This document discusses intelligence and giftedness. It provides definitions of different levels of giftedness based on IQ scores. While most people have IQs within 1 standard deviation of the average of 100, profoundly gifted individuals have IQs above 160. They are estimated to exist at a rate of around 1 in 30,000. The document discusses characteristics and needs of profoundly gifted individuals, such as asynchronous development. It also summarizes research on the achievements and accomplishments of profoundly gifted individuals as they progress into adulthood.

1. Colleen M. Farrelly

2.  IQ is theorized to be
normally-
distributed.
 Tests typically set
the test average as
100, with standard
deviations of 15
(most tests).
 This means that
~68% of people fall
within 1 standard
deviation of the
mean.
 Very few people are
thought to exist in
the tails.~95% of population
are within 30 points of
average.
Gifted individuals
are typically defined
as the top few
percent on IQ
measurements.

3.  Several definitions of gifted exist, with
definitions forming a hierarchy.
 Higher scores become rarer and rarer under
the normal distribution.
 Many students within a school system are
pretty bright and qualify as gifted under
school definition (IQ>120).
 Mensa-level intelligence occurs at a much
lower rate (1 in 50).
 Much variation occurs in the top 1% of the IQ
distribution.
 A teacher who teaches 25 students per year for 30
years likely has taught ~1 high gifted student.
 That same teacher has 1:40 odds of teaching a
student with IQ>160 during that same tenure.
 A population the size of the US would be expected
to have ~17 individuals at IQ>180.
 But, deviations from the normal distribution
exist in the right tail…
IQ Level of
Giftedness
Theoretical
Prevalence
120 Most gifted
programs’
definition
~1 in 11
132 Mensa ~ 1 in 50
135 Top 1% ~1 in 100
145 Highly gifted ~1 in 750
160 Exceptionally/
profoundly
gifted
~ 1 in 30,000
180 Profoundly
gifted
~1 in 20,000,000

4.  Recent studies have shown that profoundly gifted individuals exist at much
higher rates than expected under the normal distribution.
 This is particularly true for those with uneven talents, where only one ability is at
the profoundly gifted level (IQ>160 in that ability).
 About 1 in 10,000 people are profoundly gifted on nonverbal measurements (proxy for
mathematical talent); ~35,000 are thought to exist in the US (likely higher given skilled
immigrants).
 About 1 in 30,000 people are verbally gifted at this level, or ~12,000 individuals in the
US.
 Profound giftedness in multiple areas is rarer but occurs at a much higher level
than expected under the normal distribution.
 Estimates of profound verbal and nonverbal giftedness put this rate at ~1 in 100,000; the
average IQ in previous studies is >190 for most individuals at this level.
 Studies considering other talents, such as spatial or musical ability, put estimates of
profound giftedness across abilities at ~1 in 250,000+.
 ~1,500-4,000 are expected in the US (likely closer to 4,000 given skilled immigrants).

5.  Very few modern tests can
differentiate ability at this level,
with most tests having a ceiling of
150-160.
 The old Stanford-Binet LM ratio-
based IQ test has a higher ceiling.
 Some extended measures exist for
modern IQ tests (SB-V, WISC-
IV…).
 Talent searches are a common
way to measure deviance IQ at
the profoundly gifted levels in
children and adolescents:
 Scores of >700 on SAT math or
verbal prior to age 13
 ACT reading >34, writing >32,
math >24, or science >30 at ages
12-14

6.  At lower levels of intelligence,
people generally solve problems
and learn material similarly.
 Those at the lower gifted levels:
 Require fewer repetitions to learn
 Solve problems faster
 Those at the profoundly gifted
level (IQ>160-170):
 Solve problems very differently
 Store knowledge very differently
 Recent studies suggest this
difference in kind is related to a
difference in brain connectivity
patterns (white matter tracts).

