2x - 3 = 0, so x = …
I am all for separating or moving out highly gifted students from “regular” or even AP/Honors classes because studying with 12 year old kid who can solve math problems in 1 minute while you struggle to solve them in 10 minutes as a 17 year old can be demoralizing unless you become good friend with this precocious kid and he/she helps you with homework. lol When my kid was taking his AP Calculus as a Senior, he had many sophomore kids in his class who were the best math students. Because of this and because the class was curved, it was very difficult for my kid who barely qualified for AP Calculus class as a senior to get an A. He was happy to get a B+ instead of a B in this class.
I had one friend who was really good in math and who got into all top schools and placed top 3 consistently in state high school math competitions and eventually went to MIT where he also got As by trying pretty hard. I thought he was gifted in math, but he told me that there are some kids at MIT who barely study and get A+s in classes that if he compared himself with them, he would be demoralized. Of course, I had another friend who also went to MIT, and no matter how hard he tried, he could not break above B and graduated with lots of Bs and Cs. This just goes to show you, there are always smarter and more brilliant kids than you in certain area. My friend who got all As at MIT with a decent amount of effort would be considered “gifted” in math by ordinary people, but at MIT, he was just a smart guy; but those at MIT knew which students were gifted among themselves. I myself got 800 in SAT math but I could not hold a candle to my friend when it came to math, so it was reassuring (or not) to know that my friend also felt the same way (not very talented in math) I did toward him for some other students at MIT.
The question for me is what we can reasonably expect a public education system to do. I firmly believe there should be more ability grouping even in the younger grades, which would include giving more difficult material to more capable students. And of course educators should be able to identify top performing students, if not necessarily be able to distinguish between the 1% and the .01 %.
On the other hand, a school district isn’t going to customize a program for each student; it is going to (reasonably) build a curriculum around certain norms - including the norm that even the advanced track is going to be tailored to the “average excellent” student rather than the genius. We can argue about whether the typical sequence for the “average excellent” student should end with Calc BC or with multivariable calculus, but in the end that’s quibbling; the question of whether an accelerated student should be ready for class x at age 17 or age 18 is a judgment call.
Even the question of the age at which a given student is intellectually ready for a certain discipline strikes me as something of a red herring. In certain subjects, the 12th grade class isn’t necessarily going to be harder than the 11th grade class; it is simply going to be different, in that it covers different material. A student who takes AP American History and AP Bio in 11th grade is also intellectually “ready” for AP European History and AP Chemistry, which he or she will take in 12th. Similarly, plenty of students are intellectually ready for subjects like anthropology, psychology and forensic science, which they may not encounter until college. Life isn’t a race, and there’s actually no harm in not experiencing everything for which one might theoretically be ready all at once.
The real issue is the student who combines extraordinarily advanced intellectual potential with intense passion, in which case it is torture not to be allowed to progress. For those students, acceleration is the best and in some cases only option, and school systems should have to accommodate those students. But again, here’s where the question of intense brilliance vs. intense ambition (often intense parental ambition) becomes dicey. It is easy to say that it doesn’t matter why a student is ahead if he or she is capable of doing the work. But I would argue that it does matter, for at least two reasons.
First, because it is arguably unhealthy to encourage an arms race where average excellent students who might be quite content progressing to Calculus and no further – which is fine for a lot of people, especially if they aren’t math whizzes – feel pressure to spend their summers and after-school time on programs and self-study simply to keep up with their classmates and get that coveted “most demanding curriculum” mark on their counselor’s recommendation. This is especially true as some of these acceleration methods are pricey, and thus increase socioeconomic disparities. While I don’t think that’s a good reason to deny the genuinely extraordinary student, there’s a difference between accelerating the genius and condoning a kind of shadow-curriculum for anybody of above-average intelligence who can pay.
Second, because it affects, IMO, how obligated a school is to address the needs of those students. If the school doesn’t have a curriculum that works for the kid with the 150 + IQ, then maybe it should have to pay to have the kid to a more accelerated course at a college or online, in the same way it would have to pay for a special school for certain intellectually disabled students. But you don’t have a “need” for linear algebra just because you happen to be capable of doing it in your senior year of high school rather than waiting for freshman year of college and have been doubling up on math during summer breaks, any more than you have a “need” for anthropology and forensic science, if your high school doesn’t happen to offer it.
