Is math privileged for gifted children?

Posted by: JonahSinick

Is math privileged for gifted children? - 03/10/14 01:42 PM

In Underconfidence in gifted girls I suggested psychology, philosophy, economics and evolutionary biology as candidate subjects for gifted children to learn. I'd add history of science. Thomas Percy wrote:

As a practicing researcher in one of the areas you mentioned in point a, I actually don't think a child should focus too much in them. I think social science is still relatively subjective and requires experience even a PG child would not necessarily have an easier time acquiring beyond their age. Time is better spent in mastering a more foundational subject. Math and etymology are both fine use of time.

I think that learning math is very important for gifted children, as I argued in Gifted children could learn math much earlier. See also Cognito Mentoring's page on mathematics learning benefits.

I'd like to address the question of whether gifted children don't have enough life experience to be ready for the other subjects that I mention, relative to their readiness for math. I've worked primarily with gifted young people of ages 10 and higher, so my remarks are primarily of relevance to that age group, though they may be relevant to exceptionally gifted children who are younger than that as well.

  • Study of Exceptional Talent has found that many more children qualify based on the math section of the SAT than on the verbal section of the SAT. This suggests that gifted children can, on average, excel more in math than in subjects that require verbal reasoning. (On a recent thread it was suggested that the modern SAT's verbal section isn't a good measure of verbal reasoning, but many more people qualified for Study of Exceptional Talent before 1995 as well.) It's been hypothesized that this is because high performance in math can come either from strong verbal reasoning or from strong abstract pattern recognition (of the type that the Raven's matrices test measures).
  • The case for learning the other subjects that I mention is stronger for verbally gifted children than for gifted children whose strengths are nonverbal.
  • Because math is a subject that's taught in K-8 school whereas the other subjects that I mentioned aren't, one would expect gifted children to learn more math independently of whether they're more developmentally ready for it. It can be argued that the reason that math is taught in schools when the other subjects aren't is because children are more developmentally ready for math. But there are other possible explanations for this, such as the practical importance of arithmetic. In any case, one would have causality in both directions even if it were true.
  • Similarly, the fact that there are more math enrichment activities (largely in the form of contests) available for gifted children makes them more likely to excel in math than in the other subjects. My understanding is that math contest culture originated at least in part from the Cold War, when the Soviet Union worked to train children in preparation for quantitative occupations in research and development to feed into the Soviet Union's military power.
  • It may be that life experience enables one to understand economics more deeply. But it's equally true that learning economics early could prepare one to learn more from one's early life experiences, on account of seeing relevant economic concepts in them.
  • I think that for children, improving reading and writing skills is more important than learning the subjects that I mentioned. But one can pick up reading and writing skills through them.


Nontechnical, nonfiction books aimed at adults that have few prerequisites such as:



may be well-suited to gifted children with broad curiosity who are reading at the adult level.
Posted by: madeinuk

Re: Is math privileged for gifted children? - 03/11/14 04:08 AM

I have no intention of exposing my impressionable DD9 to books like Naked Economics that present maniacally biased opinions as facts before her BS meter has been better calibrated.
Posted by: JonahSinick

Re: Is math privileged for gifted children? - 03/11/14 10:14 AM

Hi madeinuk,

Thanks for the comment. Is your position more that:

(a) Naked Economics is biased relative to mainstream economics
(b) Mainstream economics is biased?

On the first point, I think that the book is solidly in the mainstream of economic thought (one can point to surveys of economists, the spread views of economics Nobel Prize winners, etc.) On the second point, I guess discussion would start to strain the "no politics" rule of this forum.

Concerning your higher level point (whether children are ready to read books with claims that should be treated with skepticism):

We have a list of reading recommendations for books with a contested thesis, where we write

The books in this category are of an "applied" nature. They draw on ideas across many fields to advocate for a case. The cases made in these books may be controversial among scholars. Readers of the books should not blindly accept the arguments put forth by the authors, but should use the books to obtain a richer understanding of the ideas being discussed. For a richer understanding, readers are encouraged to look for online reviews, debates, and discussions surrounding the books and the theses presented in them. [...] Readers often require a strong interdisciplinary grasp in order to be able to form independent informed evaluations of the arguments presented in the books. Readers without such a grasp should be particularly wary of accepting statements made by the authors at face value without verifying them against independent sources.

