Abstract
This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate.
Highlights
The repeated addition model is pervasively used in schools around the world to teach multiplication it cannot fully capture the essence of multiplicative situations
Additive thinking still overweighs the multiplicative thinking, when students in the upper grades interpret the situations that are open to both ways of thinking [2]
With digital technologyspecific tasks, we do not often think about what the task might offer in other technological settings
Summary
The repeated addition model is pervasively used in schools around the world to teach multiplication it cannot fully capture the essence of multiplicative situations (see below for more detail). Additive thinking still overweighs the multiplicative thinking, when students in the upper grades interpret the situations that are open to both ways of thinking [2] This has in part driven the growth of research around the use of different models [3,4,5]. These models represent multiplicative situations by illustrating a number of pre-given objects that are spatially organized different from that of the repeated addition model. Zaplify does not draw on game design elements such as time constraint, embedded tasks and level Instead, it offers an open exploratory environment for students to bodily experience multiplicative structures
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