Encouraging "gifted" students to branch out rather than just go up

Parents Forum
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Sorry to take a while to respond to an earlier question. My original plan was to homeschool my son, per @sbjdorlo’s post. But, my wife wouldn’t go for it. So we did partial homeschooling as suggested by the school.

@twoinanddone, at the time I was discussing, our son had had an IEP from 2nd grade and was now in HS. We had neuropsych testing every three years showing both the disabilities and the IQ. I was reviewing all of the results with them and discussing what it would likely mean in their class. What was clear was that the data was essentially irrelevant to them – they needed to see it with their own eyes as you said or hear it from other teachers. As a data-driven person, I naively expected that the data would be meaningful – and something they should pay attention to. My point in that post was that they took the data as irrelevant. We learned to live with it, though I think the teachers should be open to learning in more than one form. For the most part, all we were asking his teachers to do was comply with the IEP.

What were we asking for? Even in the honors courses, there was lots of busy work. I remember in freshman math, he said to me, “Dad. We discussed the idea on Monday. I get it on Monday. We’re still doing it on Friday.” Before we started the partial homeschooling, in math and science, we asked if he could just do the hard problems in the problem sets. But, more importantly he found the busywork regurgitation writing assignments in English and social studies classes boring and really tiring. Most of what we were asking was to let him skip the assignments, give him extra time on the tests (per the IEP), and just judge him on the tests (or major papers). We were also asking for him to get class notes from someone – because he can’t think and write at the same time and found it pretty fatiguing (all in the IEP). So, most of what we were asking for was that the teachers comply with the IEP, which some didn’t if doing so was inconvenient for them (remarkably none of his English teachers ever did, which is part of the reason why partial homeschooling made sense). [Side note: this is one of the better high schools in a state with very good public schools and our teachers have the highest average salaries in the state.] In honors chemistry, his freshman year, his teacher believed strictly in timed tests and in having him do his own note-taking and wanted him to do all of the problems including the trivial ones (in contravention of the IEP). He did seem to be having difficulty in the class. Once she started complying with the IEP (and she hovered over him to see that he really needed extra time) he got an A+ on every test or quiz and she became one of his biggest advocates.

College and grad school were pretty much like what we had asked for in HS. No regurgitation. Extra time on tests and note-takers (for college and the first part of grad school). Only assignments with some meaning. He was much happier in college. In college, there was a stigma he had to overcome of having LDs. His freshman year, I went to open houses and two professors said, “Kids with LDs don’t generally do well in my class. So, I have to tell you that I was surprised to see that he had the highest score on both of the tests this quarter.”

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I did study a lot of math at some very good schools and have my PhD in an applied math field, but the world has changed from the dark ages when I was a student and then professor. I was talking to a very bright Hispanic woman who attended son’s LAC. Her parents had moved from Venezuela to escape the political situation to an urban schools in Houston, which was very weak. She thought she was going to major in physics IIRC and had taken AB Calculus at her HS (the most advanced math course offered). When she got to the elite LAC, she discovered that the physics majors had all taken BC Calc and often multivariable calculus before they got to college. She realized that she was always going to be too far behind to be a physics major. The problem was not ability – that never got tested. It was the fact that her inner-city school just didn’t prepare her properly. The LAC ran an 8 (?) week summer program for kids from schools like hers, but that wouldn’t have enabled her to catch up. She ended up majoring in Black Studies or Sociology and was, when I talked with her, a star student at a grad program studying something like inter-Latin American immigration to Panama or something like that (which I recall as raising some interesting questions). She seemed bright, hard-working and a hustler and was going to be a coveted hire for various social science-y departments. But, as of a few years ago, AB Calc didn’t give her sufficient background in math to be a physics major at an LAC (arguably a fairly elite one).

