{"title":"奠定基础:构建商群的基础隐喻","authors":"Holly Zolt , Kathleen Melhuish","doi":"10.1016/j.jmathb.2025.101294","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":"81 ","pages":"Article 101294"},"PeriodicalIF":1.7000,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Laying the groundwork: The grounding metaphors that build quotient groups\",\"authors\":\"Holly Zolt , Kathleen Melhuish\",\"doi\":\"10.1016/j.jmathb.2025.101294\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":47481,\"journal\":{\"name\":\"Journal of Mathematical Behavior\",\"volume\":\"81 \",\"pages\":\"Article 101294\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Behavior\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0732312325000586\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"EDUCATION & EDUCATIONAL RESEARCH\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Behavior","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0732312325000586","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
Laying the groundwork: The grounding metaphors that build quotient groups
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.
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.