Math is difficult for children because for them it's learning a lot of unrelated rules in their head that don't even have a reflection for them in their everyday experience. And these textbooks are trying to create this connection.
Thank you for your work, I am always happy when good books are translated.
> Kiselev’s child reader is being treated as a participant in mathematics, not as a recipient of facts.
Not sure how the other makes this claim when the passage he himself cites is just another clever proof in the list of clever things that maths books throw at you:
> It is easy to convince oneself that there exist infinitely many prime numbers. Indeed, suppose the contrary, that the number of primes is finite. Then there must exist a greatest prime; let it be a. To refute this assumption, imagine the new number N formed by the rule N = (2·3·5·7···a) + 1, that is, the product of all the primes up to a, plus one… The first term is divisible by every number in the list 2, 3, 5, …, a, while the second (the unit) is not divisible by any of them. Hence there is no greatest prime, and so the sequence of primes is infinite.
The following paragraph:
>In a typical American or British arithmetic textbook of the same period — or, frankly, today — the topic “primes” would consist of the definition of a prime, a list of the first few, and perhaps a procedure for testing primality. The infinity of the primes would be asserted, if at all. The proof would not appear, and the argument that no list of primes can be completewould not be made.
I think they meant to imply that "other", maybe western, mathematical education emphasizes learning "facts" over a more demonstrable experience. The author compares how textbooks would frame the multiplication of positives and negatives in the same sense later in the article.
>The point is not that “minus times minus is plus” because some external authority says so. It is that, if we want our rules to give consistent answers when applied to physical quantities that point in two opposite directions, this is what the rules must look like.
Was it a typical textbook? I know it was used for a long time, and it's interesting that an ancient book was used in math education, but I doubt it was widespread by the 70s, or even by the time these two Russian textbooks were written.
Thank you for your work, I am always happy when good books are translated.
Not sure how the other makes this claim when the passage he himself cites is just another clever proof in the list of clever things that maths books throw at you:
> It is easy to convince oneself that there exist infinitely many prime numbers. Indeed, suppose the contrary, that the number of primes is finite. Then there must exist a greatest prime; let it be a. To refute this assumption, imagine the new number N formed by the rule N = (2·3·5·7···a) + 1, that is, the product of all the primes up to a, plus one… The first term is divisible by every number in the list 2, 3, 5, …, a, while the second (the unit) is not divisible by any of them. Hence there is no greatest prime, and so the sequence of primes is infinite.
I think they meant to imply that "other", maybe western, mathematical education emphasizes learning "facts" over a more demonstrable experience. The author compares how textbooks would frame the multiplication of positives and negatives in the same sense later in the article.
>The point is not that “minus times minus is plus” because some external authority says so. It is that, if we want our rules to give consistent answers when applied to physical quantities that point in two opposite directions, this is what the rules must look like.
British students were taught from Euclid's Elements until around the 1970s, so he's wrong.