In principle, children can fact check and read a diverse collection of books on a given subject as a guard against bias, but in practice, they might not have time or attention to.

One thought is that a parent can read a book with a contested thesis together with his or her child and raise counter-considerations as appropriate, but this takes time and interest (and sometimes subject matter knowledge) on the parent's part. I'll ponder this some more.
Posted by: Thomas Percy

Re: Is math privileged for gifted children? - 03/11/14 11:16 AM

Since you quoted me, I will write a bit more.

I think a subject like economics is beyond a young child no matter how gifted this child is. I am not talking about the Freakonomics type of cutesy economics, which I think it is both more accessible and not parcicularly important.

Most of the economists actually believe very similar things. Supply and demand, free market, and so on. Mostly, economists disagree about the degree of something. For exampole, how important is market failure in a certain market? If you think it is very important in health care, then you would support national health insurance. Not too important, then you would be against the Affordable Care Act. Much of these arguments are not based on theory but on how you read the evidence, which requires understanding of statistics and institutional knowlegde. This is before you bring in things like efficiency versu equality and how do you put a price on human life and suffering. Two very well respected economists could disagree and this seperates social science from science.

I am not saying there no gifted children who can handle ambiguity. I just simply don't see this kind of subject as a good use of their time. High school will be the earliest. But from what I see, there aren't many high school econ courses that are worth the time. Might as well wait for Econ 101 in college.
Posted by: momosam

Re: Is math privileged for gifted children? - 03/11/14 11:34 AM

Jonah, sent you a PM smile
Posted by: Thomas Percy

Re: Is math privileged for gifted children? - 03/11/14 11:58 AM

I borrowed this list from a professor in Notre Dame. He listed a bunch of courses a student interested in econ Ph.D should take. There are a lot of them, better get started young.

http://www3.nd.edu/~jsulliv4/grad_study/math_courses.pdf
Posted by: JonahSinick

Re: Is math privileged for gifted children? - 03/11/14 12:11 PM

Thomas,

I'm not sure that we disagree regarding young children: as I said, my remarks are intended to apply primarily to 10+ year olds.

Some benefits of learning economics earlier (e.g. in middle/high school) rather than later (e.g. college) are that

  • Intellectual sophistication compounds over time (with insights opening the doors to insights that depend on them, which in turn open the doors to insights that depend on them, etc.)
  • Knowledge of economics is relevant to making a good career choice (e.g. recognizing what career paths have the highest social value) and by the time one is a freshman in college, one may already have made decisions (such as what to major in) that are difficult to change and that affect one's career prospects.
  • If one learns earlier, one is better equipped to impress senior people (e.g. college professors).



I'd be very interested in feedback on our economics reading recommendations. I think that they're good choices for gifted high school students, but would appreciate pushback, because we're trying to make the best possible recommendations (both with respect to subjects to learn and with respect to the best resources to learn from).
Posted by: aquinas

Re: Is math privileged for gifted children? - 03/11/14 12:36 PM

As I see it, a parent or teacher with sufficient (graduate) training should be able to explain the nuances of economic theory and intuition to an interested young child. Note that the binding constraint is on the instructor side, not the student side. I'm of the opinion that virtually any subject can be brought down to the appropriate level of the student, provided that the instructor is knowledgeable enough to know where simplifications are being made in teaching. An instructor also needs to be able to explain why simplifications are made and how they are or aren't representative of reality. Anything less is an injustice to the student. In the absence of a good instructor, the student, IMO, is better off learning the math alone, as it can be difficult to un-learn sloppy or incorrect thinking.

Most of first and second year core micro and macro courses don't rely on anything more than algebra and basic calculus. (Some Ivy League universities, who shall remain unnamed, don't even expect their undergrads to have a knowledge of calculus of econometrics until 3rd or 4th year!) A knowledgeable instructor could easily work a motivated and mature child through basic macro models like IS-LM-FE or simple game theory to build up a conceptual economic intuition before the student has the math background required for more precise analysis.

