Jesús Eduardo Hinojos-Ramos, Diana del Carmen Torres-Corrales, Alberto Camacho-Ríos
{"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}
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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.
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