Date of Award

Spring 2023

Project Type


Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Karen J. Graham

Second Advisor

Karen J Graham

Third Advisor

Sharon McCrone


Mathematical notations not only contribute to but also confound the development of the understanding of mathematical concepts (Leinhardt, Zaslavsky & Stein,1990). Inaccurate use of calculus notations is likely to have a significant influence on student conceptual understanding and student assessment scores in the Calculus 1 course. This dissertation study aimed to examine whether or not the relationship between student’s ability to correctly write signs/symbols, interpret signs/symbols and interpret concepts using signs/symbols (students’ use of signs/symbols) and student assessment scores is statistically significant. The relationship between students’ use of sign/symbol and students’ grade performance was also examined under the effects of students’ background and attitudes toward using mathematical notations. Statistical models including paired-t test, profiles analysis, one-way multivariate analysis of variance (MANOVA), one way analysis of variance (ANOVA), restricted maximum likelihood (REML), and cumulative logit test were utilized to address the research questions. All methods were implemented in R software. Analyses employed data collected from 162 students who took the Calculus 1 course in the Fall 2022 semester at UNH. Results indicate that in addition to student prior knowledge, signs/symbols use and ordered assessments are significantly related to student grade performance. Furthermore, depending on the students’ major, the relationship between signs/symbols use and student grade performance can be significantly different. In addition, student confidence in using signs/symbols was also found to be positively correlated with signs/symbols use.