Exploring a framework for classroom culture : A case study of the interaction patterns in mathematical whole-class discussions
Exploring a framework for classroom culture : A case study of the interaction patterns in mathematical whole-class discussions
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探索课堂文化的框架：数学全班讨论中互动模式的案例研究
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发表时间：
2015
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通讯作者：
Mariah Larsson
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作者：
Mariah Larsson
培养学生数学能力的有前途的教学方法包括通过解决问题来教授数学的方法。组织全班讨论学生的想法是通过解决问题进行教学的一个重要方面。在这个领域里有一个广泛的共识，那就是对于老师来说，既要建立在学生的想法上，又要强调关键的数学概念和关系，这是非常具有挑战性的。此外，在课堂上培养对学生参与很重要的辩论也是一个巨大的挑战。面对这些挑战，教师需要支持。本文的目的是描述数学教师在组织富有成效的解决问题的全班讨论时所面临的挑战和支持，这些讨论注重数学联系和论证。特别地，本文调查了Stein等人（2008）的模型如何具有五个实践-预测，监测，选择，排序和连接学生的解决方案-可以支持教师应对挑战，以及构成基于研究和广泛使用的模型的局限性。本论文以六篇论文为基础。论文基于三个干预研究和一个对数学教师的研究，该教师擅长进行解决问题的课堂讨论。所分析的数据包括观察到的全班讨论的视频记录以及教师访谈和教师会议的录音记录。本文认为，五种实践模式支持教师通过预见性实践进行课前准备。然而，该模型并未明确支持做出详细的预测，这对培养课堂上的论证既具有挑战性又很重要。此外，监测的实践支持教师使用各种学生的解决方案来突出关键的数学思想和联系。然而，在监控实践中不支持的具有挑战性的方面是，如何在学生的探索过程中与他们互动，以实际获得各种不同的解决方案作为论证的基础。选择和排序学生解决方案的挑战是为了建立联系，而不是为了论证。在前面的练习的帮助下，最后的连接练习可以促进数学联系。然而，缺乏对区分不同类型联系的支持，也缺乏对创造辩论课堂文化的支持。由于在学生中促进辩论是一个巨大的挑战，因此在整个模型中需要对此提供支持。最后，尽管有效地提出一个问题很重要，也很有挑战性，但模型并不支持。根据挑战和支持的结论，提出了五种实践模型的发展建议。本文有助于研究工具的理论发展，这些工具支持教师在协调富有成效的问题解决全班讨论的挑战中。
Promising teaching approaches for developing students’ mathematical competencies include the approach of teaching mathematics through problem solving. Orchestrating a whole-class discussion of students’ ideas is an important aspect of teaching through problem solving. There is a wide consensus within the field that it is very challenging for the teacher to conduct class discussions that both build on student ideas and highlight key mathematical ideas and relationships. Further, fostering argumentation in the class, which is important for students’ participation, is also a grand challenge. Teachers need support in these challenges. The aim of the thesis is to characterize challenges and support for mathematics teachers in orchestrating productive problem-solving whole-class discussions that focus on both mathematical connection-making and argumentation. In particular, it is investigated how Stein et al.’s (2008) model with five practices – anticipating, monitoring, selecting, sequencing and connecting student solutions – can support teachers to handle the challenges and what constitutes the limitations of the research-based and widely-used model. This thesis builds on six papers. The papers are based on three intervention studies and on one study of a mathematics teacher proficient in conducting problem-solving class discussions. Video recordings of observed whole-class discussions as well as audio-recorded teacher interviews and teacher meetings constitute the data that are analyzed. It is concluded in the thesis that the five practices model supports teachers’ preparation before the lesson by the practice of anticipating. However, making detailed anticipations, which is shown to be both challenging and important to foster argumentation in the class, is not explicitly supported by the model. Further, the practice of monitoring supports teachers in using the variety of student solutions to highlight key mathematical ideas and connections. Challenging aspects not supported by the monitoring practice are, however, how to interact with students during their exploration to actually get a variety of different solutions as a basis for argumentation. The challenge of selecting and sequencing student solutions is supported for the purpose of connection-making, but not for the purpose of argumentation. Making mathematical connections can be facilitated by the last practice of connecting, with the help of the previous practices. However, support for distinguishing between different kinds of connections is lacking, as well as support for creating an argumentative classroom culture. Since it is a great challenge to promote argumentation among students, support is needed for this throughout the model. Lastly, despite the importance and challenge of launching a problem productively, it is not supported by the model. Based on the conclusions on challenges and support, developments to the five practices model are suggested. The thesis contributes to research on the theoretical development of tools that support teachers in the challenges of orchestrating productive problem-solving whole-class discussions.