Publication Date


Date of Final Oral Examination (Defense)


Type of Culminating Activity

Dissertation - Boise State University Access Only

Degree Title

Doctor of Education in Curriculum and Instruction


Educational Technology

Major Advisor

Young Kyun Baek, Ph.D.


In this study, an instructional mobile game was developed that focused on addition and subtraction for elementary students, and the Flow theory was used as a guide for the engagement aspect of the game design. The game aimed to engage students in learning as well as increase their mathematics achievement. This study conducted a two-group pre- and post-test comparison study and explored the effects of the designed game on mathematics achievement and engagement of 3rd grade students with different initial mathematics levels. A sample of 59 students participated in this study and played the mobile game for three weeks. Their performance on pre- and post-tests of mathematics, responses to an engagement scale, and reflections on the game play process were analyzed to compare the differences between mathematics initial high- and low-achieving groups.

The mathematics scores of all participants increased in both computational fluency and number relationship understanding. The t-tests showed there was no significant difference between the two groups’ gain scores on the computational fluency tests. However, the low-achieving group increased their number relationship understanding scores more rapidly than the high-achieving group. The results indicated that both groups had a parallel increase in their computational fluency skills, while the gap between their number relationship understandings was reduced after the gameplay activity. The low-achieving group benefited more from the study in the mathematics conceptual understandings within addition and subtraction.

Both groups reported a high level of engagement in their game playing, and showed a similar pattern in the responses on the nine elements of Flow theory. Both groups were significantly more engaged in six of the elements of the flow state: clear goals, sense of control, challenge, concentration, autotelic experience, and unambiguous feedback. However, the engagement level was lower in other three elements: action-awareness, loss of self-consciousness, and transformation of time. There was no significant relation between students’ engagement and their achievement.

This study provided implications and suggestions for designing engaging instructional games. The study suggested that flow theory and its nine elements provided a guideline for designing an engaging learning environment. The study indicated the design of instructional games should implement elements for the design of physical game characteristics and create conditions for elaborating psychological involvement to optimize engagement for learning, and move students closer to the flow state.