An earlier post quotes an example on decimals and different possible reasons behind same mistake. Do we have such collection for all concepts?
Does language have an effect on the process of learning numbers? There is research in neuroscience which seems to suggest that the language of numbers can be an important hurdle in the way of child's learning. A language which has 100 distinct names for first 100 numbers makes it difficult for a child to learn them as compared to a language like Chinese where double digit numbers don't have specific names, 23 is read as two-three and so on. Do we know of any more such insights?
There is also some existing literature on all the above five aspects. Some researchers have done good work but much more is needed, along with addressing the challenge of incorporating learnings from the existing literature into teaching processes. We should aim towards a scenario where decisions regarding teaching are taken based on rigorous research and not just from intuitions and experience.