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I read on the internet that Finland has the best education system in the world and that in Finland, students are taught to love mistakes and that's how they learn and become smarter. I could not find the details of how math is taught and why that method of teaching works. I would like a detailed explanation of how they do it and why it works, or a link to a detailed description if it is available. Maybe a scientific journal or a book explaining not how to teach students, but a researched property of how it is getting taught and why satisfying that property works. Although I might not bother with that book for now, I might bother with it sometime because it's a particularly useful book because it summarizes the education system in Finland and why it works so well.

For example, for the students who insist that $\frac{1}{3}$ is not the same thing as $\frac{2}{6}$, do they listen to how the student thinks the number system works and discuss the topic with them in the form of research instead of telling them they are crazy and wrong and do something like construct the multiples of $\frac{1}{2}$, the multiples of $\frac{1}{3}$ and the multiples of $\frac{1}{6}$ separately and explain that although $\frac{2}{6}$ belongs to a completely different system than $\frac{1}{3}$ and so it's an entirely different entity, if we work in the system of multiples of $\frac{1}{6}$, we find that $\frac{2}{6} \times 3 = 1$ and $\frac{3}{6} \times 2 = 1$ so we can redefine $\frac{1}{2}$ to have a different meaning than we previously defined it to have like you can redefine the meaning of a symbol in Python and we now redefine $\frac{1}{3}$ to mean $\frac{2}{6}$ and $\frac{1}{2}$ to mean $\frac{3}{6}$ so we can calculate that $\frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6}$?

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    $\begingroup$ Telling kids that they're crazy and wrong is, of course, a really bad idea, but the alternative here (from "do something like construct" to the end of the question) seems just as bad. I can't imagine this, even if rephrased for children, resulting in any understanding. $\endgroup$ Commented Apr 4, 2019 at 17:55
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    $\begingroup$ I can't compare to other countries and it's been a long time since I went to school myself, but as a parent in Finland I'd have to say that the exposition you are quoting is quite a bit more starry-eyed than the reality I can observe. Maybe teachers here are slightly better at helping their students learn from their mistakes or something, but it's not like this is a different universe. $\endgroup$
    – tripleee
    Commented Nov 10, 2022 at 10:41
  • $\begingroup$ @tripleee Todellakin. Ehkäpä on olemassa vertailevaa tutkimusta maiden väliltä, mutta enpä jaksa tähän hätään motivoitua etsimään. $\endgroup$
    – Tommi
    Commented Nov 10, 2022 at 18:24
  • $\begingroup$ (Translation: Perhaps there are studies comparing countries, but I can't be bothered to search.) $\endgroup$
    – tripleee
    Commented Nov 10, 2022 at 18:25

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You can find the official document describing the Finnish education system at Opetushallinto's website; in Finnish and Sápmi at https://www.oph.fi/saadokset_ja_ohjeet/opetussuunnitelmien_ja_tutkintojen_perusteet/perusopetus and in Swedish at https://www.oph.fi/lagar_och_anvisningar/laroplans-_och_examensgrunder/grundlaggande_utbildningen

There is some information in English at https://www.oph.fi/english/curricula_and_qualifications/basic_education

In case the links decay, the new links should be located somewhere in the webpages of Opetushallinto/Utbildningsstyrelsen, the national agency for education. Their current webpages are https://www.oph.fi/english

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