Students' understanding of the 'partitioned square' representation in mathematics and science contexts

In this study, we focus on a specific visual representation that is used across several mathematics and science content areas: the 'partitioned square' (PS). Previous research has examined PSs in single content areas in isolation, such as for mathematics polynomials or biology random mating, where the PS was generally in the service of other learning goals. We contribute by examining the PS as its own construct. Our study used semi-structured interviews with eight university students, where they discussed various mathematics and science contexts for which PSs were applicable. We analysed the interview data regarding (a) how they interpreted PSs in and of themselves, (b) how they used them in science and in mathematics contexts and (c) how they elaborated on them for novel contexts. In our results, we describe how the PS was useful to the students in explaining and justifying properties of a system, for creating blended spaces across STEM contexts and for constructing new knowledge. Yet the ways the students interpreted the PS representation itself varied, leading to some issues in reasoning, which suggests some possible limitations of the PS as well.