Thomas Percy cites some great recommendations for the requirements to understand graduate level economics and be an effective researcher. Most good economics programs will include all the courses he lists in their required undergrad sequence, and an interested student will want to dive into these math subjects to inform economic intuition, ideally before university or in early undergrad. I second his recommendation that students with a passion for economics would be well served learning these subjects though, if it were me, I'd introduce economic topics conceptually concurrent to covering the math so that economics problems could be used as applications of the math.

ETA: For full disclosure, if I could revisit my undergrad years, I'd have double majored in math and economics instead of just economics. I fared as well as, or better than, friends who entered economics PhD programs with math undergrads, but it required considerable independent study on my part. A math major might have an advantage by taking the CFA exams and entering a PhD in Econ.

For younger students, I think of it this way: economics and math intuition are both necessary, but not sufficient, preconditions for being an effective economist. Economics departments specialize in economic intuition. Why not build strength in math earlier and play to the departments' comparative advantage while building interest with some simple economic topics.
Posted by: GF2

Re: Is math privileged for gifted children? - 03/11/14 02:02 PM

On the narrow point of teaching a 10-year-old economics, I think aquinas is on the right track. Microeconomics 101 could readily be taught by a competent (and sensitive) instructor. Well-taught, it's positive and predictive: how will price and quantity be determined in given markets or given certain changes (including government regulation). You can use more or less math, but intuitive examples (deriving the demand curve for cookies or something) often will do. (I wonder whether macro requires more abstract thinking than a 10-year-old can manage: I tried at that age with my kids, and they glazed over at money supply and inflation. They got price change and could intuit micro dynamics (if more cookie sellers enter the market, where will price tend to go?), but the macro stuff was hard for them.) Even in micro, though, one would need to take some care: concepts like "profit" and "cost" are not intuitive to 10-year-olds as they are to HS students.

On the wider point of whether math and science are privileged in the gifted world, as a positive matter, yes. Most of the gifted sites and organizations (we are most familiar with CTY) have a strong math/science bent. Interestingly, it seems on a casual glance that that many people on these forums have kids esp. gifted in those areas. As a normative matter, whether gifted studies should emphasize math and science, I'm less certain. One of my kids is highly gifted verbally, but he has followed a different developmental path than what I understand is a math- and science-type path: he was reading (by choice), say, OLIVER TWIST as a 2nd grader but couldn't understand much given the archaic usage and historical context. But he loved just throwing himself at it to see what he could make of it. Ditto Shakespeare at 10. Re-reading Dickens as a 5th grader, he got more, and now in HS it's an easy read for him -- he prefers Joyce, Stoppard, and so on! So there's a big developmental leap somewhere around 12-13, and it isn't clear to me (as a rank amateur) how one would cultivate verbal giftedness other than letting them read, read, read, and then re-read. Are there studies of verbal giftedness and its development?
Posted by: Thomas Percy

Re: Is math privileged for gifted children? - 03/11/14 02:34 PM

I actually think a lot of kids enjoy literature. It is way more common for a young kids who read adult literature than social science. I know I read all the classics I can get my hands on as a child. I am not sure I understand everything. But I love it. Also lots of kids want to grow up to be writers.

I am not sure how many kids love social sciences. I somehow think social science as more of an adult subject. But I guess War and Peace is not exactly for kids either. We used to joke in graduate school how many of us said we wanted to grow up to be an economist. I think one of my colleagues did, but his father was a famours economist.

As far as simple economic concept goes, I think they are accessible. Particulary micro as you said. But I am not sure how much they can really get out of it either. I do think everyone should know some economics just so that they can be a competent voter, and maybe high school economics is not as bad as I always thought.

Jonah, I must say I am not a consumer of the more popular economics books. I have always liked Langsburg and Frank. But not so familiar with the others.
Posted by: Zen Scanner

Re: Is math privileged for gifted children? - 03/11/14 02:50 PM

I'm not sure what experiences you have with your kid(s), Thomas, but my eight year old has taught me to never underestimate him. He plans to dress as a math professor for career day.
Posted by: HowlerKarma

Re: Is math privileged for gifted children? - 03/11/14 03:24 PM

My DD has also taught me never to underestimate her-- starting very very young. I think that I've told the story here before about her interpretation of people (en masse) ignoring rules-- even posted ones-- as "those poor people must have a reading disability," rather than selfishness or entitlement.


