Revealing mental representations of arithmetic word problems through false memories: New insights into semantic congruence.

What can false memories tell us about the structure of mental representations of arithmetic word problems? The semantic congruence model describes the central role of world semantics in the encoding, recoding, and solving of these problems. We propose to use memory tasks to evaluate key predictions of the semantic congruence model regarding the representations constructed when solving arithmetic word problems. We designed isomorphic word problems differing only by the world semantics imbued in their problem statement.

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.

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

We argue that what we count has a crucial impact on how we count, to the extent that even adults may have difficulty using elementary mathematical notions in concrete situations. Specifically, we investigate how the use of certain types of quantities (durations, heights, number of floors) may emphasize the ordinality of the numbers featured in a problem, whereas other quantities (collections, weights, prices) may emphasize the cardinality of the depicted numerical situations. We suggest that this distinction leads to the construction of one of two possible encodings, either a cardinal or an ordinal representation.

When masters of abstraction run into a concrete wall: Experts failing arithmetic word problems.

Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical problems involving these entities? We argue that such daily-life knowledge interferes with arithmetic word problem solving, to the extent that experts can be led to failure in problems involving trivial mathematical notions. We created problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14 - 2 = 12.