Organization matters: Mental organization of addition knowledge relates to understanding math equivalence in symbolic form

• Using decomposition to solve math facts correlates with accurate equation encoding.
• Using decomposition to solve math facts correlates with accurate equation solving.
• Skill at generating equal addend pairs correlates with accurate equation encoding.
• Skill at generating equal addend pairs correlates with accurate equation solving.
• Organization of addition knowledge affects understanding of equivalence.

Two quasi-experiments examined mental organization of addition knowledge as a potential source of individual differences in understanding math equivalence in symbolic form. We hypothesized that children who mentally organize addition knowledge around conceptually related groupings would have better understanding of math equivalence. In Quasi-experiment 1, we assessed 101 second and third grade students’ mental organization of addition knowledge based on their use of decomposition strategies to solve addition problems (e.g., 3 + 4 = 3 + 3 + 1 = 6 + 1 = 7). In Quasi-experiment 2, we assessed 94 second grade students’ mental organization based on their ability to generate a set of equations equal to a target value. In both quasi-experiments, children whose mental organization better reflected conceptually related groupings exhibited better understanding of math equivalence. Results thus support the hypothesis that mental organization of addition knowledge into conceptually related groupings based on equivalent values may influence understanding of math equivalence in symbolic form.