So, I think there is a difference, and I maintain that sorting between the two groups wouldn’t always be that easy. That’s not even getting into the fact that proving need to accelerate in math would be a lot more clear-cut than proving need to accelerate in history or English, as that would tend to involve value judgments like “it is a waste of time discussing novel x with my classmates, because they just aren’t sophisticated enough.” Which might be true for some students (although I suspect not many, once you get to the later high school grades in good school districts), and arrant pretension from others.
So refreshing to read these comments from parents of gifted kids!
Decades ago read about how the next tier students actually did better when the top kids were clustered together- they got their chance to be the ones leading et al. Still remember being stuck with X Y in elementary school because we were the two top girl students (even with tracking). She was so far ahead of me. I can imagine how hard it must have been for her when there was literally no one close to her in grasping material and exploring- eventually her U prof father and her mother changed her schools et al so I lost track of her.
My HS senior son got B’s instead of A’s in AP statistics because while he had 100% on every quiz/test he had zeroes on homework. At least AP calc did not grade homework. Today’s HS students have far more access to online learning. Oh, and kid had trouble with those add/sub/mult/div flashcards. Later college honors math grad… At the same age he was a near perfect speller- even of HS lists… Go figure. The complexity of humans.
I never will understand why humility is desired. Is it because of jealousy from those less endowed with a given trait and their desire to be on top??? Taking things for granted is fine- needing to have those with exceptional skills be taken down is not. We do so much to undermine intelligence, we should be happy some humans can achieve so much.
Off that soapbox. Reminded of how good it was to have bright, but not gifted, educators who could look beyond their ability level and try to do right for kids they could (note word choice here) not comprehend.
Thoughts of My Fair Lady movie…
It was two variables and two digit numbers problem, something like 35x + 71y = 26 and 16x - 8y = 88, so x, y =
I didn’t include the friend’s answers for privacy, but Hands on Equation turned out to be already studied and was found to be too repetitive after a few pages.
As a qualifying test to skip to 3rd grade at a Bay Area private school.
And the point was how much arithmetic proficiency should precede before teaching higher math to a 1st grade kid who naturally understand concept of algebra and beyond but with still developing number senses.
How is the student supposed to solve the algebra problems in #120 and #124 without knowing division and fractions as you mentioned in #119?
Actually it isn’t hard to separate students based on ability. There have been metrics for years. Also, yes there are
kids for whom history is quite easy. This is also measurable. The issue arises when we refuse to use metrics to delineate natural skills. Some kids get stuck for years with the OP thinking because the OP doesn’t believe in giftedness. No child should be forced to relearn things over and over. Each child should be able to advance through the use of technology in the classroom. No child should be forced into a homeschool because the school cannot subscribe to an online course. We need to think of giftedness like we do Special needs, something that needs focus to provide the right tools. And I cannot fathom why we need to have kids wait 9 years (until high school) to be separated by ability. Are you kidding me? Please tell me 80% of these kids were not the same kids who learned to read early, learned quickly etc. For parents of the gifted, there are few resources. Not every parent has the resources for private school, nor the interest in home schooling. We are surrounded by those who think like the OP and we don’t want to rock the boat too much --else the Admin and teachers will take it out on the student. We tell our gifted students not to complain or say anything. But they know. They know they are being cheated out of a proper education. And they wonder why.
Being ahead because you studied something early is not gifted. Gifted is being able to learn things faster, deeper and with more insight than others. This really cannot be taught.
mistake
Should the measure of a successful school be in the performance of the students or in how much each learned beyond what they knew starting the school year? Too many gifted kids learn little in school because they already know it. They need to be allowed to run faster and further than their agemates. Both ends of the Bell curve need special education.
Going back to the original post, I recently interviewed students from two public high schools for a highly selective college. One of those high schools followed the standard group students to “go up” type approach that I expect most on here are familiar with – offers a couple dozen AP classes, offers a few DE classes including multi-variable calculus and linear algebra, in a good neighborhood without a lot of SES diversity, etc.
