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Anonymous wrote:
Anonymous wrote:
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Anonymous wrote:What makes you think parents are adding summer school to keep up with the Joneses?
It’s not summer school—summer school is nearly eight weeks long, offered at the home school, requested by the home school, and for remediation.
This is cramming to get ahead instead of appreciating and really absorbing fundamental math upon which the highest levels really depend by taking advantage of a program designed for kids who failed the class the first time.
If a kid was that passionate about and gifted in math that they’re willing to give up their entire summer for cramming, they would have been in algebra in 6th to begin with.
Ok, but just to be clear here: You're not including kids who have already done a year of geometry outside the school (a seemingly more common thing these days and in this area) in your argument, right? If you are, then explain how they'd be giving up their entire summer if they already learned the material and just want to check it off?
This is exactly the reason why testing should be the norm anytime a family wants to skip a year. The kids who already spent a year (and did well) shouldn't have to waste 6 weeks checking things off; an administered test is much quicker. At the same time, the kids who were enrolled to get ahead and have never seen the material before should be thoroughly tested by the school to make sure they've truly 'absorbed fundamental math', as you said.
Algebra and geometry are important subject. But we pass kids through those subjects all the time when they don't have proficiency. By your reasoning, shouldn't we also require an achievement test to make sure kids understand algebra before we allow them to take geometry?
I don't disagree. I think we graduate way too many math illiterates.
But there would be waaay too many kids that would never make it past algebra if we actually had achievement standards.
It is not possible to thoroughly and truly learn a year of material in six weeks at that age. One can't just make a scaling argument, i.e. that if you quadruple the amount of time spent per day, it will lead to 4x the learning. The brain simply does not work this way because it needs time and rest; both necessary inputs to learning. All teachers know this. Therefore, departments of education should recognize and be able to differentiate between kids who already did a year of rigorous geometry and do not want to repeat it verbatim in school, with the kids who are being hyper accelerated to essentially 'absorb' and immediately 'regurgitate' the material. This doesn't even take into account that it's almost all being done virtually in 6 weeks.
Wait. So their brain can handle 5+ hours of learning if it is split up into half a dozen subjects but cannot handle 3 hours of learning in a single subject? Do you have any evidence for this?
First, how did you conclude 3 hours? It is around 5-6 hours of geometry because it's a 6 week to a year compression ratio.
Second, yes, developing brains (and even mature adult brains) need time to digest abstract concepts. We are not purely information processors where we can just absorb and retain mathematical information without reflection and practice. Hence, what is happening here is that the geometry is diluted or stripped down so that kids can absorb it all in this short time period, which is inversely proportional to mastery and understanding of the subject.
Yes, we should have standards, but as you said, it would mean failing a lot of people. But in extreme situations like this where natural learning cycle is modified and compressed, there should definitely be a gate check afterwards to see that we're not actually causing more harm than good to kids.
What is the "natural learning cycle?"
It's 6 straight hours of geometry a day for like 30 days??? Then they're still getting 180 hours of geometry instruction. If the kid doesn't like math, this will be torture but if the kid is proficient at math, they can absorb it just fine. Sure it's more intensive focused study but I don't see how doing 6 hours of one subject is worse than doing 45 minutes of 8 subjects.
Do you have any studies showing that mathematically gifted kids cannot absorb geometry over 180 hours if those 180 hours occurs over 6 weeks? I mean we are talking about mathematically gifted kids, right?
No, we are not talking about mathematically gifted kids, (whatever that may mean). Most kids taking summer geometry are accelerated and would certainly not be able to learn 6 hours of math very well. Most kids would just memorize what they can and hope to pass the test at the end. Is that an adequate experience? Crucially, skipping geometry means one doesn't get to do any more geometry in the k12 American education system.
Mathematically gifted kids taking the class would have likely learned most of the material and would not be learning much new info, they'd be checking off the class. The rare kids who are mathematically gifted by some measure (I don't know, AMC scores or something like that) would again have already been exposed to some of the material, otherwise they wouldn't do very well on things such as the AMCs or Mathcounts.
But suppose there exist a few mathematically gifted kids who have never been exposed to basic geometry; yes I believe they'd be fine with learning 6 hrs of math. But my definition of mathematically gifted is not the same as yours. In fact, I believe those kind of kids would not be interested in going wide and fast; they are normally interested in going deep into topics, which is the exact opposite experience of summer geometry.
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