I’d say that in that case you should either go ahead with the child’s interest (if it is something useful), or try to find some kind of intersection between what the child wants and what you want (e.g. if you want the child to be a painter, but the child is only interested in dinosaurs, let them paint dinosaurs).
Related: Building Islands of Expertise in Everyday Family Activity discusses how to take a child’s intrinsic interest in something and then finding bridges between the “island of expertise” that the child develops around that, and everything else. A specific example used is a boy who’s been very interested in trains:
By the time the boy turns 3-years old, he has developed an island of expertise around trains. His vocabulary, declarative knowledge, conceptual knowledge, schemas, and personal memories related to trains are numerous, well-organized, and flexible. Perhaps more importantly, the boy and his parents have developed a relatively sophisticated conversational space for trains. Their shared knowledge and experience allow their talk to move to deeper levels than is typically possible in a domain where the boy is a relative novice. For example, as the mother is making tea one afternoon, the boy notices the steam rushing out of the kettle and says: “That’s just like a train!” The mother might laugh and then unpack the similarity to hammer the point home: “Yes it is like a train! When you boil water it turns into steam. That’s why they have boilers in locomotives. They heat up the water, turn it into steam, and then use the steam to push the drive wheels. Remember? We saw that at the museum.”
In contrast, when the family was watching football—a domain the boy does not yet know much about—he asked “Why did they knock that guy down?” The mother’s answer was short, simple, stripped of domain-specific vocabulary, and sketchy with respect to causal mechanisms—“Because that’s what you do when you play football.” Parents have a fairly good sense of what their children know and, often, they gear their answers to an appropriate level. When talking about one of the child’s islands of expertise, parents can draw on their shared knowledge base to construct a more elaborate, accurate, and meaningful explanations. This is a common characteristic of conversation in general: When we share domain-relevant experience with our audience we can use accurate terminology, construct better analogies, and rely on mutually held domain- appropriate schema as a template through which we can scribe new causal connections.
As this chapter is being written, the boy in this story is now well on his way to 4- years old. Although he still likes trains and still knows a lot about them, he is developing other islands of expertise as well. As his interests expand, the boy may engage less and less often in activities and conversations centered around trains and some of his current domain-specific knowledge will atrophy and eventually be lost. But as that occurs, the domain-general knowledge that connected the train domain to broader principles, mechanisms, and schemas will probably remain. For example, when responding to the boy’s comment about the tea kettle, the mother used the train domain as a platform to talk about the more general phenomenon of steam.
Trains were platforms for other concepts as well, in science and in other domains. Conversations about mechanisms of locomotion have served as a platform for a more general understanding of mechanical causality. Conversations about the motivation of characters in the Thomas the Tank Engine stories have served as platforms for learning about interpersonal relationships and, for that matter, about the structure of narratives. Conversations about the time when downtown Pittsburgh was threaded with train tracks and heavy-duty railroad bridges served as a platform for learning about historical time and historical change. These broader themes emerged for the boy for the first time in the context of train conversations with his parents. Even as the boy loses interest in trains and moves on to other things, these broader themes remain and expand outward to connect with other domains he encounters as he moves through his everyday life.
[...] although some of the learning may be highly planned and intentional, much of it is probably driven by opportunistic “noticing” on the part of both the parent and the child. Recent efforts to consider parent input into children’s categorization decisions, for example, have predominately been directed at developing an account for how parents structure a fixed interpretation for children. As Keil (1998) pointed out, casting parents as simple socializers who provide fixed didactic interpretations for children is unlikely to be the right model. There is nothing more annoying then someone who provides you with pedantic explanations that you do not want or that you could not make use of. In reality, however, everyday parent-child activity hinges on a dual interpretation problem. The parent needs to decide what is worth noting, based on their own knowledge and interests, their understanding of their child’s knowledge and interests, and their current goals for the interaction. Children are making the same calculation, simultaneously. Over time, the family interprets and re-interprets activity, bringing out different facets: Sometimes they highlight the science, sometimes the history, sometimes the emotion, sometimes the beauty, and so on. Thus, the family conversation changes to become more complex and nuanced as it traces the learning history of the family and extends through multiple activities.
Related: Building Islands of Expertise in Everyday Family Activity discusses how to take a child’s intrinsic interest in something and then finding bridges between the “island of expertise” that the child develops around that, and everything else. A specific example used is a boy who’s been very interested in trains: