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

Benefits of “concreteness fading” for children's mathematics understanding

“…Children were given feedback about correctness after each problem, and they were included in the study if they solved all four problems incorrectly. Similar measures of math equivalence understanding have been used in many previous studies of children in this age range (e.g., Chesney et al, 2014;Cook, Mitchell, & Goldin-Meadow, 2008;Matthews & Rittle-Johnson, 2009;. One child had to be excluded due to experimenter error during instruction.…”

Activation of Operational Thinking During Arithmetic Practice Hinders Learning And Transfer

“…However, the command "If you see A × B, write C" does not. Indeed, recent research (Chesney et al, 2014) has demonstrated that children who have a better understanding of equivalence relations are also better able to make use of solving strategies that rely on these interrelations (e.g. decomposition strategies: 9 + 3 = 10 + 2 = 12).…”

“…Studies with children have indicated that arithmetic practice that highlights relational thinking about the equal sign helps children learn correct strategies for solving problems with operations on both sides of the equal sign (Chesney, McNeil, Petersen, & Dunwiddie, 2012;Chesney et al, 2014;McNeil et al, 2012;McNeil et al, 2011), and that arithmetic practice that activates operational ways of thinking hinders transfer of arithmetic knowledge . These findings are predicted by the change-resistance account and underscore that bidirectional relations are not necessarily implied when one interprets the symbol "=" operationally (e.g., if 2 × 2 = 4 means "when you see '2 × 2 =, ' you should write '4' at the end, " then it does not follow that when you see '4 =, ' you can write '2 × 2' at the end).…”

Consequences of Individual Differences in Children's Formal Understanding of Mathematical Equivalence

“…One may be tempted to trivialize the hypothesis that correct understanding of mathematical equivalence predicts future mathematics achievement, partly because it may be assumed that children who succeed on mathematical equivalence problems are just more intellectually advanced or better at mathematics overall. However, it is not that simple, given that there have not been consistent positive associations between understanding of mathematical equivalence and arithmetic calculation skill (e.g., Chesney et al., ; McNeil, ; McNeil et al., , ; Sherman & Bisanz, ). Children who improve their calculation skill after receiving extra practice with traditional arithmetic problems do not exhibit corresponding improvements in their understanding of mathematical equivalence (McNeil et al., , ).…”