Design knowledge scaffolds to facilitate students’ probabilistic thinking skills for solving classical probability problems: An exploratory study

Students encounter numerous difficulties in solving probability problems. Although there have been efforts to enhance students’ probabilistic thinking, most of these studies focused on extrinsic approaches such as contextual settings and visual representation aided by certain technologies. Few studies adopted an integrated perspective to design scaffolds from contextual, conceptual, and procedural dimensions and to examine their impact on students’ probabilistic thinking skills. This quasi-experimental study explored the effectiveness of integrated contextual-conceptual-procedural scaffolds of combinatorial knowledge to enhance middle school students’ performance in sample space and probability comparison tasks in compound experimental contexts. In this study, we divided four parallel seventh-grade classes from a school in Shanghai, China, involving 132 students into the experimental and control groups. Two classes in the experimental group received tailored instructional intervention, while two classes in the control group did not receive any additional intervention. The post-test revealed that the experimental group performed better than the control group on the sample space task. Still, the experimental group’s advantage on this task did not produce a chain effect. We propose three implications for improving textbook design and teaching practices by analyzing the potential reasons for the above findings.