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Even if some asynchronies are not really associated with impairments, well they need to be accounted for and there is some leeway with DSM interpretation. I myself don't particularly like the DSM criteria for SpLD.

Highlighting the why is important, though at some point these reminders should be lessened.

The crux of the matter - which study skills is she perhaps lacking in?

Yes, I generally agree, although I also see an end game of parenting as defending liberty and ensuring that the child retains freedom, even if they are not as healthy or holistic.

Sometimes, if one wants a goal, such as early admission/skipping levels, some sacrifices may need to be made. Which ones are you willing to make? Which ones is she willing to make?

Are there any behavioral matters which could put college admissions off her early admission? Be careful, some universities are not supportive or worse harassing towards early entrants.

Frameist, I think there are multiple possible perspectives on the topic of asynchrony. I would agree that large asychronies can be as impactful subjectively as normative deficits in another individual. In my professional work, I actually do not favor the DSM criteria for SLD --which reference only age-appropriate--when in the context of gifted-level cognition (I prefer ICD-10, which includes intellectual ability--"unexpected underachievement".) ADHD does not really focus primarily on developmental level; the focus is impairment. Likewise most emotional disorders. So I think there is more latitude to consider that impairments in high cognitive individuals may look quite different from impairments in those of average cognition. This is why I generally weight functional impacts more than pure numbers--but I also am careful to look at subtle functional impacts, such as the amount of time and fatigue required to accomplish tasks, impacts on self-concept, and relational challenges--the costs of compensation, in other words. I am sympathetic to your experience, as I have been the first to identify twice exceptionality (or even disabilities in learners who were only above average, and not nominally gifted--though some of those may well have been artifacts of prolonged lack of access to appropriate instruction and remediation) in numerous upper grades students, and regret that 2e is not better understood among my co-professionals.

But some asynchronies do not appear to be associated with impairments. There is no particular reason to consider developmental coordination disorder in a five year old who can generate expressive language at a high school level but is still working on letter formation. (Unless there are motor delays that appear unexpected even for five-year-olds.) It is not necessarily an impairment for a 10-year-old who is conceptually capable of calculus to struggle with managing the independent note-taking, homework completion and classroom etiquette expectations of an university classroom. Not to mention navigating a 40,000-student open campus on their own. These are really environmental deficits that originate from our society's traditional age-grade-locked educational institutions, with rigid curricula. Homeschooling allows parents to adjust expectations so that most aspects of development are in their zones of proximal development, even if they are at very diverse levels.

To your point about executive functions, that is certainly an area that should not be overlooked in any learner, but needs special attention in gifted learners. I appreciate your responses, as they encourage greater clarity in my communications. I also did not really learn study skills until my third round through graduate school, when I already had multiple degrees behind me. Ultimately, it was my higher level of interest and motivation in that field (as well as, I suspect, frontal lobe maturation) that brought me to the point of acquiring some study skills. I applaud you for having had the insight as a child to try to acquire higher-level study skills. My approach to teaching EF in my own children has been to weave practice into meaningful activities of daily life, as well as to stay on top of instructional level so that the intrinsic challenge will create immediate feedback and application of study skills.

In the homeschooling environment (where the OP is), it is possible to highlight the why of study skills much more easily, by attaching them to personally-meaningful goals and consequences, rather than restricting them to checklist items that may feel like busywork. Many of the strategies that parents teach their children for activities of daily living are equally useful for academic tasks. On a practical level, we used schedules, routines and checklists for schoolwork, which were scaffolded by a parent initially (i.e., one-on-one instruction, to numerous reminders, to fewer reminders), and then transitioned gradually to student-managed. Student voice and choice were also important, such as when one DC decided that they would use extreme block scheduling (one entire school day devoted to a week's worth of science, one to history, the other three weekdays for English and math). At the beginning of middle school age, it was predominantly parent-directed, but by 15 or 16 it was almost entirely student-directed. As a side note, the DCs who went into brick and mortar high school had markedly better study skills and self-directed learning skills than most of my students do, I think in large part because of practice managing their own learning and time.

If OP wants specific resources for executive functions and study skills, here are a couple of classic works:

https://www.amazon.com/Smart-but-Scattered-Revolutionary-Executive/dp/1462554598/ Peg Dawson & Richard Guare's Smart But Scattered.
(Their website, with some freebies: https://www.smartbutscatteredkids.com/)

https://www.amazon.com/Improving-Childrens-Homework-Organization-Planning/dp/0932955509/ HOPS, from the National Association of School Psychologists

But if the OPs actual concern is simply with rote memorization of math facts, rather than broader study skills, the above may be a lot more words than strictly necessary! In that case, Frameist's tips for memorization are probably the way to go.

Thanks for your clarifications, Frameist. You are correct that there can be many other factors which would warrant formal evaluation. If you read my other posts, you'll see that I often reference the need for a question to be answered or a problem to be solved as the drivers of evaluation. In this case, the OP did not report any particular concerns other than an appropriate match between cognition and instruction. But it is certainly helpful to remind readers that there are many reasons to evaluate (especially since most parents are not professional evaluators).

Obviously, I am generally pro-testing, or I would not be in my current profession! At the same time, it's important to empower parents as critical observers of their children. Evaluation data is only one source of information regarding a child, obtained during a short time frame under specific conditions, and should always be interpreted in the context of the human first, rather than interpreting the human in the light of the numbers. Involved parents--especially homeschooling parents--have a much broader and deeper experience of their children's learning needs and strengths, over more diverse contexts and a much longer time frame. I find that their insights are extremely helpful. As you are likely aware, research on gifted identification has found that parent nomination is much more accurate than teacher nominations, and not too far off of standardized testing.

