Scaffolding Multiplicative Concepts Formation: A Way of Digital Support

The balance scale problem is a widely known material for studies on the development of thinking. It is hard for students to master the multiplicative concept of equilibrium, even though the general idea “the further from the fulcrum – the heavier” is commonplace and students are often provided with real or digital simulations of the lever – so they could explore it as much, as they need. The psychological researches since Piaget regard the concepts, based on logical multiplication (i.e. the consideration of the changes of two parameters) as those, which demand acquisition of special intellectual operations by students. As we examine the early stages of multiplicative concepts’ formation within the activity approach framework, we include special modelling means to support students’ own inquiry in order to promote their actions to the conceptual level of orientation in the coordination of two magnitudes’ changes. Thus, students’ manipulations with weights – adding, moving and removing – become mediated by the specially organised additional work: the evaluation of the contribution of each weight unit to the total load on each side of the lever. Within this approach, students are able to start from the trickiest tasks with several weights located in different positions (which were considered to be exceedingly difficult since Siegler’s studies) and the concept is acquired from their own actions mediated with this “additional” modelling. The digital support design, thus, has to serve several purposes, among which most important is to scaffold problematization, modelling and distribution of operations among partners. Though many modern lever simulations provide students with functionality enough to test different combinations of weight units, they do not provide the educational designers with enough ways to challenge and test students’ modelling. The educational module on the concept of balance, which we have designed based on the principles of the learning activity theory, shows, that a significant number of functions has to be added to the computer simulation of the lever to support the tasks modifications, which will make students rely on modelling.