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If she needed to attend a summer catchup program, there are bigger issues than having taken AB calculus instead of BC. It’s quite common for students who attend highly selective colleges to have only taken AB calculus in HS. In the Harvard freshman survey I mentioned earlier, 35% to 40% of students report their highest HS math level being AB calculus or less (depending on year), and I’m sure that this large a portion of the student body doesn’t need special summer catchup programs.

With their smaller student bodies, LACs often have fewer underclassmen course sequence levels than HYPSM… However, the few I checked still had different math options for different backgrounds. For example, Willams’ math placement chart is at https://math.williams.edu/courses/placement/ . Students may start at math 130, 140, 150, 151, 200, or beyond… depending on math background. The intro physics classes taken by physics majors require a prerequisite of math 130 or equivalent. Students who took AB calculus and scored at least a 2 on their AP exam would meet this requirement. Of course some students would still feel intimidated by classmates with as stronger background. If the intro physics class has a lot of students who took AP physics in HS and have previously covered similar material, then some students who only took basic HS physics would likely feel intimidated.

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@Data10, I agree that not taking BC Calc was not the only issue generally, but she had no difficulty outside of the STEM area and did quite well in both undergrad and grad school. Her issue was that starting with only AB Calc meant that she would be a semester to a year behind the other math/physics majors.

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Even starting from Calc 1, you can take all the math a physics major needs in 2.5 years Who cares if you are a semester or a year behind some other students as long as you finish in 4 years?

My daughter decided to start with the first course in the math sequence at her UK Univeristy rather than the second one that most stem majors start with. She wasnt quite confident in her ability. It just means she will finish required math one semester later and will get one less elective.

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My oldest wouldn’t have put up with a lot of added math courses in high school even though he could handle whatever was thrown his way (he was a NMS and graduated from college with honors). He put extra efforts into intellectually challenging and interesting EC’s including debate and news editing (he won awards and “championships” in these fields in high school), as well as into his hobbies. He majored in economics in college, which allowed him to develop applied statistical and computer skills as well as an understanding of economic theory and history. All of these aspects of his background have played into an interesting career. He chose not to seek an advanced degree.

I don’t believe in force feeding a kid who is already intellectually engaged. I do believe in offering the kid challenges and opportunities. But it was important not bore this kid with makework and repetition. He wasn’t going to become a natural scientist or an engineer. Had he shown any such career interests we had extended family members who would have stepped up to guide and challenge him (as they did for me and my own sibs). And so – understanding HIS personality and capabilities and interests – we put stuff out there meant to engage him. And he took it from there.

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At all LACs I checked, students who take AB calc in high school can start the physics courses taken by physics majors in the first semester of their freshman year, without any semester to a year delay. A list of min AP exam scores to start the physics major sequence in first semester freshman year at different LACs is below:

Williams – Requires a 2+ on Calc AB exam
Amherst – Requires a 4+ on Calc AB exam
Swarthmore – Requires a 4+ on Calc AB exam
Bowdoin – Requires AB Calc, no min score listed
Weselley – Math course credit with 4+ on Calc AB exam, “If you do not take the AP exam or you do not score high enough to get credit for a course, you may still be placed into a higher course so that you do not repeat material that you have already studied”

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I think technically one could start the sequence but that may be ignoring reality. I believe that she was saying was that the group of majors was way a year or so ahead of her and she wouldn’t be able to compete.

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You aren’t competing with students in different classes that are a year ahead of you in some sequence. You are competing with the students in the classes you are taking right now. This is exactly the sort of thinking that keeps people (especially women, minorities and kids from lower performing high schools) out of STEM careers/majors because they weren’t really in to coding (for example) in middle school. You can start with Comp Sci 101 and major in Comp Sci. It’s perfectly ok.

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The difference between calc AB and calc BC isn’t a year, and more importantly the freshman physics sequence at all highly selective LACs I checked do not require HS calc BC knowledge. I don’t doubt she felt behind certain other students, and a weaker STEM background no doubt contributed to those feelings, but that doesn’t mean students need to take calc BC or multivariable calculus during HS to be a physics major.