In any case, the big picture is that the end game of parenting is a happy, healthy, holistically growing human who has satisfying relationships internally and externally. As you note so astutely, intellect is only one component of this.

I would reply with my own experience in hindsight as well as from mentoring and research. I do not fully agree with aeh's opinion on the matter.

I would say it is important to learn study skills early especially if your daughter is gifted (standardised testing?) as often we learn to coast by osmosis until it affects us down the line, such as myself when I was a freshman at university and had to transfer to another university due to a significant discriminatory conflict. It would teach her ways to study especially when she arrived at HS or university and begins struggling against the curve (especially some T20 unis in the US).

I wouldn't be the man I am today without the study skills I attempted to learn at 11. I would have been close to flunking out of university and I am an intellectually gifted dude.

I would first start out by introducing shortcuts to memorise some parts of the multiplication table, for instance 4x4 = 16 = 4^2 = 2x8 = 1x16 to see the factors involved in 16. Similar for 25: 5x5 = 25 = 1x25. Perhaps she could time herself with the Pomodoro method, and if her executive function is weak maybe start with 10-minute study and 10-minute breaks then after three 10-min study sessions take a 25-min long break? It's not much, but some people are weak in EF and ADHD is a more common disorder than you might think.

Just because she may be "very much on track with her age-peers in this respect" does not mean there is no weakness. If your daughter is gifted then it could perhaps be arguable she is weak in EF and attention compared to her developmental age (not chronological age). How was she like when she was younger? Is she physically healthy?

For my experience, I got diagnosed with ADHD after starting another university after transferring myself out due to a discriminatory conflict. That is a genuine, correct diagnosis at the time and probably before.
The huge mistake that psychiatrists made was to interpret symptoms relative to age. This is incorrect and this is where I believe aeh has erred. The DSM criteria for ADHD states that symptoms should be excessive compared to developmental level (including age, IQ and intellectual maturity). This doesn't imply that your daughter has ADHD or other disorders but it may be worth considering. Even for social emotional development they benchmark against developmental stage (not age only).

As people, we live in a society, and there are certain inherent requirements in the society. Perhaps you could read The Social Contract for a libertarian political perspective of this.

Perhaps your daughter could teach your siblings or begin paid tutoring if possible? Does she have medium-term or long-term goals?

I would personally say your child is gifted, especially if she used the SB-5 and got a 143. The other stuff is academic tests and perhaps your child is relatively weak in attention or processing speed or even executive functioning. That is an interesting difference. Personally I would say a 130s or above IQ is gifted.

I would rely on the FSIQ to say that she is gifted, and technically under many definitions it works (130+ or 140+) so I would say she is gifted. But the SB is supposed to be taken in exam conditions in the conditions set, not online.

If I had to make a decision based on your child, I would say she is gifted but needs confirmation with a genuine IQ test in full standardised conditions.

Unlike aeh I do not necessarily believe that simply monitoring development and being aware of needs with "clinical judgement" could suffice for homeschooling in many cases. There are many complex conditions such as personality-related problems if the teen/preteen is very egocentric and has a pattern of it. That is why I prefer standardised testing too as a junior mentor/researcher and former teacher/tutor.

How early admission do you want to lobby for her and how many levels do you want her to skip? What other courses in other subjects did she take? I would probably focus on enrichment in non-academic hobbies as well as other holistic attributes, for instance survival skills. Besides, if your daughter is not perfect (for instance, has a vice or similar) at least she has many other decent qualities and decent friendships who will accept her. I personally am not willing to be extremely harsh on a teen for enjoying some vaping while keeping to between lectures and spend their money responsibly but soem parents are black and white it seems.

If she is doing Algebra I and Chemistry then it seems she would be ready to enter university maybe 3-5 years later or 6. While I personally favor early enrollment I would prefer if the college she goes to is a quite decent college, perhaps top 100 or a decent liberal arts school. In my personal experience in hindsight I would go to a college who is supportive of people including early-entrants as well as decent. And hopefully they would be able to fit in, join parties and all that.

I do see a need for advocacy based on labels as whether she is gifted or simply an extremely hard worker changes things. If the latter, people may be skeptical. If the former, perhaps it would be better. Sometimes gifted girls can hide disabilities better by compensating with their great intelligence (especially if the 143 IQ is genuinely 143 IQ in standard conditions). If daughter has some executive function or personality or personal problems, in my opinion a label could not only help give them autonomy but also accountability for her as well as others. Some people discriminate others because they perceive others as disabled even if they are not. This is where I appreciate aeh's opinion but don't fully agree in this aspect.

Welcome NT!

Unfortunately it seems as if the school has misguided views on giftedness. You can be gifted while struggling with one aspect and not be able to demonstrate it academically.

I'd personally push a little bit harder but don't push too much, perhaps lean on supplementary Ed Psych report or transfer him elsewhere.

Any other concerns? While enrichment may be sufficient to maintain a child's intellectual curiosity, it may not work as well for 2e. Also... perhaps be transparent and remember that for gifted children they do not need to "fail" in one area to be learning disabled or dyspraxic. If all other areas are highly superior but one is average, that suggests a very clear weakness.

Perhaps typing or a laptop might suit him better as an accommodation in some areas.