How Do Children Know That What They Learn in Mathematics Is True?

Abstract

One of the distinctive marks of mathematical thinking is that we do not need to rely on memory or authority to know whether or not an assertion is true. In mathematics, we can prove our theorems. For students, however, the road to formal proofs is a long one. The ways in which children ascertain that a statement or fact in mathematics is true, accurate, and free from error evolve over time. The kind and amount of convincing evidence, or proof, that is appropriate for a child change as the child's mathematical thinking develops. Children must also learn at a young age that they do not need to rely on authority or memory to know that what they learn in mathematics is true.