Well, so just goes to show that she was THINKING quite deeply about the human condition and motivations even then, and she was around 4 at that time, as I recall.


She began reading pop sociology/psychology/political science when she was 6-8yo.

She didn't LIKE econ, but she certainly took the course as a high school freshman. Now, that's your typical micro-macro-mashup which is almost entirely qualitative, and she loathed the subject and found it intellectually dishonest as a "science" and morally bankrupt as a humanitarian matter, but still-- she certainly UNDERSTOOD it.

I'd say that she is far more gifted on the social science side than in mathematics. Oh, to be sure she is gifted in mathematics-- at least EG there. But that is nothing compared to the ease with which she understands cause and effect in human systems, or can devise experimental design or critique someone else's. She's better than some grad students I've known in those disciplines.

Quote:
As I see it, a parent or teacher with sufficient (graduate) training should be able to explain the nuances of economic theory and intuition to an interested young child. Note that the binding constraint is on the instructor side, not the student side. I'm of the opinion that virtually any subject can be brought down to the appropriate level of the student, provided that the instructor is knowledgeable enough to know where simplifications are being made in teaching. An instructor also needs to be able to explain why simplifications are made and how they are or aren't representative of reality. Anything less is an injustice to the student. In the absence of a good instructor, the student, IMO, is better off learning the math alone, as it can be difficult to un-learn sloppy or incorrect thinking.


VERY nicely stated. I agree wholeheartedly-- and the entire reason to have expert subject instruction is to avoid that nasty business of needing to UNlearn things that weren't actually true. It's a matter of seeming semantics or trivial nuance unless you truly understand at that higher level, but-- it's a real effect nonetheless.
Posted by: HowlerKarma

Re: Is math privileged for gifted children? - 03/11/14 03:32 PM

Originally Posted By: Thomas Percy
Since you quoted me, I will write a bit more.

I think a subject like economics is beyond a young child no matter how gifted this child is. I am not talking about the Freakonomics type of cutesy economics, which I think it is both more accessible and not parcicularly important.

Most of the economists actually believe very similar things. Supply and demand, free market, and so on. Mostly, economists disagree about the degree of something. For exampole, how important is market failure in a certain market? If you think it is very important in health care, then you would support national health insurance. Not too important, then you would be against the Affordable Care Act. Much of these arguments are not based on theory but on how you read the evidence, which requires understanding of statistics and institutional knowlegde. This is before you bring in things like efficiency versu equality and how do you put a price on human life and suffering. Two very well respected economists could disagree and this seperates social science from science.

I am not saying there no gifted children who can handle ambiguity. I just simply don't see this kind of subject as a good use of their time. High school will be the earliest. But from what I see, there aren't many high school econ courses that are worth the time. Might as well wait for Econ 101 in college.





With all due respect, I think that it depends (strongly) upon the child.

Ambiguity is what makes problems interesting to my daughter. She has always been like this. Ambiguity slows her down enough to promote retention of what she's doing/thinking, honestly. At least that is how it seems to me.

Perhaps this is so in STEM. I'm not sure that I completely buy into it even there-- because I think that it promotes a rigidity in thinking that (probably) doesn't serve them so well in the long term.

But in the humanities, certainly, a fluent level of comfort with ambiguity is essential for any authentic study at all.

I think that schools fail children like my DD profoundly in this regard. She is much like her +3y classmates who are HG/EG otherwise, but in terms of her ZEAL for dissection and exploration of topics without "right" answers, she stands out among them even now. She also stands out among STEM undergraduates for her ability to take multiple perspectives, often simultaneously.

It's a valuable skill, and it is one that I think is well worth cultivating in those that have the innate gift for it.
Posted by: Thomas Percy

Re: Is math privileged for gifted children? - 03/11/14 06:46 PM

My son is five. So we have not discussed economics other than I have to work so someone will pay me so that he can have shelter, food and toys.