7.  Extreme need for mental stimulation
 Example: voracious reading in subject of
interest or across many subjects
 Combining steps in problem-solving
into one large step
 Can cause issues in mathematics,
particularly as children (long division,
multiplication…)
 Intensity of existing personality traits
 Dabrowski’s overexcitabilities,
amplification of traits like extraversion
or openness to experience
 Divergent thinking
 Examples: filling in the blank in h_r
with “helicobactor” or “honor” rather
than “her”
 Preference/ability to think in analogies
 Translates into the ability to process and
explain complex material intuitively
 Interconnecting knowledge
 Knowledge webs vs. knowledge filing
cabinets when assimilating new
knowledge
 Projection of self into a problem
 Example: visualizing a mathematics
problem and literally “walking through
it” to a solution
 Example: imagining oneself as a novel
character in a particular situation to
write a scene of fiction
 The simple is complex; the complex is
simple.

8.  Asynchronous development:
 A child may be mentally 14,
physically 7, and socially 10.
 Learning rates may vary within
and across subjects.
 A child may be at a 4th grade level in
math/science and a 2nd grade level in
the humanities.
 A child may go through a year’s
worth of math in 1 month but a
year’s worth of literature in 2
months (and a year’s worth of social
studies in a weekend).
 This makes meeting the needs of
profoundly gifted learners
challenging, particularly in an age-
based classroom.

9.  Acceleration
 This can involve moving up in a single subject or
across subjects (whole grade acceleration).
 Radical acceleration involves moving up multiple
grades, either within a subject or across subjects.
 Longitudinal studies suggest most students benefit
academically, socially, and motivationally from
acceleration, including radical acceleration.
 Accelerated students also tend to have higher adult-
level achievement in their fields.
 Many accelerated students are satisfied with their
acceleration, with most dissatisfied students
preferring more acceleration.
 However, many teachers and administrations
don’t welcome acceleration.
 Some believe it is harmful, despite the studies.
 Some are outright hostile to profoundly gifted
students, who often don’t fit educational
assumptions or “molds.”
 Some dismiss these students’ extremely high
scores as incorrect or the result of cheating.

10.  A follow-up study of profoundly gifted
students at ~ age 23 showed:
 56% planned to pursue doctoral degrees
(or were already) compared to 1% of the
general population.
 Degrees pursued tended to match ability
pattern, with mathematically-gifted
students pursuing STEM degrees.
 Many were already accomplished in
their fields (patents, academic/creative
writing publications, national awards,
Phi Beta Kappa membership).
 Accomplishment rates were higher for
verbally-gifted and evenly-gifted
individuals.

11.  This same group of 320 individuals achieved much in their fields by age 38:
 133 STEM patents
 392 STEM publications
 687 software contributions
 922 dance and music productions
 191 creative writing publications
 79 works of art
 46 social science/law/business publications
 16 companies founded
 $26 million in grant funding
 These findings have been replicated in other samples of profoundly gifted
individuals.
 Achievements tended to separate into STEM and humanities
accomplishments according to intellectual profile (ability tilt).

12.  Of these impressive individuals, some
outshone others in their field:
 57% of fine arts accomplishments were
attributed to one person.
 34 of 39 poems were created by one person.
 Three individuals produced 100 software
contributions (44% of total).
 This held in the replication sample:
 One person produced 60 of 68 publications in
chemistry.
 40% of NSF grants went to one researcher.
 43 of 86 Fortune 500 patents were filed by one
person.
 These individuals are rare even within the
rare profoundly gifted population.

13.  Another rare subpopulation consists
of those who are profoundly gifted
across multiple fields.
 They are about 10-25 times rarer than
individuals who are profoundly gifted
in only one area.
 Their average IQ is higher than
unevenly gifted individuals (IQ>200
estimated in one study, vs.
 Their early accomplishments span
STEM and humanities, and little has
been published about their adult-level
accomplishments within and across
fields.
 Recent studies suggest they are a
unique subpopulation relative to the
unevenly gifted at this level of ability.
Evenly-gifted

14.  A few interesting research directions exist, including:
1. A longitudinal study of wranglers to identify how their academic and achievement
trajectories develop over time, as well as early signs of wrangler potential.
2. Studies examining achievement trajectories over time by type of academic intervention
types in this population, by demographic factors (women, minorities…), or by ability
profile.
3. A more in-depth follow-up of achievement profile among different ability profiles to
understand how unevenly-gifted populations might differ from evenly-gifted
populations in adulthood.
4. A neuroimaging study of different populations (unevenly profoundly gifted, evenly
profoundly gifted, more moderately gifted, and average populations, for instance) to
understand how brain activity patterns and connectivity relates to field-specific and
general talent on verbal and mathematical problems.

