How sixth graders engage with others' balance rules: The role of adaptive number knowledge

The present study investigates how students engage with others' balance rules when they are working on digital balance scale tasks in small groups. A second objective of this study is to ascertain whether students' adaptive number knowledge that is, knowledge of relations between numbers and arithmetic operations plays a role in the engagement situations. The participants of this study comprised 61 sixth graders who underwent two distinct data collection sessions: a paper-and-pencil test designed to evaluate their adaptive number knowledge and a balance lesson, during which they were asked to develop a rule on how to balance a scale. We identified six distinct ways through which students engaged with others' balance rules. Three were similar to those previously identified in related studies: elaborating, challenging, and asking a clarifying question. However, new ways of engagement with balance rules among students were also identified, namely, using someone else's rule, adapting someone else's rule to a different situation, and repeating someone else's rule with different words. The results show that students with higher adaptive number knowledge were more likely to engage with others' proportional balance rules if they had the opportunity to do so. Therefore, adaptive number knowledge, defined as the ability to recognize and use relevant numerical characteristics, holds the potential to facilitate the discernment of relevant characteristics in the reasoning of other students.