ϵ -Approximate Coded Matrix Multiplication Is Nearly Twice as Efficient as Exact Multiplication

Jeong, Haewon; Devulapalli, Ateet; Cadambe, Viveck R.; Calmon, Flavio P.

doi:10.1109/JSAIT.2021.3099811

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can per-form a true multiplication operation, ﬂexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruc-tion. We presented 5- to 8-year-olds with nonsymbolic multipli-cands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a vis-ible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multipli-cation, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between chil-dren’s Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children’s emerging symbolic math competence. These ﬁndings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

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