I guess I personally was very comfortable with literature as a child but wouldn't have been with economics. I have seen students who somehow got indoctrined in a way of thinking that is hard to unlearn. I also have never really met many or any who claimed they liked econ as a child. It is very possible that the dearth of good econ teacher at that level was the root cause. I still don't think anyone will miss much by waiting until college, whether that is 14 or 18, simply because the quality of the course is likely much higher.
Posted by: jeimey

Re: Is math privileged for gifted children? - 03/12/14 12:38 PM

I definitely think that kids can and should learn about social sciences if they're interested. DK has a wonderful series for kids (maybe aimed at ages 8-12) that introduces social science topics. One of the books is called "Show me the money: How to make sense of economics." My DD7 loved reading this book because it introduces complex and interesting topics that are not covered in school. It's got beautiful charts and graphics that help make it accessible and interesting. She's definitely able to relate the ideas to what she's experienced in her life. She also enjoyed "What do you believe?" (in that series) which has a very contextualized overview of different religions and discusses the idea of belief and non-belief in general. There's also a book on psychology (What goes on in my head?) and Government (Who's in charge?). These books introduce ideas that get her wheels spinning. I really wish there were more of these kinds of materials available, but there are some amazing YouTube channels that my daughter loves that present complex concepts in an accessible way: SciShow, Vsauce, CrashCourse, Ted-Ed, CGP Grey, etc. At this age (7) I don't think she'd be interested in the books recommended by JonahSinick, but I will make note of them for later.
Posted by: Quantum2003

Re: Is math privileged for gifted children? - 03/12/14 01:00 PM

Originally Posted By: JonahSinick
[*]Study of Exceptional Talent has found that many more children qualify based on the math section of the SAT than on the verbal section of the SAT. This suggests that gifted children can, on average, excel more in math than in subjects that require verbal reasoning. (On a recent thread it was suggested that the modern SAT's verbal section isn't a good measure of verbal reasoning, but many more people qualified for Study of Exceptional Talent before 1995 as well.) It's been hypothesized that this is because high performance in math can come either from strong verbal reasoning or from strong abstract pattern recognition (of the type that the Raven's matrices test measures).
[*] The case for learning the other subjects that I mention is stronger for verbally gifted children than for gifted children whose strengths are nonverbal.
[*] It may be that life experience enables one to understand economics more deeply. But it's equally true that learning economics early could prepare one to learn more from one's early life experiences, on account of seeing relevant economic concepts in them.
[*] I think that for children, improving reading and writing skills is more important than learning the subjects that I mentioned. But one can pick up reading and writing skills through them.


Thank you for posting such an interesting series of questions. It took me a long time to determine that DS10 really had strong math talent in part because he also was strong verbally and does tend to approach math with verbal reasoning more than through strong abstract pattern recognition. Of course, he is only +3 rather than +10 years ahead in math as he is just finishing up Algebra I in school. However, he was capable of more acceleration (at least Algebra I at age 9 instead) at school if that would have been our preference. Had I been aware of this hypothesis sooner I might have been less confused a few years back!

I do agree with you that learning those other subjects (econ, etc.) makes more sense for verbally gifted rather than non-verbally gifted kids as they are the ones more likely to pick up various non-fiction sources out of curiousity. However, everything is inter-related. DS has some rudimentary understanding of economics due to his interest (driven by interest in stock markets and math applications) that are more properly labeled of a non-verbal origin.

I also agree with your last two points quoted above as applied to DS. His understanding is more sophisticated than one might expect but his interests were self-selected and he had someone somewhat qualified (me: degrees in Econ/Math & actively investing) with whom to bounce his ideas. I would not limit a child's interest in areas that presumably require more life experience but I also would not push them on a child unsolicited either.
Posted by: JonahSinick

Re: Is math privileged for gifted children? - 03/12/14 09:10 PM

@ Thomas Percy — But it's not necessary to learn in the context of courses, one can learn on one's own.
@ jeimey — Thanks for the reference!
@ Quantum2003 — Glad to have helped :-)