Algebraic reasoning in 3- to 5-year-olds


The current study asks when children begin to understand that when an object is added to a set, the numerosity of the set has increased regardless of set size. This knowledge can be expressed algebraically as ‘x + 1 > x’. In Experiment 1, 3- to 5-year-old children were asked to reason about transformations (i.e., addition, subtraction, rearrangement) performed on a visible set of objects. We found that 5-year-olds were able to reason about how each transformation affected numerosity, and 4-year-olds showed limited understanding. In Experiment 2, children were asked to reason about transformations performed on a hidden set of objects. Similar results were found. Together, we showed that the ability to reason about number algebraically develops gradually between the ages of 3 and 5. Implications for number word acquisition were discussed.

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