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[quote=Anonymous][quote=Anonymous][quote=Anonymous]I think some of it is that math is more linear.

Let's say that your school's 9th grade curriculum is early World History.  It's not like a kid can be "finished" with that.  There are adults with PhD's who are still finding things about World History to study and explore.  Similarly, if your freshman English class is studying personal narratives, there is always more work to be done, always room for improvement. So, theoretically, even the very brightest kids can find ways to engage and grow in these topics.  Acceleration makes less sense than enrichment.

But in math, there is a point at which there is no longer work on solving systems of linear equations that is meaningful.  So, it makes sense to move on to the next thing.  [/quote]

Math (at least what is taught in K-12) is linear.  Each new concept is heavily dependent on mastery of previous building block concepts and once mastered will make learning more advanced concepts easier.

Unfortunately, most of pre-Algebra math instruction uses a spiral approach to curriculum.  They introduce concepts in small doses each year and the next year they spiral around to the concept again.  Theoretically, this is supposed to provide reinforcement.  What it actually does is slow down/hinder learning.  Students who mastered the material initially the first time get bored and frustrated.  Meanwhile while students who didn’t master it the first time have a year to forget the material and get more muddled before they have to learn more complex material on a topic they remember being bad at.

Other pedagogical trends like teaching elementary students to rely on calculator and jumping to unrelated topics making it hard for students to see connections don’t help, either.  Worse, many American teachers may not have a deep understanding of math themselves.  The approach to teaching elementary mathematics tends to be remarkably inefficient.  If smart, motivated students are effectively taught, it is entirely feasible that they could progress beyond Calculus.  On the other hand, if some kids need more time to master basic math, that’s fine too.  It isn’t a race.  The key element is to make sure that every student has a solid mastery of the math up to their current level.

I think as long as kids have had Precalc in high school so that they are prepared for Calculus when they get to college, they can still flourish in any career (including STEM) that they wish to pursue.  Calculus and advanced math classes may give students an edge in the admissions game as it relates to taking the most challenging courses, but degree programs still look at Calculus as a college level course, which is why those who take it in high school can get college credit for it.  [/quote]

Lots of really great points and very well written. I have a feeling those who don't want to listen to what you are saying (i.e. those who are in a big rush) will ignore it but you are spot on.

The only minor comment I will make is that Geometry is the one outlier to the curriculum path - it could largely be taught simultaneously with algebra and there would not be a great loss or challenge.

Back to your primary point, I have found a number of kids who were in a rush to race through math classes, thinking they knew it all. Then they get to a competitive college and realize that their allegedly top notch high school really hadn't taught them that well and they didn't have the fundamentals down. I actually often advocate for kids to start at the lowest level class possible in college (without being 100% overqualified and bored) and reinforcing the fundamentals there. There is no shame in it. They will generally end up in the same place. Most of these kids racing through math aren't going to actually major in math and/or do math research. So it doesn't really matter.[/quote]

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