Logical thinking and reasoning of geometric space are among the key abilities of science and technology education. This research developed a framework of an alternate reality-based board game incorporating augmented reality (AR) exploration with multi-dimensional scaffolding, including "cognitive scaffolding," "metacognitive scaffolding," and "peer scaffolding." Features included alternate reality games, board games, and AR technology. An educational alternate reality game "Lost in Space" based on the above framework was developed, and scaffolding was designed to help players focus on spatial and logical thinking. Participants were 127 tenth-grade students from northern Taiwan. Empirical analysis was conducted with the aim of exploring the learners' learning outcomes, flow state, and perceptions of the multi-dimensional scaffolding as well as its usefulness. The results showed that there was no significant difference between the learning achievement of the students in the experimental group (using game learning) and the control group (using general teaching materials). However, students in the experimental group showed significant improvement in learning achievement after the game, while students in the control group showed no significant improvement in learning achievement. Moreover, experimental group learners could sense most of the cognitive scaffolding, metacognitive scaffolding, and peer scaffolding.