Our objective in this research is to compare the usability of three distinct head gaze-based selection methods in an Augmented Reality (AR) hidden object game for children: voice recognition, gesture, and physical button (clicker). Prior work on AR applications in STEM education has focused on how it compares with non-AR methods rather than how children respond to different interaction modalities. We investigated the differences between voice, gesture, and clicker based interaction methods based on the metrics of input errors produced and elapsed time to complete the tutorial and game. We found significant differences in input errors between the voice and gesture conditions, and in elapsed tutorial time between the voice and clicker conditions. We hope to apply the results of our study to improve the interface for AR educational games aimed at children, which could pave the way for greater adoption of AR games in schools.