Abstract Findings discussed in this paper are from a larger research project exploring mathematical fluency characteristics, and teacher noticing and interpreting of mathematical fluency. The current study involved students from seven primary classes (Kindergarten – Grade 6, N = 63 students) and investigated students’ written work samples and oral discussions as they collaborated in small groups to solve mathematical tasks. Students displayed mathematical fluency both orally and in written/drawn form. Certain aspects of mathematical fluency were easier to identify orally (adaptive reasoning) particularly for younger students and when students did not provide any written reasoning. Analyzing the oral responses was often needed to identify mathematical fluency beyond knowledge of a correct procedure (strategic competence). Findings suggested that the various representations students used were valuable for observing mathematical fluency. These results suggest that oral assessments as a means to understand and interpret students’ mathematical fluency are necessary.

中文翻译：

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分析学生在小组任务中的交流和数学流畅性的表现

摘要 本文讨论的结果来自一个更大的研究项目，探索数学流畅性的特征，以及教师对数学流畅性的关注和解释。当前的研究涉及来自七个小学班级（幼儿园至 6 年级，N = 63 名学生）的学生，并调查了学生在小组合作解决数学任务时的书面作业样本和口头讨论。学生以口头和书面/绘画形式表现出数学流畅性。数学流畅性的某些方面更容易通过口头（自适应推理）识别，特别是对于年幼的学生以及当学生没有提供任何书面推理时。通常需要分析口头反应以识别超出正确程序知识（战略能力）的数学流畅性。结果表明，学生使用的各种表示法对于观察数学流畅性很有价值。这些结果表明，口头评估作为理解和解释学生数学流畅性的一种手段是必要的。