Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

Abstract

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., one bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial decrease problems impose higher cognitive load on children than the corresponding increase problems, even though both are solved with addition. However, the source of this cognitive load is unclear. It could be the direction of the depicted change or the position of the unknown (start vs. end set). To address this question and disentangle the sources of the load, we presented the problems in two different formats: (1) the conventional static one-picture problems and, (2) an adapted three-picture problem-format, which depicted the dynamic change in sequential steps. We also examined whether the three-picture problem-format makes the decrease problems easier. Seventy-nine first-graders participated in this study. Results showed that, overall, problems with the position of the unknown at the end were easier to solve than the ones in which the unknown was at the start. Furthermore, three-picture decrease problems with the unknown in the last position were easier than the one-picture decrease problems, and therefore appear to be a meaningful way to make such problems easier for children to understand.