Understanding Students' Misconceptions in Combining Like Terms

Educators tend to diagnose a misconception by examining whether students choose a distractor option that reflects a common misconception. However, few studies examine the factor structure of a misconception and factors that might affect it. Using an empirical example of an algebra skill learning of combining like terms, this study showed how students’ misconceptions can be studied as latent traits using distractor options of concerned misconceptions as indicators. Results of model comparisons showed two sub-types of the misconceptions. While high achievers tended to have problems with those concerned misconceptions, students who read the textbook before the assessment were found less likely to make mistakes related to one sub-type of the misconception that requires relatively low cognitive load.