I think it is a shame to give a student a D or F in some building-block subject, then pass them on to the next level. There should be two grades: "ready for the next step" and "not ready".
If a student struggles identifying nouns and verbs, it's probably not useful to push them on to prepositions or all the forms of participles. If you haven't memorized times tables up to 5x5, moving on to 12x12 might not be wise.
On the other hand, struggling with subject/object shouldn't prevent you from taking a turn at haiku.
So it would be helpful to have a decent graph of dependencies. But letting everybody progress along the graph of their proficiency would make instruction and administration very challenging. Especially when you throw in social aspects. Having a 10-year-old in the same welding class as the 17-year-olds could be problematic regardless of welding aptitude. And repeatedly putting a 17-year-old with the 12-year-olds studying geometry is also questionable.
But in the end, a grade should mean something useful. It should lead to some useful action that facilitates better education. If it does not, then it is only useful to signal potential employers. And that use is indeed dubious for 8-year-olds. But not so dubious for 18-year-olds who did not progress past their 8-year-old level of proficiency.
So I say grade everyone, then make the grades matter. If a 17-year old wants to take one more shot at geometry, let them. If they want to quit after the third try when they are 15-yo, let them. If they want to quit after the first try, let them. But once you quit, you can't move along the dependency graph for that subject.
Of course, "geometry" is much too broad. You could get stuck on one small concept. You take as much time as you need to go back over it again and again until you get it well enough to be able to study the next concept that depends upon it. This might take one hour or it might take 2 hours per day for 3 days. It doesn't have to set you back 15 weeks or half a school year.
But again, that level of individualized instruction is expensive.
You might be interested in the idea of Sudbury schools. Though there's not exactly a dependency graph of subjects, they do emphasize learning things appropriate to the individual student at the student's own pace, rather than forcing subjects based on the student's age. And it would certainly not be abnormal for a 7 year age difference.
That's because IT isn't "properly trained in the nuance of teaching."
There's so much dissonant crap in teaching that nobody really knows exactly what the days pedagogy is. And AB testing is right out. So what do you do? You do the minimum effort to make sure the state or feds don't cut your funding.
If a student struggles identifying nouns and verbs, it's probably not useful to push them on to prepositions or all the forms of participles. If you haven't memorized times tables up to 5x5, moving on to 12x12 might not be wise.
On the other hand, struggling with subject/object shouldn't prevent you from taking a turn at haiku.
So it would be helpful to have a decent graph of dependencies. But letting everybody progress along the graph of their proficiency would make instruction and administration very challenging. Especially when you throw in social aspects. Having a 10-year-old in the same welding class as the 17-year-olds could be problematic regardless of welding aptitude. And repeatedly putting a 17-year-old with the 12-year-olds studying geometry is also questionable.
But in the end, a grade should mean something useful. It should lead to some useful action that facilitates better education. If it does not, then it is only useful to signal potential employers. And that use is indeed dubious for 8-year-olds. But not so dubious for 18-year-olds who did not progress past their 8-year-old level of proficiency.
So I say grade everyone, then make the grades matter. If a 17-year old wants to take one more shot at geometry, let them. If they want to quit after the third try when they are 15-yo, let them. If they want to quit after the first try, let them. But once you quit, you can't move along the dependency graph for that subject.
Of course, "geometry" is much too broad. You could get stuck on one small concept. You take as much time as you need to go back over it again and again until you get it well enough to be able to study the next concept that depends upon it. This might take one hour or it might take 2 hours per day for 3 days. It doesn't have to set you back 15 weeks or half a school year.
But again, that level of individualized instruction is expensive.
Edit: spelling