Date of Graduation


Document Type


Degree Name

Doctor of Education (Ed.D.)


Learning and Instruction

First Advisor

Mathew Mitchell

Second Advisor

Gini Shimabukuro

Third Advisor

Xornam Apedoe


Many students struggle to learn mathematics in K-8 grades. Research has shown that lower grade students often misconceive equivalence as an operation rather than a relation, and that students also form various misconceptions of literal symbols. Many students arrive at college seriously underprepared in mathematics, but there is scant research on the difficulties and misconceptions of these college students. The purpose of this research was to learn if underprepared community college students harbor misconceptions of equivalence and of literal symbols similar to K-8 students.

For this study, 191 underprepared college students were surveyed for misconceptions by a questionnaire of 43 items selected from the established suite of effective items. The items for each concept were further partitioned into the definition, properties, and applications of each concept.

Many students (84%) were expert regarding the definition of equivalence. An additional 13% of the students also demonstrated knowledge of the concept, although they did not always take advantage of it. Similarly, over 40% of the students demonstrated expert understanding of the properties of equivalence, but an additional 53% demonstrated a restricted understanding of the concept. Only 5% of the students were considered expert with the fundamental applications of equivalence and less than 60% demonstrated a basic knowledge of the applications.

Few students (33%) were knowledgeable of the definition of literal symbols, and fewer (< 5%) demonstrated knowledge of the properties of the literal symbol. Consequent to their minimal knowledge of the concept, very few students were able to demonstrate knowledge of literal symbol applications.

Community college students underprepared in mathematics are generally aware of the relational definition of equivalence, but many are not fluent in its use. Most attention needs to be directed to the applications of equivalence. The same students are generally not aware of the concept of literal symbols and much attention needs to be directed not only at the applications of literal symbols, but also at their definition and properties.