> What do you do between doing your times tables and fractions in maybe 3rd or 4th grade and 9th grade? Geometry?
Other countries do a sort of "pre-algebra", mostly focusing on non-trivial word problems which are then solved by setting up the equivalent to an algebraic equation, but in natural language arguments as opposed to symbols. AIUI, this sort of onboarding towards algebra is lacking in the U.S. system, and much of the difficulty that folks seem to experience w/ algebra and higher-level math might have something to do with that. (Of course, Geometry could also play a role in filling that gap. Euclidean geometry has traditionally been studied quite early, as a general introduction to mathematical rigor.)
Edit: Discussed in Andrei Toom, Word Problems in Russia and America [pdf] http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd... The reference to Russia is a bit misleading - of course Russian math education is traditionally among the strongest and most effective, but the same approach to using word problems as an introduction to algebra is found in plenty of other places.
Sure, but what do they do in grade 4 and 5, after basic arithmetic and fractions? I'd be surprised if the answer didn't involve quite a bit of proto-algebraic "word problems" of the sort described in my comment, and in the attached reference.
In the US states I've lived in students start first grade at age 6 or 7, sometimes depending on the month they were born in, but also depending on readiness, but also depending on what age they started kindergarten or preschool if they did. Kindergarten is nearly universal in the US, hence the K-12 system, and preschool (the grade before kindergarten) is what is optional, and daycare before that. I was 12 myself in 6th grade. So though he seems to be in another country (Estonia), his system seems to me to be similar to the US as regards grade numbering. I am not aware of 5 yr olds in the US commonly being in 1st grade. May I ask what country you are in where first grade begins at age 5 on average?
Pre-algebra was standard 8th grade in my school district in the US, with algebra in highschool. Advanced kids were able to take algebra in 8th, though typically only if they did pre-algebra in 7th grade.
Yes, but what US schools call "pre-algebra" is largely review of earlier material, with a few random concepts tacked on such as how to factor natural numbers. It's nothing like the comprehensive introduction to algebraic thinking that the reference above talks about, that, to reiterate, is extremely widespread outside the US (barring a few places where the negative influence of US- Ed School fads was especially strong - the reference talks about this, as well).
Other countries do a sort of "pre-algebra", mostly focusing on non-trivial word problems which are then solved by setting up the equivalent to an algebraic equation, but in natural language arguments as opposed to symbols. AIUI, this sort of onboarding towards algebra is lacking in the U.S. system, and much of the difficulty that folks seem to experience w/ algebra and higher-level math might have something to do with that. (Of course, Geometry could also play a role in filling that gap. Euclidean geometry has traditionally been studied quite early, as a general introduction to mathematical rigor.)
Edit: Discussed in Andrei Toom, Word Problems in Russia and America [pdf] http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd... The reference to Russia is a bit misleading - of course Russian math education is traditionally among the strongest and most effective, but the same approach to using word problems as an introduction to algebra is found in plenty of other places.