Laying the groundwork: The grounding metaphors that build quotient groups

IF 1.7 Q3 EDUCATION & EDUCATIONAL RESEARCH
Holly Zolt , Kathleen Melhuish
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引用次数: 0

Abstract

Quotient groups are a foundational topic within abstract algebra courses, and they provide a context in which rich, powerful, and vivid language can be used to convey an understanding of the mathematics at play. We examined the language mathematicians used to describe their instruction on quotient groups and found that mathematicians draw on several source domains and use various metaphorical expressions when discussing their teaching practices. Of prominence in these findings was the use of a construction source domain which spanned all major aspects of quotient groups. The use of this source domain afforded the use of many metaphorical expressions that are tied to various formal content goals. We detail these findings and discuss how the metaphorical expressions used relate to the formal mathematics content that mathematicians are trying to convey.
奠定基础:构建商群的基础隐喻
商群是抽象代数课程中的一个基础主题,它们提供了一个背景,在这个背景中,可以使用丰富、强大和生动的语言来传达对数学的理解。我们检查了数学家用来描述他们对商群的教学的语言,发现数学家在讨论他们的教学实践时利用了几个源域并使用了各种隐喻表达。在这些发现中,突出的是使用了跨越商群所有主要方面的构造源域。这个源域的使用提供了许多与各种形式内容目标相关联的隐喻表达的使用。我们详细介绍了这些发现,并讨论了所使用的隐喻表达如何与数学家试图传达的形式数学内容相关联。
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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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