The students' learning values mainly comes from the experiences when participating in activities, such as engagements in hands-on related competition. Based on the Expected Value Theory, the study explored how students gain learning value from participating in the PowerTech, a competition of STEAM (Science, Technology, Engineering, Art, and Mathematics). Therefore, research model was constructed to analyze the relationship between self-efficacy, three types of competition inputs (intellectual input, emotional input, behavioral input) and learning value. This study invited primary and middle school students who participated in the PowerTech competition to fill out the questionnaire. A total of 488 questionnaires were collected, after removing invalid responses, a total of 456 surveys was analyzed by using structural equation modeling. The results indicated that hands-on self-efficacy is positively related to the engagement of cognition, emotion, and behavior; and three types of competitive engagement show a positive correlation to learning values after participation.