I’m not exactly sure where your questions originate, but here’s my take on intelligence and abstract learning.
To address your question about IQ in my state, I have the following response. IQ’s vary by race, so states with a population like Mississippi will have lower IQ’s than states like Maine. Pennsylvania, where I live, essentially reflects the national average, since the racial makeup of Pennsylvania approximates the nation as a whole. Thus, Pennsylvania’s IQ’s align with the chart above.
I don’t understand why you ask about my state since all states have their share of students with differing cognitive abilities. That does change the approach to education, only the percentage of students learning at different speeds and depths.
Regardless of location, children with IQ’s below 80 have no business being in public school. They are incapable of learning and it is a waste of money. Instead, they need to spend years learning the most basic of daily tasks that have nothing to do with academics.
The questionable IQ range for public education is between 80 and 90. These are your special education students. They are capable of learning the basics of language, arithmetic, science, and history. I think these children are best served by being specialized education that is tailored to their needs, particularly the speed at which they learn. It is unfair to them and more intelligent students to be placed in the same classroom.
When it comes to college bound students, I believe that an IQ above 110 should be required. That’s approximately 20% of the population. SAT and ACT exams are a proxy for IQ tests by the way. Any large collection of random test questions of varying difficulty that have been given to a suitably large population and produce a normal distribution od test results can be used as a proxy for cognitive ability tests (IQ test). Unfortunately, many colleges no longer require SAT’s or ACT’s for admission.
My understanding about abstract learning is that it varies by age, sex and individual. It would be fair to assume more 12 year old girls are cable of abstract learning than 12 year old boys. Differences will disappear in similar intelligence children as the children mature. I haven’t read anything about the correlation between IQ and abstract learning ability, but I highly suspect there is a semi-strong relationship. Logically, it would appear that people with low IQs never develop the ability to learn abstract concepts. Likewise, highly intelligent people can process many and complex abstractions. Most mathematics through calculus II only requires a modicum of abstraction in comparison to higher level mathematics.
My take on mathematics is that any slightly above average intelligent child is capable of learning calculus with proper instruction. That would align with the set of all college bound students.
My experience homeschooling my children followed a natural progression in mathematics topics. They were prepared to do algebra when they mastered the requisite arithmetic topics for algebra. Our schedule was based on mastery, not age, grade or any other arbitrary factor. In other words, new topics in any subject, but particularly for mathematics, were not introduced until mastery of requisite topics. Both of my children completed calculus with analytical geometry (I & II), linear algebra, differential equations, and a two term calculus-based probability and statistics course prior going to college. I used my college textbooks for their textbooks. We went at a college level pace beginning in their “sophomore” years. Most of their mathematics study was independent. I would teach three to four hours per week and offer occasional help with problems after they exhausted all other means of learning. They had full access to problem solver type books, the internet, MIT Open Courseware, and instructor manuals.