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首页> 外文期刊>Journal of Mathematics Teacher Education >Using three levels in design of effective teacher-education tasks: The case of promoting conflicts with intuitive understandings in probability
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Using three levels in design of effective teacher-education tasks: The case of promoting conflicts with intuitive understandings in probability

机译：在有效的教师教育任务的设计中使用三个层次：通过对概率的直觉理解来促进冲突的情况

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This paper describes a three-level framework (technical, domain, and generic) which enables some generalisability across mathematics topics for effective teacher–education (TE) task design. It argues that TE tasks which encompass these levels increase preservice and inservice teachers’ interest because they transcend the particular mathematical focus and pedagogical activity within the TE tasks and enable translation to classrooms (technical), enhance the success of student learning (domain), and facilitate transfer to other topics (generic). The paper then uses the levels to analyse an effective probability task (based on circular spinners) which involves cognitive conflict between formal and intuitive probability at all three levels, namely, with regard to facilitating non-random results (technical), differences between probabilistic and deterministic mathematics and area and set models (domain), and non-prototypic exemplars and validation in probability experiments (generic). The paper concludes with reference to the power of effective TE tasks in showing how connectivity of mathematics (e.g., fractions and probability) requires similar connectivity in pedagogy.
机译：本文描述了一个三级框架（技术，领域和通用），该框架为有效的师生（TE）任务设计提供了跨数学主题的某种通用性。它认为包含这些级别的TE任务增加了职前和在职教师的兴趣，因为它们超越了TE任务中特定的数学重点和教学活动，并能够翻译到课堂（技术），增强了学生学习的成功（领域），并且促进转移到其他主题（通用）。然后，本文使用这些层次来分析有效概率任务（基于循环微调器），该任务涉及所有三个层次上形式和直观概率之间的认知冲突，即在促进非随机结果（技术性），概率和概率之间的差异方面确定性数学，面积和集合模型（域），非原型示例和概率实验中的验证（通用）。本文以有效的TE任务的力量作为结论，以说明数学的连通性（例如分数和概率）如何在教学法中要求类似的连通性。

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