Examining the task and knowledge demands needed to teach with representations
Examining the task and knowledge demands needed to teach with representations
复制标题
检查表征教学所需的任务和知识需求
DOI：
10.1007/s10857-013-9253-4
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发表时间：
2014
影响因子：
2.1
通讯作者：
H. Hill
中科院分区：
文献类型：
--
作者：
R. Mitchell;Charalambos Y. Charalambous;H. Hill
表征通常用于教学，以突出关键的数学思想和支持学生的学习。尽管他们在脚手架教学和学习的中心，我们的理解与使用表征在教学中的任务和知识要求强加给教师时，使用这些辅助工具是理论上的。本文通过教学实践，探讨了带表示的整数运算教学的任务和知识需求。教学整数运算被用作强度的情况下，整数运算是具有挑战性的学生，教师往往需要采用几种表示来教这个话题。遵循以实践为基础的方法，同时也考虑到以前的文献，我们首先生成一个列表的任务，在教学中所涉及的表示，然后讨论的知识要求强加给教师，以成功地开展这项工作。我们强调这些任务和知识的需求，通过分析和讨论一个整数加法和一个整数减法插曲，每两个老师，博妮塔和凯伦。基于我们的分析，我们组织生成的知识组件使用的数学知识教学框架。最后，我们绘制教师教育和课程开发的影响。
Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is theoretical. In this study, we examine the task and knowledge demands for teaching integer operations with representations by analyzing teaching practice. Teaching integer operations is used as an intensity case, as integer operations are challenging for students, and teachers are often required to employ several representations to teach this topic. Following a practice-based approach while also taking prior literature into consideration, we first generate a list of tasks entailed in teaching with representations and then discuss the knowledge demands imposed on teachers to successfully undertake this work. We highlight these tasks and knowledge demands by analyzing and discussing an integer addition and an integer subtraction episode for each of two teachers, Bonita and Karen. Based on our analysis, we organize the generated knowledge components using the Mathematical Knowledge for Teaching framework. We conclude by drawing implications for teacher educators and curriculum developers.