The nature of quantities influences the representation of arithmetic problems: evidence from drawings and solving procedures in children and adults


When solving arithmetic problems, semantic factors influence the representations built (Gamo, Sander & Richard, 2010). In order to specify such interpretative processes, we created structurally isomorphic word problems that could be solved with two distinct algorithms. We tested whether a distinction between cardinal and ordinal quantities would lead solvers, due to their daily-life knowledge, to build different representations, influencing their strategies as well as the nature of their drawings. We compared 5th grade children and adults in order to assess the validity of this hypothesis with participants of varying arithmetic proficiency. The results confirmed that the distinction between cardinal and ordinal situations led to different solving strategies and to different drawings among both age groups. This study supports the ontological distinction of cardinal versus ordinal quantities and calls for the consideration of the role of daily-life semantics when accounting for arithmetic problem solving processes.

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