未来教师对身份结构的统一理解

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH
Kaitlyn Stephens Serbin
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引用次数: 0

摘要

美国课程标准建议数学教师教学生注意结构并理解数学概念是如何关联的。这要求教师对跨越课程的数学结构有一个结构视角和连贯、统一的理解。本研究探讨了未来中学数学教师(PSMT)对同一性的统一理解,并表征了PSMT关注的同一性结构特征。我对他们在推理加性、乘性和组合身份之间的结构联系时所展示的身份模式的一致性水平进行了分类。我举例说明了对恒等式的统一、连贯的理解如何导致PSMT对逆函数和恒等式进行富有成效的推理,而对恒等式不连贯的理解可能导致对逆函数或恒等式进行不准确的推理。最后,我提出了对培养PSMT学生对代数概念的统一理解的教学启示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prospective teachers’ unified understandings of the structure of identities

United States curriculum standards advise mathematics teachers to teach students to attend to structure and understand how mathematical concepts are related. This requires teachers to have a structural perspective and a coherent, unified understanding of mathematical structures that span curricula. This study explores Prospective Secondary Mathematics Teachers’ (PSMTs) unified understandings of identities and characterizes the structural features of identities that PSMTs attend to. I contribute a theoretical framework of three ways in which PSMTs reason about identities: a do-nothing element, a result of undoing something, and a coordination with inverse, binary operation, and set. I classify the level of coherence of their identity schemas demonstrated as they reasoned about the structural connections among additive, multiplicative, and compositional identities. I illustrate how having unified, coherent understandings of identities can lead PSMTs to reason productively about inverse and identity functions, while having incoherent understandings of identities can lead to inaccurate reasoning about inverse and identity functions. I conclude with teaching implications for fostering PSMTs’ unified understandings of algebraic concepts.

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来源期刊
Journal of Mathematical Behavior
Journal of Mathematical Behavior EDUCATION & EDUCATIONAL RESEARCH-
CiteScore
2.70
自引率
17.60%
发文量
69
期刊介绍: The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics. We are interested especially in basic research, research that aims to clarify, in detail and depth, how mathematical ideas develop in learners. Over three decades, our experience confirms a founding premise of this journal: that mathematical thinking, hence mathematics learning as a social enterprise, is special. It is special because mathematics is special, both logically and psychologically. Logically, through the way that mathematical ideas and methods have been built, refined and organized for centuries across a range of cultures; and psychologically, through the variety of ways people today, in many walks of life, make sense of mathematics, develop it, make it their own.
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