# Targeted Mathematical Equivalence Training Lessens the Effects of Early Misconceptions on Equation Encoding and Solving

- Kristen Johannes, WestEd, Alameda, California, United States
- Jodi Davenport, WestEd, Alameda, California, United States

**Abstract**Many students fail to develop adequate understanding of mathematical equivalence in early grades, with detrimental consequences for later algebra learning. The change resistance account (McNeil, 2014) proposes that students struggle with equivalence because traditional arithmetic practice overexposes students to mathematical expressions where all the operators are on the left of the equal sign. Students erroneously believe the equal sign means to “do something” or “give the answer” – and fail to see equations as relations between two expressions. These operations-based misconceptions affect how they perceive, conceptualize, and approach math problems and interfere with developing correct understandings of equivalence. The current paper explores 1) are these misconceptions evident as encoding errors in second graders? 2) do item properties make specific error types more or less likely? 3) do misconceptions in encoding impact solving performance? and 4) can targeted training mitigate the effects of prior misconceptions on both equation encoding and solving? We identify a category of misconception-based encoding errors that negatively impacts equation solving and replicate findings that a conceptually rich research-based intervention program is maximally effective in training students to overcome problematic misconceptions.