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首页> 外文期刊>Journal of mathematics teacher education >Examining the task and knowledge demands needed to teach with representations
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Examining the task and knowledge demands needed to teach with representations

机译：检查以表征进行教学所需的任务和知识需求

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摘要

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.
机译：表示法经常用于教学中，以突出关键的数学思想并支持学生学习。尽管它们在脚手架教学中处于中心地位，但我们对教学中使用表示形式所涉及的任务以及使用这些辅助工具时对教师的知识要求的大多数理解是理论上的。在这项研究中，我们通过分析教学实践，考察了使用表示法进行整数运算的任务和知识需求。由于整数运算对学生具有挑战性，因此教学整数运算被用作强度案例，并且经常需要教师采用几种表示形式来教授该主题。遵循基于实践的方法，同时也考虑了先前的文献，我们首先生成了用表示法进行教学所需要完成的任务清单，然后讨论了成功完成这项工作对教师的知识要求。通过分析和讨论Bonita和Karen的每位老师的整数加法和整数减法插值，我们强调了这些任务和知识需求。根据我们的分析，我们使用“教学数学知识”框架来组织生成的知识成分。最后，我们总结了对教师教育者和课程开发者的影响。

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