everyone who claims to have removed the "hard work" has thrown the baby out with the bath water, instead of inventing an ingenious breakthrough.

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