Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Cooperating University

University of Louisville


Early Childhood and Elementary Education

Degree Program

Curriculum and Instruction, PhD

Committee Chair

Karp, Karen

Committee Member

Bay-Williams, Jennifer

Committee Member

Brown, Elizabetht Todd

Committee Member

McGatha, Maggie

Committee Member

Ronau, Robert

Author's Keywords

equal sign understanding; misconception; mathematics; elementary mathematics; student understanding


The purpose of this study was to investigate the impact of two different policies for implementing new mathematics standards in two schools, for grades two through five, on student understanding of the equal sign. The study also examined teachers’ knowledge of the equal sign. The research used a mixed methods design to explore differences in student understanding of the equal sign as a result of how standards were implemented in two adjoining states with two different decisions as to when the standards would be implemented. This dissertation shares research that may be of interest to teachers, administrators, teacher educators and other stakeholders. The main constructs under investigation were student understanding of the equal sign, teacher knowledge regarding the equal sign including how it is taught and assessed, and the impact of different implementation schedules for new mathematics standards on student performance on their knowledge of the meaning of the equal sign - a standard that was not previously explicit in either state. The study was conducted in two adjoining Midwestern states in three separate schools (fifth grade students from one of the states are housed in a middle school building for overcrowding reasons and are equivalent to fifth grade students in an elementary setting). Each school as per their state mandates, followed the timeline for new mathematics standards implementation with one school in the fourth year of implementation and the other two (same district) in their first year. The sample was 1,182 students in second, third, fourth and fifth grade and their forty-two classroom teachers. Students and teachers from the three schools were given the Mathematical Equivalence Knowledge Assessment (MEKA) as a measurement of teacher knowledge and student understanding of the equal sign. Data from teacher interviews and surveys were used to complement findings related to their students’ understanding of the equal sign and their classroom practices related to this topic. A hierarchical linear model was used to detect differences between student scores on the MEKA in each school in the two states. To determine the impact of teacher knowledge of the equal sign on student understanding of the equal sign an unconditional hierarchical linear model and a follow up ANCOVA were conducted using the MEKA results from both teacher and student participants. The same model was also used to detect significant differences found between student scores on the MEKA in one state and student scores on the MEKA from another state where each state followed a different timeline for new standard implementation. Findings from the study reveal that the different timeline for the implementation of the mathematics standards in the two states appears to have an impact on students’ understanding of the equal sign and indicated that teacher knowledge was not a significant predictor of student understanding of the equal sign. However, the results also show that state implementation timeline and a students’ grade level were significant predictors of student understanding of the equal sign. Through the interviews teachers were also found to have difficulty predicting their students’ performance on the MEKA, had varying definitions of the meaning of the equal sign, and many suggested that they did not explicitly teach or assess the meaning of the equal sign.