Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption,…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…