Hi Kathleen, as Jenny says, below, its very relevant.
Much of what I learnt about emergence comes from Montessori preschools. The approach starts a little differently, in my experience. It assumes children want to explore writing first, and in an embodied way - so ... they get to isolate a few letters (the f of food - see Sesame Street) is a favourite of mine, and food is such an interesting thing for young children, who love to explore what 'is' food and what 'isn't'.
Then they can explore sandpaper letters, and the practice of writing one letter at a time, then put them together, and so on - reading comes much later, as it is not - in the same way - based on the development of agency in the child, and it is someone else's text. (Reading aligns with agency later on, sure, but not at the beginning).
Our eldest daughter was going through this process at the time her sister Alice was born, and the next step for her was to write "Alice", and then to repeat that - almost without pause, for 3 days - she did little else during this time, except to write Alice, Alice, Alice .... until she decided she had 'got' it. Then she left that behind, and went on to other things.
Point is, the process was driven by the availability of 'intentional' learning objects and learning practices, which she could choose from, and pursue until she had decided she had got it / mastered it, and then never had to return to it, or be 'assessed' in doing it.
Internal motivation, linked into 'intentionallly designed' learning objects - (see the discussion elsewhere in these forums on 'intention', and what we might call the dance between the intention of the open learning environment / structure and the emerging intention of the learner) - if sustained, can go a long way (all the way? I dont know - it depends on whether the designer is astute enough to recognise the emergent intentionality of the learner, and translate/transcribe that into intentionally designed learning objects / learning practices - its a big ask for anyone, and we're not all designers - certainly not at that level.
More problematic is base 10, which Napoleon imposed on us to the exclusion of all other counting systems (although some survive, like our base 60/12/24 for time). There is nothing intuitive about base 10 - I for one much prefer 12 (or 5 if you must), but Montessori (who was firstly a mathematician) managed to design intentional learning objects for that too - like the wonderful 'pink tower'.
There's also a whole trajectory of 'embodied' learning to consider, and its role in emergence and 'natural' learning - not only at preschool level - but that's another story.