摘要：This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by collecting data through documentation, interviews, and classroom observations. The HLT was implemented in the classroom to investigate students’ actual learning trajectory. The results of this research indicate that the games helped students understand the concept of probability. The learning trajectory for probability based on game-based learning is seen from the perspective of four levels of emergent modeling. In the first level – ‘situational level’ – Sudoku and Ladder-and-Snake games were played by students. The second level is the ‘referential level’ where the rules of the games were used as a starting point to learn the concept of probability. Communication during game playing stimulated students' knowledge about random events, sample spaces, sample points, and events. At the third level – ‘general level’ – students used tree and table diagrams to generalize possible outcomes of an experiment and develop an understanding of sample spaces and sample points. Lastly, at the ‘formal level’ students developed their informal knowledge into formal concepts of probabilities .
关键词：design research;four levels of modelling;game-based learning;learning trajectory;probability