Most students at highly selective colleges are used to being at the top of the class in HS. It can be tough to suddenly not be at the top of the class, need to go get extra help from TAs/professors, get their first B, etc. When I was at Stanford, so many students were trouble by getting their first Bs, that they had counselors come to my dorm after first quarter midterms. It was my limited experience that this reaction had more to do with personality than HS background. If anything, the students who were most freaked out by by getting a B (or in few cases freaked out by getting an A-) tended to be students from stronger HS backgrounds. Some students choose to switch majors when in this type of challenging situation, but plenty do not.

I used to date a woman who was working towards a math degree, even though she didn’t take any math beyond algebra 1 in HS. This obviously wasn’t at an elite college, but she was still likely among the least prepared in the class based on her HS background. She knew she was less prepared than other students and knew she’d have to work harder than many of the other students, and she did so. She graduated with a math degree and grades towards the upper end of her class. By the time she graduated, she found the higher level math classes easier than the general education requirements.

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@shawbridge, my kid graduated as a Physics major from Harvey Mudd with only AB Calc going in. If it can be done there, it can be done anywhere. It isn’t that big a deal.

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Barbara Oakley, who didn’t do well in math in HS and joined the Navy to focus on languages. Later, she decided to learn engineering and had to study math and became a Professor of Engineering at someplace called Oakland University. She wrote a book on how to study math (https://www.amazon.com/Mind-Numbers-Science-Flunked-Algebra-ebook/dp/B00G3L19ZU). But, as you point out, it can be done albeit at a slower pace.

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She did not have to take anything out of sequence or behind her class.

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I really didn’t mean to derail this thread into a discussion of math education. I appreciate your service, OP, and recognize that working in education today is a difficult and often thankless task. Sadly, I am afraid that I, like so many other parents, are facing the anxieties of a diminishing economic pie and doing our best for our kids to prepare them to withstand that. In that context, I don’t necessarily have confidence in school administrators to prepare my kids for the future.
So I do what I think is best.

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@roycroftmom, I’m not a big proponent of just pushing people ahead. When the school system is curriculum-centered like the vast majority of US public and private schools, being promoted to higher grades is a very mixed bag. In a student-centered system (like the school I attended in the UK for a year and like an “essential” charter school that we looked at in Massachusetts in which students go at their own pace in each subject regardless of chronological age, all kids including gifted kids go faster in the subjects in which they continue to demonstrate mastery. The best we can get to in curriculum-centered US school systems is either full or partial home-schooling. We opted for partial as our schools were pretty OK at lab science, great a social studies and good at art, but could not help my kid at Math or English. I suspect that in a curriculum-centered system, the best one can do is pick and choose…

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Unfortunately, no school is an island. My eldest didn’t take all the AP courses available to her, opting for more interesting ones to her, and a more customized educational experience. But her college, like many others, I have learned, registers in the order of semester hours. So she will still feel the consequences of her high school course decisions as she registers for senior year college courses, in terms of priority for getting the sections or professors she prefers. I now understand why parents start worrying earlier.

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@jonri , I often respond to multiple posts in one post of my own. I wasn’t implying that you made both comments; I simply had thoughts to share about both of them and responded to both in the same post. I extended the example mathematical genius from one to the other, but that was more for convenience.

Oh, I don’t believe it’s early schooling in math for math geniuses or students who are very gifted in math is unimportant. My point was simply that there’s no empirical evidence for the idea that mathematical ability peaks at a ‘very early age.’ There doesn’t seem to be any scientific consensus about a “peak” in mathematical ability. There’s some research out there that has tried to determine an age, but most of the ages that are discussed are between the mid-20s and late 30s/early 40s - certainly not any time in childhood.

