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Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving

机译:教学教师的数学知识:数学教师教育者使用和开发的知识在学习通过问题解决方面教授

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摘要

In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures.
机译:在本研究中,我们报告了教师教师(MKTT)数学教师教育者(MTES)使用和发展的哪些类型的数学知识以及在帮助潜在的小学教师(PTS)产生的同时在练习社区中的教学中使用和发展他们通过问题解决学习数学教学的数学知识。两个新手MTES与经验丰富的MTE合作,反映了通过问题解决和支持PTS教学的学习过程,在发展基础数学思想的深刻理解中。在姿态征询询问时,我们通过问题解决来检查我们的经验教学数学内容课程的PTS。我们发现所有MKTE都使用并开发了一些MKTT,通过(a)了解并决定了各个课程的数学目标和整个两门序列的数学目标,(b)选择和促进任务,(c)利用问题到脚手架PTS学习,并在数学过程中与他们啮合,例如制作猜想,证明他们的推理,证明或劝阻猜想。

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