{"title":"用变异原理连接操作选择问题:六年级学生的操作或更深的关系路径","authors":"Cristina Zorrilla , Anna-Katharina Roos , Ceneida Fernández , Salvador Llinares , Susanne Prediger","doi":"10.1016/j.jmathb.2023.101104","DOIUrl":null,"url":null,"abstract":"<div><p>Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and fractions/decimals, but so far, this approach was hardly investigated empirically. In this study, we investigate 17 sixth graders’ modelling pathways through sets of operation-choice problems that are systematically designed according to the variation principle. In the qualitative analysis, we identify five pathways by which students solve the problems and sometimes connect them. While one pathway uses deep relational connections, others only draw superficial and operational connections and others stay with informal strategies without connecting them to formal operations.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0732312323000743/pdfft?md5=8c124bd03ba8ef2782606b5062156520&pid=1-s2.0-S0732312323000743-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways\",\"authors\":\"Cristina Zorrilla , Anna-Katharina Roos , Ceneida Fernández , Salvador Llinares , Susanne Prediger\",\"doi\":\"10.1016/j.jmathb.2023.101104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and fractions/decimals, but so far, this approach was hardly investigated empirically. In this study, we investigate 17 sixth graders’ modelling pathways through sets of operation-choice problems that are systematically designed according to the variation principle. In the qualitative analysis, we identify five pathways by which students solve the problems and sometimes connect them. While one pathway uses deep relational connections, others only draw superficial and operational connections and others stay with informal strategies without connecting them to formal operations.</p></div>\",\"PeriodicalId\":47481,\"journal\":{\"name\":\"Journal of Mathematical Behavior\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0732312323000743/pdfft?md5=8c124bd03ba8ef2782606b5062156520&pid=1-s2.0-S0732312323000743-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Behavior\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0732312323000743\",\"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/S0732312323000743","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways
Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and fractions/decimals, but so far, this approach was hardly investigated empirically. In this study, we investigate 17 sixth graders’ modelling pathways through sets of operation-choice problems that are systematically designed according to the variation principle. In the qualitative analysis, we identify five pathways by which students solve the problems and sometimes connect them. While one pathway uses deep relational connections, others only draw superficial and operational connections and others stay with informal strategies without connecting them to formal operations.
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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