“True mathematical potential” is a very tricky thing, because it’s a counterfactual. It’s kind of like the psychological idea of intelligence - we can never really know precisely what it is, only how we as humans define it. We can assume that a person has the potential

OK, sure, and I guess I didn’t fully understand what I was thinking. What I was thinking is…who cares if he actually was only an ‘average’ math graduate student while he was at Cambridge, if he was a mathematical prodigy before and made very significant contributions to the science after he finished? I guess this point is really what was at the heart of my thoughts when I made the original post. If you have a student who is happy and healthy and truly brilliant in math and making good contributions, does it matter that they’re only 4 years ahead instead of 6 or 7? Or that they’re only a truly excellent mathematician instead of the best mathematician of their generation? (And to be clear, I’m not implying that’s an argument that you made - I’m injecting my own thoughts and musings into this.)

They don’t know, either. Nobody knows this for sure, whether an individual person would’ve done X if only we had done Y at some earlier point in time. It’s a counterfactual statement. It’s also possible that he could’ve gotten overwhelmed and quit math, or that he would’ve done exactly what he already had done. It’s possible that he still did reach his full potential, just a bit later in life than he otherwise would.

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@juillet,

Regarding importance of learning to get along with others;

You are spot on that “some kids run the risk of feeling lonely or ostracized if not given the opportunity to socialize with some peers around the same age as them. There’s no reason a well-rounded kid can’t have both”

However, while it’s very important, the devil is in the details.

For a happy and successful professional life, you don’t need to get along with uneducated and undeveloped childish mind always. Well, maybe you do when you become a parent. But you don’t have to go through what the first time parents go through while you are also a 6 years old child, albeit highly precocious. I won’t be able to handle being in a 1st grade class room everyday as a teacher, and I don’t even want to imagine if I would be a pupil as a teenager trapped in a 6 years old body.

Average kids become much more reasonable, with decent moral standard, and … grown up sometime in their teens. It becomes much easier, or simply becomes possible, to socialize with age peers at that time. Some amount of interaction with average 6 years old kids, depends on each kid, would still be beneficial. But they don’t have to be put into a 1st grade classroom all day, day after day.

Meanwhile, you can help the loneliness and building social skills by interacting more with adults, older kids, and other gifted same age kids. Some homeschooling parents of 8 years old gifted kids see them having play dates with other 8 years old gifted kids writing a short story together or discussing astrophysics all day and socialize with age peers that way, while also being happy and having great fun.

Eventually most of average children will grow up, and gifted kids, as they get older, may find there are more and more kids who are fun to socialize, and also may find higher concentration of people like them as their education and professional life advance.

I believe that, if a 19 years old professor finds that she lacks social skills to teach college kids, that would be more due to her genetics and not because she was not forced to stay in the 1st grade class room with age peers. For all I have seen, she could have ended up as a college dropout, still lacking social skills, if she were put it to the age peers class room.

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@juillet,

also, regarding “I don’t believe it’s early schooling in math for math geniuses …”;

Whether early calculus is necessary to raise a math genius in the correct way, that’s what outside people, like many experts in this thread or professors at Cambridge care. The actual parents of those kids don’t, at least not over raising a well functioning healthier and happier adult.

Almost all homeschooling parents of gifted children, and I know many, don’t care or don’t have emotional resources to care for raising a math genius. It’s all about raising a happy kid with reasonably intellectually challenged schooling as developmentally necessary. Sometimes early math advance is necessary. Sometimes early delaying is beneficial for various learning disabilities or asynchronous brain development. Many don’t overly care if their child prodigy will invent quantum computing someday, although that would be nice for the world and the kid. Most will and do make choices that increase the child’s happiness over more successful academic and professional career in a heartbeat.

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At the Ivies and MIT of the math majors upon entering college approximately 95 per cent have taken single value calculus, 70 per cent had taken multivariable calculus, 50 per cent had taken linear algebra and 27 per cent have taken differential equations.

If anyone wants a cite for this data please send me a PM