Little Children, Big Mathematics: Learning and Teaching in the Pre-School.

We examined elementary school teachers' justifications to number- theoretical "for all" propositions and existence propositions, some of which are true while others are false. We also assessed whether teachers regarded their justifications as mathematical proofs. About half of the teachers produced formal algebraic proofs. A smaller number of teachers produced non-formal proofs appropriate for presentation in elementary school classes. However, a substantial number of teachers applied inadequate methods to validate or refute the propositions. Finally, many teachers were uncertain about the status of the justification they gave. (Author)