This is really interesting, but I don't agree with this conclusion: "These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal maths." (My own opinion is that educational curricula are generally not very important at all; that people are learning machines that learn what they need to in the contexts they find themselves; and that people -- as shown by this study -- struggle to effectively apply what they've learnt in one context into a different context.)
> My own opinion is that educational curricula are generally not very important at all
We spend an incredible amount of time and effort on educational curricula, so it's worth thinking about.
My opinion is everything you learn before you start actually using knowledge is "just" familiarization. In my opinion, pedagogical instruction should do a much better job of explaining this and incorporating this realization. I do think individual teachers understand this.
