{"title":"\"定理说......\":工科学生理解常微分方程解的意义","authors":"Paul Hernandez-Martinez , Svitlana Rogovchenko , Yuriy Rogovchenko , Stephanie Treffert-Thomas","doi":"10.1016/j.jmathb.2023.101116","DOIUrl":null,"url":null,"abstract":"<div><p>There is a need for further studies on students’ learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students’ demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students’ interpretation of theorems and their use as tools in argumentation and problem-solving. This paper takes a sociocultural stance on learning and employs <em>dialogical inquiry</em> – a methodology rooted in Bakhtinian theory, newly developed for collaborative inquiry and qualitative data analysis – to investigate the meanings that senior engineering students made while working on a task designed to evaluate their understanding of Existence and Uniqueness Theorems (EUTs) of solutions of DEs. We identified two important epistemological disconnections that explain the difficulties that some of our students faced in making meaning of solutions of DEs and the EUT.</p></div>","PeriodicalId":47481,"journal":{"name":"Journal of Mathematical Behavior","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S073231232300086X/pdfft?md5=f75789b683634c34ebd322e8c2d186ad&pid=1-s2.0-S073231232300086X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"“The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations\",\"authors\":\"Paul Hernandez-Martinez , Svitlana Rogovchenko , Yuriy Rogovchenko , Stephanie Treffert-Thomas\",\"doi\":\"10.1016/j.jmathb.2023.101116\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>There is a need for further studies on students’ learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students’ demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students’ interpretation of theorems and their use as tools in argumentation and problem-solving. This paper takes a sociocultural stance on learning and employs <em>dialogical inquiry</em> – a methodology rooted in Bakhtinian theory, newly developed for collaborative inquiry and qualitative data analysis – to investigate the meanings that senior engineering students made while working on a task designed to evaluate their understanding of Existence and Uniqueness Theorems (EUTs) of solutions of DEs. We identified two important epistemological disconnections that explain the difficulties that some of our students faced in making meaning of solutions of DEs and the EUT.</p></div>\",\"PeriodicalId\":47481,\"journal\":{\"name\":\"Journal of Mathematical Behavior\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S073231232300086X/pdfft?md5=f75789b683634c34ebd322e8c2d186ad&pid=1-s2.0-S073231232300086X-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/S073231232300086X\",\"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/S073231232300086X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
“The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations
There is a need for further studies on students’ learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students’ demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students’ interpretation of theorems and their use as tools in argumentation and problem-solving. This paper takes a sociocultural stance on learning and employs dialogical inquiry – a methodology rooted in Bakhtinian theory, newly developed for collaborative inquiry and qualitative data analysis – to investigate the meanings that senior engineering students made while working on a task designed to evaluate their understanding of Existence and Uniqueness Theorems (EUTs) of solutions of DEs. We identified two important epistemological disconnections that explain the difficulties that some of our students faced in making meaning of solutions of DEs and the EUT.
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.