Date of Award

Fall 12-21-2018

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Middle and Secondary Education

First Advisor

Iman Chahine

Second Advisor

Joseph Feinberg

Third Advisor

Mandy Swygart-Hobaugh

Fourth Advisor

Ying Zhu


This study examined the effects of a researcher-designed digital game-based learning (DGBL) environment called Adventures of Krystal Kingdom on undergraduate students’ mathematics achievement and motivation in a Multivariable Calculus course. Multivariable Calculus is a specific area of computational and applied mathematics that focuses on the differentiation and integration of functions of several variables in fields like physics and engineering. The study employed a single exploratory embedded case study design with quantitative and qualitative techniques. A case study is the appropriate methodology for this study, which is a bounded system that facilitates a deeply contextualized understanding of a case through giving descriptions, analyses, and interpretations (Yin, 2014). The quantitative sample comprised 29 undergraduate students, and the qualitative sample included 6 students selected through stratified sampling based on the level of achievement. Quantitative data was collected using two surveys: demographic and motivation surveys, and two tests: academic achievement test and a game performance test. Analysis of quantitative data used a paired sample t-test. Qualitative data were collected from interviews, observations, and artifacts. Analysis of qualitative data used coding procedures suggested by Creswell (2014) where patterns were identified and grouped to allow the emergence of themes. The results of the study indicated no statistical significance in achievement (p=0.88 >0.05), however, there was overall improvement found in achievement scores of the students who played the game. Three themes emerged from the study: 1) Undergraduate students saw the use of the Adventures of Krystal Kingdom as learning tool to enhance their understanding of concepts in Multivariable Calculus.; 2) Undergraduate students saw the use of the Adventures of Krystal Kingdom as a way to engage themselves in mathematical fun in a digital environment; and 3) Undergraduate students saw input semiotics, automated reflexes, Task Relevant Support and other core mechanics as components that affect students’ gameplay. Results of the interviews, observations, and artifacts revealed that students benefited from using DGBL as an alternative approach to learning mathematics and to use such advanced techniques in biology, engineering, and computational neuroscience. The overall results indicate that DGBL used in the study was an appropriate teaching and learning tool to improve students' mathematics skills.