The role of variables in relational thinking: an interview study with kindergarten and primary school children

Abstract Relational thinking and dealing with variables are two essential aspects of algebraic thinking. means viewing mathematical expressions equations as a whole rather than individual computing processes. It is characterized by using relationships between objects, refers to the relations equality inequality. In this study, examine relational kindergarten primary school children, perspective was applied non-symbolic representations in form boxes marbles. Using multiple very powerful but also difficult tool algebra. The study had aim examining how children establish several which represented real materials. interview conducted aged 5–10 years. Marbles different colored unknowns quantities depending on each other. Initially, approaches could be differentiated, namely, number-oriented structure-oriented approaches. shown that certain conceptualizations were related children’s ability show Kindergarteners stimulated think relationally unknown can determined. This process observed depended addition, conceptualization examined. concepts general number variable changing quantity categorized. Further resulted from data, categories undeterminable, specific number, quasi-general.