A comparative study of pre-service teachers' understandings of the equal sign
This multipart study looked at pre-service teachers' (PSTs') understandings of the equal sign using an experimental measure, the EQ score. The data were analyzed for PSTs as a group and cross-sectionally at three key points during their elementary teacher education program. Relationships between equal sign understandings and other variables (e.g., endorsement, teaching mathematics confidence ranking, Mathematical Knowledge for Teaching (MKT) scores) were explored. Results indicate that most PSTs vary in their understanding of the equal sign with very few consistently exhibiting a fully relational view of the symbol. PSTs struggled to define the equal sign in a relational manner although this did not necessarily hinder successful task completion. PSTs struggled with "strings" (primarily in the true-false format) indicating that PSTs may have an "answer goes next" (operational) understanding of the equal sign when evaluating other people's work but may have some form of relational understanding when the task is in a solving format.
Inferential statistics suggest that there were significant difference between PSTs' understandings of the equal sign based on: (1) mathematical background, (2) pursuing a mathematics endorsement, and (3) confidence to teach mathematics. There also were significant results between PSTs' EQ scores and their MKT scores, even when controlling for the opposite measure and the influence of their confidence to teach mathematics. PSTs beginning their second mathematics content course outperformed their peers enrolled in their first mathematics content course or methods course. Pre- and post-test analysis does support that completing a mathematics methods course (based on CGI principles of understanding students' thinking) did improve PSTs' understanding of the equal sign. There was no statistical evidence to suggest a relationship between gender and EQ scores.