What children know about multiplicative reasoning before being taught

Abstract

We investigated children’s informal knowledge of multiplicative reasoning. Data were collected at the end of first grade, before this mathematical domain was explicitly taught. A large sample of children (n = 1176) was assessed in a relatively formal test setting, through an online test containing 28 multiplicative problems with and without contexts. On average, the children correctly answered more than half (58%) of the problems, indicating that before formal instruction on multiplicative reasoning, children already have a considerable amount of knowledge available in this domain, which teachers can build on when teaching them formal multiplication and division. We found that multiplicative problems with an equal groups semantic structure and context problems with a picture involving countable objects were easiest to solve.