The other HS was quite different and followed more of an individualized “branch out” approach. It offered no AP classes and no more than 2 levels per class. Instead classes were project focused with a lot of integration between different classes and a lot of applying concepts from the classes outside of the classroom. Students pursued their passions through individualized projects, rather than having a static curriculum that was the same for all students in the class, regardless of ability or interests. Internships were standard, as was a individualized thesis. Both high schools had students who were accepted to highly selective colleges last year, such as Stanford and Harvard.
I think which high school’s approach is better depends on the student. Some students will function better in the “go up” approach with an emphasis on advancing to higher level classes on the standard curriculum and/or accelerated/AP/DE type classes. While other students will function better in the “branch out” approach, with an emphasis on individualized projects and learning beyond the standard curriculum, outside of the classroom.
Branch out IN the classroom is what many parents would like to see.
@springboard Your educational philosophy sounds exactly like the educational philosophy of my kid’s elementary school principal.
I will be forever grateful to my kid’s principal for sharing his thoughts with me when my kids were little as he is the reason we began homeschooling over a decade ago.
I reread the OP. I agree that there is more to life than starting college at 16 and most elite colleges do not like 16 year olds. That is a simple fact. If a kid is good at math then have him take another foreign language or teach him how to debate or teach him a computer language or maybe have him learn how to sculptor.
Stephen Smale got lots of Cs in college and even a F. He almost got kicked out of graduate school. He also said that he did some of his best work “on the beaches in Rio” He is one of the greatest mathematicians of all time.
Then the question becomes, how well do teachers and parents make the “correct” assessment on whether a given student who finds the regular school environment unchallenging will do better in a “go up” or “branch out” school environment (assuming both are actually available to place a student in)? Or do teachers and parents tend to have their own biases as to which is preferable, even if a given student would do better in the other school environment?
@collegdad So the kid maxes out Math by 9th grade and doesn’t take another math class in HS? That doesn’t make sense. Plus, a gifted kid doesn’t always (in fact, hardly ever) have the same equal thirst for all subjects. Deliberately denying them access and progress in their strongest area of interest is kind of cruel in my opinion.
@intparent If the kid maxes out in 9th grade there is usually a community college or other college nearby to take a class. A gifted kid may not have the thirst for all subjects but they can learn and IMO I think it makes for a better student and person. It wouldn’t hurt a kid who is good in physics or math to take an art or British History class.
There are a lot of so called gifted individuals who have difficulty communicating or relating to others. That doesn’t help them or the rest of the world.
In the hopes of not going too far afield there is another problem with students who become too nerdy and don’t branch out. When they go into academia or industry they can get involved with sexual or other harassment with or with not drinking too much alcohol. The excuse that they were a nerd in high school (which is actually used a lot) doesn’t hold water.
Brad Carlin and Steven Scott from Google have made news lately regarding this issue.
In Google’s case and the tech industry in general, I expect the problem relates to a combination of the tech industry being male dominated with few females and issues with the typical US culture, rather than “students who become too nerdy and don’t branch out”. I’d expect harassment to be even more prevalent in most other industries with a similarly poor male-female ratio.
Talking about high school math, I in fact think that branching out for talented students would be preferable to calculus, calculus and more calculus. It would be better to get a better idea of what math is about by taking number theory, group theory, applied math, even recreational math (which is not all about winning contests). However, I know we can’t expect schools to have all these classes, but they’re also not easy to find online or in colleges during summer .
The thing is, not many people will jump through that many hoops to make learning happen for their kids. People work, they pay bills, they might have adequate or semi-adequate local public schools. The thing is, the OP and others use their position and opinions on gifted kids to stop them from learning. Realistically, people just cannot do all those things unless they homeschool. And for those who are gifted in multiple areas, things get really bad. Imagine yourself instead as that gifted child trapped by someone else’s excuses for why even though they are educators will not meet your needs. They won’t even try. Maybe it’s because they don’t have resources (unlikely), maybe it’s because they don’t want to create new curriculum, or maybe it’s just that they cannot believe in that others can be gifted. They will stand in front of you and stop you from learning especially if you know then they want you to know. They will make the supposition that you are difficult because you make them stretch and they don’t want to do more than their basic job.
And please, there are many people who have social issues and cannot communicate or are not very caring, etc. This is NOT a function of being/not being gifted. It is a component of their social skills. Not related at all to learning. This is a myth. The myth of the forgetful genius is just that a myth.