> Hmm, that could potentially cause confusion later [...]
(Q: Do you have kids?)
Our experience is that pretty much everything parents tell young children could potentially cause confusion later.
In no particular order: Father Christmas aka Santa Claus, The Tooth Fairy, Where Babies Come From... it's a long list, our eldest is 13 and we're not done yet.
(sorry for responding after so many days - didn't see reply before)
Ha! Certainly a fair and good point.
I would propose that there is a spectrum when it comes to the 'damage', as a term that comes to mind right now, (likely to be) caused by various kinds potentially confusing information.
Given differences in the way different people understand, well, pretty much anything, I'd propose that it might best be thought of as some set of statistical distributions. Using this kind of framework*, we might be able to reasonably improve thinking about what these distributions might look like, how we might tailor the information we provide and how much work we put into trying to avoid introducing possibilities for confusion, etc. Further, I suggest 'set' as we might benefit from 'parameterizing' (thinking about distinct distributions) in terms of traits - autism, ADHD, anxiety, etc.
In my mind, and based on my experiences, I would (in part, thinking terms of the model I'm proposing here) be much more wary of asserting potentially incorrect information in the realm of math and some of the more 'abstract' subjects that people tend to have more trouble in the first place. A concept like 'Santa Claus' isn't something that a child may need to be able to use as a basis for building serious skills on, say. Of course, 'Santa Claus' can be helpful for building imagination, ability with storytelling, developing narratives, etc. ... but the fundamental information regarding some specific entity 'Santa Claus', is not really problematic, in terms of the perspective I'm trying put forward here. On the other hand, statements that are 'too strong' (or 'too weak' possibly) or using terms in ways that aren't standard in mathematical discourse ... these sorts of things can make it feel like the ground is really slipping away as you try to learn other bits about a subject that, again, for many people is ... nebulous ... it's not (so) visual, tactile, ... it's very strange in many ways, early on.
That's the best I can do, right now, in response, I think.
You raise a good point, for sure. And I'm sure there are entire books, there are papers out there in the literature, etc. Personally, I can HIGHLY recommend books like Polya's "How to Solve It" ... as a starting point regarding 'math pedagogy'. That book is a gem, IMO, and gives some real insight into how to think and problem solving in general. And, it's a good gateway to many more resources and research into these areas.
As with everything human and 'complex', there's really no 'optimum' or chance of finding any such thing, I think. Avoiding the worst impacts ... essentially, in terms of opportunities and establishing bases etc., that's doing pretty well - raising children / 'new humans' is hard.
* Which is a way I've been trained to think, sorry if it's not a great model for you - kind of best I can think of off the top of my head and with limited time this moment
(Q: Do you have kids?)
Our experience is that pretty much everything parents tell young children could potentially cause confusion later.
In no particular order: Father Christmas aka Santa Claus, The Tooth Fairy, Where Babies Come From... it's a long list, our eldest is 13 and we're not done yet.