The objective of this thesis was to investigate pre-service teachers and student misconceptions of the equal sign, and then offer suggestions to pre-service teachers, teachers, university programs, and schools to prevent common misconceptions from occurring in classrooms. Some students do not realize the equal sign can have two different functions, operational and relational. There are several different reasons for this misconception, beginning with the lack of defining what the equal sign is and what it means in the classroom.
In the first study, eighteen participants were interviewed to explain their responses when evaluating student work to gain an in-depth knowledge of pre-service teachers' perceptions of the equal sign and their ability to evaluate a students' response to a specific math task. Results showed that pre-service teachers have a better understanding of the equal sign and may be ready to teach the equal sign as a relationship between numbers. Furthermore, pre-service teachers would benefit greatly from evaluating students' work and looking for common misperceptions that students may have.
In the second study, six fifth grade classes were studied to determine if there was a positive relationship for teaching atypical type equivalence statements to students and performing better on equivalence questions. Three classes from Spring 2011, were administered a test; two of the test items were used to analyze their understanding of the equal sign. In Fall 2011, another three fifth grade classes participated in lessons, which required students to analyze atypical type equivalence statements, and then they were given the same two test items. Results from this study supported the use of atypical type equivalence statements because more students in the experimental group correctly responded to the two items and were also able to justify their responses with work that exemplified good understanding of the equal sign as being a relationship.
Both of these studies support increasing student and pre-service teachers understanding of the equal sign and the misconceptions students have regarding the equal sign. University programs and schools should utilize these results to require preservice teachers and teachers to evaluate student work to identify common misconceptions and teach the equal sign as a relationship between both sides and not as an operation.
