在范启艾和费马的基础上构造曲线弧长积分

IF 0.6 Q3 MATHEMATICS

British Journal for the History of Mathematics Pub Date : 2023-01-02 DOI:10.1080/26375451.2023.2168880

Jesús Eduardo Hinojos-Ramos, Diana del Carmen Torres-Corrales, Alberto Camacho-Ríos

{"title":"在范启艾和费马的基础上构造曲线弧长积分","authors":"Jesús Eduardo Hinojos-Ramos, Diana del Carmen Torres-Corrales, Alberto Camacho-Ríos","doi":"10.1080/26375451.2023.2168880","DOIUrl":null,"url":null,"abstract":"We present the research outcomes of a project in Mathematics Education about the design and implementation of an instrument to learn the integral for the arc length of a function by using differential elements as the strategy for its construction. The research was done via a didactic intervention in a regular Integral Calculus course. The instrument was designed based on historical-epistemological analyses of the works of van Heuraet and Fermat. The main result of this research was that students achieve a more robust conceptualization of the integral for the arc length, supported by its construction with differential elements and its geometric foundation.","PeriodicalId":36683,"journal":{"name":"British Journal for the History of Mathematics","volume":"38 1","pages":"41 - 54"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The construction of the integral for the arc length of a curve based on van Heuraet and Fermat’s works\",\"authors\":\"Jesús Eduardo Hinojos-Ramos, Diana del Carmen Torres-Corrales, Alberto Camacho-Ríos\",\"doi\":\"10.1080/26375451.2023.2168880\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the research outcomes of a project in Mathematics Education about the design and implementation of an instrument to learn the integral for the arc length of a function by using differential elements as the strategy for its construction. The research was done via a didactic intervention in a regular Integral Calculus course. The instrument was designed based on historical-epistemological analyses of the works of van Heuraet and Fermat. The main result of this research was that students achieve a more robust conceptualization of the integral for the arc length, supported by its construction with differential elements and its geometric foundation.\",\"PeriodicalId\":36683,\"journal\":{\"name\":\"British Journal for the History of Mathematics\",\"volume\":\"38 1\",\"pages\":\"41 - 54\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"British Journal for the History of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/26375451.2023.2168880\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"British Journal for the History of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/26375451.2023.2168880","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们介绍了数学教育中一个项目的研究成果，该项目涉及一种工具的设计和实现，该工具通过使用微分元素作为构建函数弧长的策略来学习函数弧长积分。这项研究是通过对常规微积分课程的教学干预来完成的。该仪器是基于对范·豪雷特和费尔马特作品的历史认识论分析而设计的。这项研究的主要结果是，学生们在用微分元素构造积分及其几何基础的支持下，对弧长积分实现了更有力的概念化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The construction of the integral for the arc length of a curve based on van Heuraet and Fermat’s works

We present the research outcomes of a project in Mathematics Education about the design and implementation of an instrument to learn the integral for the arc length of a function by using differential elements as the strategy for its construction. The research was done via a didactic intervention in a regular Integral Calculus course. The instrument was designed based on historical-epistemological analyses of the works of van Heuraet and Fermat. The main result of this research was that students achieve a more robust conceptualization of the integral for the arc length, supported by its construction with differential elements and its geometric foundation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

British Journal for the History of Mathematics Arts and Humanities-History and Philosophy of Science

CiteScore

0.50

自引率

0.00%

发文量