An investigation of algebra performance and conceptual knowledge of arithmetic in adults

Conceptual understanding of arithmetic is considered a key component for success in advanced mathematics topics such as algebra, but the link between them has rarely been investigated, particularly in adults. Participants solved conducive (3 × 26 ÷ 26) and nonconducive (26 × 3 ÷ 26) inversion problems, conducive (3 × 26 ÷ 13) and nonconducive (26 × 3 ÷ 13) associativity problems, and multiplication (3 × 6 × 12 = 3 × ?) and division (36 ÷ 8 ÷ 4 = 36 ÷ ?) equivalence problems and completed an algebra task. Conceptually based shortcut use on the nonconducive inversion problems was the strongest predictor of algebra scores. Participants who used conceptually based shortcuts on more problem types had higher algebra scores than participants who had low use of conceptually based shortcuts on most problem types. The results support the relationship between algebra and conceptual understanding of arithmetic and demonstrate that even in adulthood there are pronounced individual differences in conceptual understanding of arithmetic, which may impact success in advanced mathematics. (PsycInfo Database Record (c) 2025 APA, all rights reserved).