Wow, this is a great read! I'm on page 18 so far. It's been discussing how "word problems" are key to developing critical thinking skills, and how far behind the US seems to be in them. One point made: the idea that word problems can wait till algebra, which gives a universal method for solution, totally misses that they develop logic skills and practice with problem solving, which makes learning algebra so much easier.

This isn't the case anymore. US Common Core Math lessons use word problems from the first grade onward.

Finished it - there is uneven editing in the second half: some passages reappear in multiple places, some thoughts are unfinished. Still found it well worth the read.

Huh. That doesn't really match my American experience at all.

True, in elementary school I don't recall any word problems -- because everything was practical arithmetic through sixth grade. I think sixth grade was long division?

But seventh grade was algebra, and all the Russian examples of word problems look like the stuff we got all the time, seventh grade through eleventh grade. Twelfth grade was calculus, and I seem to recall word problems mostly disappearing then, since everything was just graphs and derivatives and integrals.

Granted I was in honors classes and also did extra-credit "Mathcounts" and "Mathletics" after school, where we definitely got more of that stuff too. But that was just a difference of difficulty and, well, even more practice.

Now obviously different countries have different math standards and different cultural attitudes towards the value of math.

But the difference the author is describing doesn't resonate at all with what I learned growing up in a small town in upstate New York.

[1] has some word problem examples for every year of primary school in England. Year 1 is age 5-6:

"Chris is going to buy a cake for his mum which costs 80p. How many 20p coins would he need to do this?"

I remember lots of these "coin problems" when I was 5 or 6, since we had plastic money to help understanding, but I don't remember other problems.

If I'm equating the grades correctly, the Russian problems appear to be about 1-2 years "harder" than the English problems, at least around age 9-10 (Russian grade 4, English year 5).

https://thirdspacelearning.com/blog/maths-word-problems-expl...

That is what I am noticing with my son's maths lessons. He is in year 5 at a British curriculum international school. The word problems seem a bit too easy, in my opinion.

I don't see a conflict - what you're describing is very consistent with the paper. No problem-solving until algebra starts, then focusing on using algebra to solve 'word problems'.

I've noticed that a lot of students seem to have issues with "word problems"–as in, they have difficulty translating the problem into its mathematical form–and it's often treated as an entirely separate class of problem that you can be bad at. I guess that there's a lack of early training (it doesn't even have to be that much) to do this conversion?

I remember I had issues with word problems in primary school, main issue being I hated them. Trying to recall the specifics, I think they just didn't resonate with me - I've seen them as some weird tales of people I don't care about doing nonsensical things, that you then had to translate into numbers and equations while minding the non-obvious caveats, or that real-life intuition didn't apply.

On the other hand, I was a stupid kid back then.

Singapore's maths curriculum for primary-level students is full of word problems. It may be confusing at first but it lets students get good with interpretation of the situation and derive the essence of the problem from the scenario which is a useful skill irrespective of level.

Yes. The paper includes a number of examples of word problems from Singapore primary maths and the author says "the Russian and Singapore programs go roughly hand in hand in style and difficulty of arithmetical problems."

I wish this was at the top. It would make the discussion here more interesting.

That's a really interesting document.

I have been using it to supplement my son's maths lessons, using some of the problems the author gives as examples and creating more in similar style.