This study investigated novice mathematics teachers participating in an online teacher education course focused on covariational reasoning and understanding the behavior of functions. The analysis centered on documenting the emergence of participants’ sociomathematical norms for engaging in online asynchronous discussions. In this paper, we characterized participants’ initial mathematical discourse and documented two emergent sociomathematical norms, namely explaining why and emergent shape discourse. When participants explained why, they used specific quantities or symbolic representations of functions to justify why function graphs have particular visual features. When participants engaged in emergent shape discourse, they coordinated change between covarying quantities to justify why function graphs behave in certain ways. This study provides evidence that online settings can provide context for mathematics teachers engaging in legitimate collaborative mathematical activity and that activity can be enhanced by participation in discourse featuring specific sociomathematical norms. We discuss conjectures regarding the potential of reflective discussion activities paired with the Notice and Wonder Framework to support the emergence of generative sociomathematical norms. We also discuss potential relationships between characteristics of participants’ mathematical discourse and their membership with the core and periphery of a social network.

本研究调查了参加在线教师教育课程的新手数学教师，该课程侧重于协变推理和理解函数的行为。分析的重点是记录参与者参与在线异步讨论的社会数学规范的出现。在本文中，我们描述了参与者最初的数学话语，并记录了两个新兴的社会数学规范，即解释为什么和涌现的形状话语。当参与者解释为什么时，他们使用特定的数量或函数的符号表示来证明为什么函数图具有特定的视觉特征。当参与者参与紧急形状话语时，他们协调了共变量之间的变化，以证明为什么函数图以某些方式表现。这项研究提供的证据表明，在线设置可以为从事合法协作数学活动的数学教师提供背景，并且可以通过参与具有特定社会数学规范的话语来增强这种活动。我们讨论了关于反思性讨论活动与 Notice and Wonder Framework 相结合以支持生成社会数学规范出现的潜力的猜想。我们还讨论了参与者的数学话语特征与他们在社交网络核心和外围的成员身份之间的潜在关系。