Talking to children about their values, their beliefs and their mathematics can be like going on a holiday of experimentation. Never make any assumptions about what you think they know and how you think they got to know it. From 1985 to 2005 my job was to visit children and adults, individually in their houses, in their schools, and lots of other different places. I just talked to them about this stuff. I think I learnt more that they did. My personal criteria for a session being sucessful was the number of times they laughed at the mathematical idea we were discussing! And that applied to the conversations had with adults, as well! If a piece of mathematics was funny then I wrote it down, so now I have seventeen 280 - page note books = nearly 5,000 mathematical 'jokes' that were rooted in someone's values and believes about the concepts and principles they were being asked to digest
Reading Jack's 1989 paper in 2012 changed my life.
Whitehead, J., 1989. Creating a living educational theory from questions of the kind,‘How do I improve my practice?’. Cambridge journal of Education, 19(1), pp.41-52.
I remember reading it over and over when sitting on a train. Going somewhere, but not sure where!