Abstract Previous research has documented the importance of setting up productive norms in mathematics classrooms. Studies have also shown the potential for activities involving interactive simulations (sims) to support student engagement and learning. In this study, we investigated the relationship between norms and sim-based activities. In particular, we examined the social and sociomathematical norms in lessons taught with and without the use of PhET sims in the same teacher’s middle-school mathematics classroom. There were statistically significant differences in indicators of social norms between the two types of lessons. In sim lessons, the teacher more frequently took the role of a facilitator of mathematical ideas, and students exhibited conceptual agency more often than they did in non-sim lessons. On the other hand, there was substantial overlap: the teacher usually acted as an evaluator, and the students usually exhibited disciplinary agency in both types of lessons. However, there was a stark contrast in sociomathematical norms between the two types of lessons. Students’ specifically mathematical obligations in non-sim lessons consistently included practicing procedures in isolation and appealing to rules. Obligations in sim lessons included developing and sharing strategies, making conjectures and providing justifications. In both types of lessons, students were obligated to recall mathematical facts and vocabulary. Thus, the social norms were broadly consistent except for important differences in frequency, whereas we found substantial qualitative contrasts in the sociomathematical norms in the two types of lessons. This case provides evidence that contrasting norms can exist within the same classroom. We argue from our data that these differences may be mediated by curricular choices—in this case, the use of sims.

中文翻译：

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两组规范的故事：比较有和没有交互式模拟的数学课程中学生能动性的机会

摘要 先前的研究记录了在数学课堂中建立生产规范的重要性。研究还表明，涉及交互式模拟 (sims) 的活动具有支持学生参与和学习的潜力。在这项研究中，我们调查了规范与基于 sim 的活动之间的关系。特别是，我们检查了在同一位老师的中学数学课堂中使用和不使用 PhET 模拟教学的课程中的社会和社会数学规范。两类课程在社会规范指标上存在统计学显着差异。在模拟课程中，老师更频繁地扮演数学思想促进者的角色，学生比在非模拟课程中更频繁地表现出概念能动性。另一方面，存在大量重叠：教师通常充当评估者，而学生通常在两种类型的课程中都表现出纪律处分。然而，两种类型的课程在社会数学规范上存在鲜明对比。学生在非模拟课程中的特定数学义务始终包括孤立地练习程序和诉诸规则。模拟课程的义务包括制定和分享策略、做出猜想和提供理由。在这两种类型的课程中，学生都有义务回忆数学事实和词汇。因此，除了频率上的重要差异外，社会规范大体上是一致的，而我们发现两类课程中社会数学规范存在实质性的定性差异。这个案例提供了证据，证明在同一个教室中可以存在对比规范。我们根据我们的数据认为，这些差异可能是由课程选择所介导的——在这种情况下，是使用模拟人生。