{"title":"学生在使用平方反比律矢量时容易犯的四个错误","authors":"Colin S Wallace, Liam Jones, Alex Lin","doi":"10.1088/1361-6404/ad2391","DOIUrl":null,"url":null,"abstract":"In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the <italic toggle=\"yes\">r</italic> (or <italic toggle=\"yes\">r</italic>\n<sup>2</sup>) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"68 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Four errors students make with inverse-square law vectors\",\"authors\":\"Colin S Wallace, Liam Jones, Alex Lin\",\"doi\":\"10.1088/1361-6404/ad2391\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the <italic toggle=\\\"yes\\\">r</italic> (or <italic toggle=\\\"yes\\\">r</italic>\\n<sup>2</sup>) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.\",\"PeriodicalId\":50480,\"journal\":{\"name\":\"European Journal of Physics\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6404/ad2391\",\"RegionNum\":4,\"RegionCategory\":\"教育学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"EDUCATION, SCIENTIFIC DISCIPLINES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6404/ad2391","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
Four errors students make with inverse-square law vectors
In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students (1) add vectors as if they were scalars, (2) project the r (or r2) in the denominator, instead of the entire vector, when attempting to find the vector’s components, (3) incorrectly apply the Pythagorean theorem when attempting to calculate the magnitude of the resultant vector, and (4) incorrectly relate the signs of the components of an electric field (or force) to the signs of the electric charges. While these are not the only errors students make, they are the most frequently occurring based on our analysis of 678 exams taken by students in either introductory mechanics or electricity and magnetism (E&M). We then show how these errors can be encoded into a new type of activity or assessment question which we call a ‘student error task.’ Introductory physics instructors can use the student error task in this paper as a way to engage or assess their students’ understandings of how to add two inverse-square law vectors.
期刊介绍:
European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education.
Authors submitting articles must indicate the usefulness of their material to physics education and make clear the level of readership (undergraduate or graduate) for which the article is intended. Submissions that omit this information or which, in the publisher''s opinion, do not contribute to the above mission will not be considered for publication.
To this end, we welcome articles that provide original insights and aim to enhance learning in one or more areas of physics. They should normally include at least one of the following:
Explanations of how contemporary research can inform the understanding of physics at university level: for example, a survey of a research field at a level accessible to students, explaining how it illustrates some general principles.
Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks.
Descriptions of novel laboratory exercises illustrating new techniques of general interest. Those based on relatively inexpensive equipment are especially welcome.
Articles of a scholarly or reflective nature that are aimed to be of interest to, and at a level appropriate for, physics students or recent graduates.
Descriptions of successful and original student projects, experimental, theoretical or computational.
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Reports of new developments in physics curricula and the techniques for teaching physics.
Physics Education Research reports: articles that provide original experimental and/or theoretical research contributions that directly relate to the teaching and learning of university-level physics.