Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning
Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning
复制标题
中学代数：通过定量推理发展函数关系
DOI：
10.1007/978-3-642-17735-4_13
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Amy B. Ellis
中科院分区：
文献类型：
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作者：
Amy B. Ellis
理解函数是代数推理的一个重要方面，建立函数关系是低年级鼓励的一项活动，以培养学生的关系思维。培养功能性思维的一种方法是利用学生的能力来推理数量及其关系。本文阐述了直接用量进行推理的方法对中学生理解一次函数和二次函数的帮助。它探讨了如何建立定量关系，可以支持从协变的角度初步功能的理解，后来作为一个基础，建立一个更灵活的功能，包括对应的角度来看。
Understanding function is a critical aspect of algebraic reasoning, and building functional relationships is an activity encouraged in the younger grades to foster students’ relational thinking. One way to foster functional thinking is to leverage the power of students’ capabilities to reason with quantities and their relationships. This paper explicates the ways in which reasoning directly with quantities can support middle-school students’ understanding of linear and quadratic functions. It explores how building quantitative relationships can support an initial function understanding from a covariation perspective, and later serve as a foundation to build a more flexible view of function that includes the correspondence perspective.