What are some mathematical problems that are feasible for preschool children to stimulate their intellectual development?
There are multiple natural laws that are not apparent to them, for example:
- the conservation of number/quantity,
- sets are not disjoint classes (i.e. might overlap),
- fallacy of circular arguments.
I posted the examples as answers, so they aren't privileged. Also, it would be great if we could have one problem per answer, so the votes would represent our opinions more precisely.
Edit: First, I would not ask a child a bare question. Some posts suggests games and games are great. In fact, all of examples I posted are easily transformable into games (the symmetry-related actually is a game already). In this light, the question could be understood:
If I had to ask a question or set a mathematical problem (in whatever form, game or not, that would be appropriate for the child), which questions and problems would be most suitable for a preschooler?
I'm looking for concrete examples. Posts like "use another approach", or "use questions that arise because of natural situations", or "just let it play some Lego" are not valid answers. In other words, I do acknowledge Lego as a great educational toy/tool, but "Lego" by itself does not answer the question. If you insist on games, how and which mathematical ideas would you incorporate into your play?