15.  Profoundly gifted individuals are, by definition, rare.
 Small sample sizes present statistical challenges, and few methods exist that can
compare samples of <30 individuals.
 Persistent homology and its simplified cousin, single-linkage hierarchical clustering,
provide statistically robust methods for sample comparison at small sample sizes.
 These methods also provide good visualization methods (example shown below).

16.  Coyle, T. R., Purcell, J. M., Snyder, A. C., & Richmond, M. C. (2014). Ability tilt on the SAT and ACT predicts specific abilities and
college majors. Intelligence, 46, 18-24.
 Farrelly, C. M. (2017). Topological Data Analysis for Data Mining Small Educational Samples with Application to Studies of the Gifted.
 Gross, M. U. (1992). The use of radical acceleration in cases of extreme intellectual precocity. Gifted child quarterly, 36(2), 91-99.
 Gross, M. U. (2000). Exceptionally and profoundly gifted students: An underserved population. Understanding Our Gifted, 12(2), 3-9.
 Gross, M. U. (2003). Exceptionally gifted children. Routledge.
 Gross, M. U. (2015). Characteristics of Able Gifted Highly Gifted Exceptionally Gifted and Profoundly Gifted Learners. In Applied
Practice for Educators of Gifted and Able Learners (pp. 3-23). SensePublishers.
 Janos, P. M. (1987). A fifty-year follow-up of Terman's youngest college students and IQ-matched agemates. Gifted Child Quarterly,
31(2), 55-58.
 Kell, H. J., Lubinski, D., & Benbow, C. P. (2013). Who rises to the top? Early indicators. Psychological Science, 24(5), 648-659.
 Lubinski, D. (2009). Exceptional cognitive ability: The phenotype. Behavior genetics, 39(4), 350-358.
 Lubinski, D., Webb, R. M., Morelock, M. J., & Benbow, C. P. (2001). Top 1 in 10,000: a 10-year follow-up of the profoundly gifted.
Journal of applied Psychology, 86(4), 718.
 Makel, M. C., Kell, H. J., Lubinski, D., Putallaz, M., & Benbow, C. P. (2016). When lightning strikes twice: Profoundly gifted,
profoundly accomplished. Psychological Science, 27(7), 1004-1018.
 Prescott, J., Gavrilescu, M., Cunnington, R., O'Boyle, M. W., & Egan, G. F. (2010). Enhanced brain connectivity in math-gifted
adolescents: An fMRI study using mental rotation. Cognitive Neuroscience, 1(4), 277-288.
 Ruf, D. L. (2005). Losing our minds: Gifted children left behind. Great Potential Press, Inc..
 Singh, H., & O'boyle, M. W. (2004). Interhemispheric interaction during global-local processing in mathematically gifted adolescents,
average-ability youth, and college students. Neuropsychology, 18(2), 371.
 Wai, J., Cacchio, M., Putallaz, M., & Makel, M. C. (2010). Sex differences in the right tail of cognitive abilities: A 30year examination.
Intelligence, 38(4), 412-423.

17.  http://www.davidsongifted.org/Young-Scholars
 http://www.hoagiesgifted.org/
 https://cty.jhu.edu/set/index.html
 https://tip.duke.edu/
 http://www.davidsongifted.org/Search-Database/entry/A10108
 https://robinsoncenter.uw.edu/programs/eep/
 http://www.calstatela.edu/academic/eep
 https://www.talentigniter.com/