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The Genesis of a Theorem 一个定理的起源
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.lmmv7107
O. Marrero
{"title":"The Genesis of a Theorem","authors":"O. Marrero","doi":"10.5642/jhummath.lmmv7107","DOIUrl":"https://doi.org/10.5642/jhummath.lmmv7107","url":null,"abstract":"Synopsis We present the story of a theorem’s conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question’s origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it includes some preliminary work that facilitates the proof; therefore, the theorem can also serve as a nice exercise in induction. Additionally, we use well-known facts from calculus to clarify and enhance what is intrinsically a discrete problem. Making an unexpected but welcome explanatory appearance, the number e is pertinent.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46836193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes 空间坍塌，地点碰撞:利用人文地理学建构探索数学课堂
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.lmpq5945
Valentin A. B. Küchle, Shiv Karunakaran, Mariana Levin, John J. Smith III, Sarah D. Castle, Jihye Hwang, Yaomingxin Lu, R. Elmore
{"title":"Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes","authors":"Valentin A. B. Küchle, Shiv Karunakaran, Mariana Levin, John J. Smith III, Sarah D. Castle, Jihye Hwang, Yaomingxin Lu, R. Elmore","doi":"10.5642/jhummath.lmpq5945","DOIUrl":"https://doi.org/10.5642/jhummath.lmpq5945","url":null,"abstract":"Humanistic geographers distinguish between space and place: \"What begins as undifferentiated space becomes place as we get to know it better and endow it with value\" [19, page 6]. In this essay, we seek to demonstrate how mathematics education researchers and mathematics instructors may find space and place il-luminating for understanding important aspects of students' learning experiences during the coronavirus pandemic - and possibly beyond. Specifically, after in-tro ducing the terms and relating them to the context of a university mathematics class, we exemplify how home and class places collided for three undergraduate mathematics students forced to deal with the abrupt transition to online educa-tion. We conclude by discussing implications of attending to space and place for designers and researchers of (pandemic) online instruction and make connections to how the pandemic and attending to space and place can serve as a catalyst for reshaping undergraduate mathematics education.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70801391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Book Review: Algebra the Beautiful: An Ode to Math’s Least-Loved Subject by G. Arnell Williams 书评:《美丽的代数:对数学最不受欢迎的学科的颂歌》，作者:G.阿内尔·威廉姆斯
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.bffk4651
J. Grabiner
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引用次数: 0
The Babelogic of Mathematics 数学的逻辑
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.bgui1643
Vijay Fafat
{"title":"The Babelogic of Mathematics","authors":"Vijay Fafat","doi":"10.5642/jhummath.bgui1643","DOIUrl":"https://doi.org/10.5642/jhummath.bgui1643","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Nothing That Really Matters 什么都不重要
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.podj4118
Szilárd Svitek
{"title":"The Nothing That Really Matters","authors":"Szilárd Svitek","doi":"10.5642/jhummath.podj4118","DOIUrl":"https://doi.org/10.5642/jhummath.podj4118","url":null,"abstract":"Synopsis Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, for natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state of balance between positive and negative assets was also given. We now take them for granted, but the history of science shows that it was far from a smooth process, and interesting mistakes about zero still occur in education today. I present a few examples below, and how they have been resolved.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70801394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Where Does Mathematics Come From? Really, Where? 数学从何而来？真的，在哪里？
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2023-01-01 DOI: 10.5642/jhummath.xjfo9325
M. Huber, Gizem Karaali
{"title":"Where Does Mathematics Come From? Really, Where?","authors":"M. Huber, Gizem Karaali","doi":"10.5642/jhummath.xjfo9325","DOIUrl":"https://doi.org/10.5642/jhummath.xjfo9325","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46312549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Foundational Mathematical Beliefs and Ethics in Mathematical Practice and Education 数学实践与教育中的基础数学信仰与伦理
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2022-07-01 DOI: 10.5642/jhummath.gosn2205
Richard Spindler
{"title":"Foundational Mathematical Beliefs and Ethics in Mathematical Practice and Education","authors":"Richard Spindler","doi":"10.5642/jhummath.gosn2205","DOIUrl":"https://doi.org/10.5642/jhummath.gosn2205","url":null,"abstract":"Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based founda-tion for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the practice and education of mathematics in the mathematical community. This is compared to the potential of a belief in evidence-based mathematical foundations on mathematical practice and education.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematics Education as Dystopia: A Future Beyond 作为反乌托邦的数学教育：超越的未来
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2022-07-01 DOI: 10.5642/jhummath.sqek5024
Peter Appelbaum, C. Stathopoulou, Constantinos Xenofontos
{"title":"Mathematics Education as Dystopia: A Future Beyond","authors":"Peter Appelbaum, C. Stathopoulou, Constantinos Xenofontos","doi":"10.5642/jhummath.sqek5024","DOIUrl":"https://doi.org/10.5642/jhummath.sqek5024","url":null,"abstract":"Synopsis We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempower-ment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in society. Embracing dystopia rather than trying to circumvent it generates new questions and pathways.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48384118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Doughnut at the End of Space 太空尽头的甜甜圈
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2022-07-01 DOI: 10.5642/jhummath.gasu8191
Deborah Coy
{"title":"Doughnut at the End of Space","authors":"Deborah Coy","doi":"10.5642/jhummath.gasu8191","DOIUrl":"https://doi.org/10.5642/jhummath.gasu8191","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45470078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Circular Meditations 圆形的冥想
IF 0.3
Journal of Humanistic Mathematics Pub Date : 2022-07-01 DOI: 10.5642/jhummath.djaw4668
Kevin Farey
{"title":"Circular Meditations","authors":"Kevin Farey","doi":"10.5642/jhummath.djaw4668","DOIUrl":"https://doi.org/10.5642/jhummath.djaw4668","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47381353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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