What we count dictates how we count: A tale of two encodings

The influence of semantics and numerical representation on the SNARC effect

World semantics refers to how individuals comprehend and ascribe meaning to phenomena within specific sociocultural and environmental contexts. And it significantly influences how people conceptualize numerical properties, such as quantity ("how many") and order ("which"), influencing their resolution of cardinal and ordinal numerical task. In order to reveal the influence of world semantics on the joint effects of encoding spatial-numerical responses related to cardinal and ordinal numbers, this study conducted three experimental contexts with distinct numerical representations: (1) a non-symbolic context, where numbers were represented using dot arrays; (2) a symbolic context, where numbers were presented as Chinese characters; and (3) a word problem solving context, where numerical values were embedded in real-world mathematical scenarios. To investigate how numerical attributes (cardinality vs. ordinality) influence on the SNARC effect under varying level of world semantics across these three contexts. Results showed that in the non-symbolic context, the SNARC effect is primarily observed for cardinal numbers. In the symbolic context, ordinal number elicited a stronger SNARC effect. However, in the word problem context, no significant SNARC effect was observed. The findings suggest that as world semantics become more prominent, the SNARC effect diminishes, particularly in applied numerical contexts. Additionally, ordinal numbers exhibited a stronger SNARC effect than cardinal numbers, supporting the role of sequential processing in spatial-numerical associations.

Uncovering the interplay between drawings, mental representations, and arithmetic problem-solving strategies in children and adults

There is an ongoing debate in the scientific community regarding the nature and role of the mental representations involved in solving arithmetic word problems. In this study, we took a closer look at the interplay between mental representations, drawing production, and strategy choice. We used dual-strategy isomorphic word problems sharing the same mathematical structure, but differing in the entities they mentioned in their problem statement. Due to the non-mathematical knowledge attached to these entities, some problems were believed to lead to a specific (cardinal) encoding compatible with one solving strategy, whereas other problems were thought to foster a different (ordinal) encoding compatible with the other solving strategy. We asked 59 children and 52 adults to solve 12 of those arithmetic word problems and to make a diagram of each problem. We hypothesized that the diagrams of both groups would display prototypical features indicating either a cardinal representation or an ordinal representation, depending on the entities mentioned in the problem statement. Joint analysis of the drawing task and the problem-solving task showed that the cardinal and ordinal features of the diagrams are linked with the hypothesized semantic properties of the problems and, crucially, with the choice of one solving strategy over another. We showed that regardless of their experience, participants' strategy use depends on their problem representation, which is influenced by the non-mathematical information in the problem statement, as revealed in their diagrams. We discuss the relevance of drawing tasks for investigating mental representations and fostering mathematical development in school.