If an eleven-year-old were to become immortal would they still mentally mature? I suppose this might be more a neurological question than anything. If someone's body and brain were to stop developing at a young age but they were still able to learn and observe things, would they mature? Or would they just be a really smart kid? The only example I can really think of is Claudia from Interview with the Vampire and her whole problem was her brain being older than her body.
That would depend on the story world and how the author sets it up. I see no reason why becoming immortal would necessarily halt certain brain functions, unless it's because of something like becoming a vampire, which means dying (well, except for you know, being able to move and talk and all). Another type of immortal being is a god, and they would probably have far better development emotionally and mentally than humans, depending on what type of god. Many of them do seem childish and exceptionally jealous/vengeful, as if they did suffer from stunted brain development, but then some are incredibly wise or intelligent. Taking a broad view across the spectrum of different forms of immortality, it looks like you've got a pretty open field to play in.
Children's brains are sponges so they could definitely continue to learn and become wise with experience. However if they never age into/past puberty I don't think it'd be likely for them to develop adult sexuality. They would still have notions of romance based off observation but it'd be different since their body wouldn't be producing those hormones we associate with being a teenager.
Using Claudia as the example - not just immortal, but forever imprisoned in a child's body - I certainly think the accumulation of experience will mature the person to a degree, but not in the same way as for you or me. The person will forever be engaged by others as a child. I can imagine this causing a period of frustration, followed by another period of murderous rage at the fact. I mean, think how smug and prickly people are when in the throws of the Quarter-Life Crisis. Now imagine an immortal child passing through the same phase of revaluation, and, like the rest of us, finding that very few things are objectively true or real, followed by the realization that the child, even centuries on, will be engaged as a child by those who are physically adult. Do I think the immortal child will mature? Possibly. But I think it will be a twisted maturation.
Not really, no. You would essentially end up with a very experienced and superficially precocious child, but he or she would be perpetually immature in an emotional sense. They would still fundamentally think and react to situations the way a child their biological age would. It turns out our brains keep on developing as we grow up - the brain of a child is literally still "unfinished" - which is why children and even teenagers tend to be more emotional and less rational than adults, being less adept at making sound judgements by predicting long-term consequences. (This is because the amygdala develops faster than the prefrontal cortex, both of which affect decision making.) From what I can tell, the general consensus is that the human brain doesn't reach full biological maturity until the age of 25 or so.
I cannot talk about Claudia without envisaging Dopinder going "10 year old Kirsten Dunst..." in Deadpool.
The best thing about writing speculative fiction is that you get to make up the rules for things like this. If your version of immortality prevents physical development of the body and brain, it follows that an immortal child wouldn't mentally mature either. But there's no reason immortality has to prevent development if you don't want it to.
This here precisely. IQ as a measurement didn't start with "100 is average, what are you on the scale?", but as a comparison of a child's mental age to their physical age. A child 6 years old but with the mental capabilities of a 9 years old was the definition of an IQ of 150. IQ develops over time, finally "settling" around 21 but never static. Assuming that you don't provide any specific explanation along with the immortality, one would assume the child's physiological (and nervous / psychological) development remains static as well, thus fixing them to the IQ of their age and leaving their abstract reasoning, problem solving and thinking inferior to adults.
In many ways that matter, maturity is a series of decisions. A six-year-old can behave extremely maturely for their age and a thirty-year-old can be extremely stunted with no physical reason to be. I believe a physically stunted, permanent child would be capable of maturing a great deal over the years in some ways and inhibited in others. An adept child can learn a great deal of emotional control for their age and use better decision making tools than their peers. Coping mechanisms can account for a great deal of emotional maturity, and experience teaches a certain amount of maturity at any age. As @Fervidor and @TheOtherPromise noted though, there would be extreme limits in areas due to the fact that the brain is underdeveloped in vital centers and lacks adult hormones. The result, I think would be a potentially mature child, but one with less emotional control than an adult, less ability to process complex emotions in healthy ways, less willingness to make consequence-driven decisions and little to no sexual drive, all depending on physical age, of course. As to intelligence, depending on the age of the child, we might have a bit of a mystery on our hands. On the one hand, we have the fact that a child's brain absorbs information like a sponge. On the other, we have the fact that retention is severely reduced in younger children. Ask a four-year-old about something that happened a few months ago. Unless it made an impact, they might not know what you're talking about. This is less true the older the child is, but information seems to stick and accumulate if taught correctly, while memories are less often permanent.
I have no idea about whether an immortal child matures mentally into adulthood, but I echo those who say experience helps making someone mature, and even if not completely compensating for the lack of developmental growth at a neurological level, I would imagine that a lot of experience would help a child learn at least to pretend to be more mature than she really is. But a mature child is still a child. So, I will consider the matter from the point of view of someone interacting with a (immortal) child. Even if you treat a mature child like someone older than their age, it never happened to me to think or treat a mature and smart child as an adult. I may talk to them as equal to a certain extent, but I see the ways in which they are still children, just never tell them, because I know with age they will learn. Of course, when you spend a lot of time with someone the perception of who they are, including age, changes.
I would say it would depend if the brain of the child dose not suffer modifications through time, like new neurological connections when they learn something new. Also they indeed would not be able to experience almost all of the things that a human adult will experience, so there is that to take into account. However, from my perspective, if the child in question is the main character or at least very important to your story I would suggest to make them fit the narrative that you wish and not change the story to fit a fiction where no one knows the answer if the child could or could not mature. If the child is a secondary character, my guess is to play around both scenarios, one where you have a 11 year old that holds the secrets of the universe, and one where you have a immortal being that is not capable of understanding the world around him. Alternatively, you can also make a mix of these two where for example you can have the child give incredible life advice and in the next paragraph he/she can start making a tantrum for not getting the promised ice cream for his advice.
Is their body permanently stuck at the age they gained immortality? If yes, then I'd say they'd be somewhat limited mentally. However, you can get around this by having them already been alive/around for a good long while. Experience is a good teacher- a child raised in abject poverty in a warzone who becomes a child soldier at age 8 is going to come across as less childlike than a child brought up in an upper middle class western family. The immortal would probably still have some 'childlike' personality traits but intermix that with very aged views.