Pub Date : 2023-01-01DOI: 10.5642/jhummath.bzxw2115
Omid Khatin-Zadeh, Z. Eskandari, Danyal Farsani
When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely per-ceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and we may view it as a kind of mathematical metaphor, in the sense that a certain representation of a mathematical problem is described in terms of a visual representation of that problem. Furthermore, since a graphical representation is visual, it can be depicted by gestures. Therefore, visual and motor systems can be actively employed to process a given problem and find a solution for it. In this way, mathematical metaphor offers us a way to employ a wider range of cognitive resources to understand mathematics.
{"title":"The Roles of Mathematical Metaphors and Gestures in the Understanding of Abstract Mathematical Concepts","authors":"Omid Khatin-Zadeh, Z. Eskandari, Danyal Farsani","doi":"10.5642/jhummath.bzxw2115","DOIUrl":"https://doi.org/10.5642/jhummath.bzxw2115","url":null,"abstract":"When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely per-ceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and we may view it as a kind of mathematical metaphor, in the sense that a certain representation of a mathematical problem is described in terms of a visual representation of that problem. Furthermore, since a graphical representation is visual, it can be depicted by gestures. Therefore, visual and motor systems can be actively employed to process a given problem and find a solution for it. In this way, mathematical metaphor offers us a way to employ a wider range of cognitive resources to understand mathematics.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42079526","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.tjax3296
Marcio Luis Ferreira Nascimento
{"title":"Where Do Babies Come From?","authors":"Marcio Luis Ferreira Nascimento","doi":"10.5642/jhummath.tjax3296","DOIUrl":"https://doi.org/10.5642/jhummath.tjax3296","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44840311","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.vkes4181
Joel A. Doat
{"title":"Self-Reference and Diagonalisation","authors":"Joel A. Doat","doi":"10.5642/jhummath.vkes4181","DOIUrl":"https://doi.org/10.5642/jhummath.vkes4181","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42943712","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.ckuh2790
K. Hyun Lim, Anthony Matsuura
Synopsis Mathematics can be intellectually demanding, engaging, and fulfilling. Learning mathematical concepts adequately warrants an environment where students can err without penalty, shame, or hurtful consequences. Teaching mathematics efficaciously depends on the trusting relationship between the teacher and the students. We advocate blending mathematics teaching with kindness because it benefits the teacher, the students, and society. Kindness, niceness, caring, and benevolence are interrelated but not synonymous. We outline four progressive levels of kindness: conditional, superficial, optimal, and genuine. Blending mathematics teaching and kindness effectively requires the teacher to decenter from their own perspectives and adopt the student’s perspective as the student struggles through a challenging math problem. The efficacy of blending teaching and kindness depends on the teacher’s inner cultivation of benevolence. In one’s journey towards teaching with genuine kindness, one would need self-knowledge, unwavering commitment, continual practice, collegial support, spiritual guidance, and mindful awareness.
{"title":"Blending Mathematics Teaching with Kindness","authors":"K. Hyun Lim, Anthony Matsuura","doi":"10.5642/jhummath.ckuh2790","DOIUrl":"https://doi.org/10.5642/jhummath.ckuh2790","url":null,"abstract":"Synopsis Mathematics can be intellectually demanding, engaging, and fulfilling. Learning mathematical concepts adequately warrants an environment where students can err without penalty, shame, or hurtful consequences. Teaching mathematics efficaciously depends on the trusting relationship between the teacher and the students. We advocate blending mathematics teaching with kindness because it benefits the teacher, the students, and society. Kindness, niceness, caring, and benevolence are interrelated but not synonymous. We outline four progressive levels of kindness: conditional, superficial, optimal, and genuine. Blending mathematics teaching and kindness effectively requires the teacher to decenter from their own perspectives and adopt the student’s perspective as the student struggles through a challenging math problem. The efficacy of blending teaching and kindness depends on the teacher’s inner cultivation of benevolence. In one’s journey towards teaching with genuine kindness, one would need self-knowledge, unwavering commitment, continual practice, collegial support, spiritual guidance, and mindful awareness.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44302875","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.fhpm8098
Sarah Voss
Drawing from
从
{"title":"Mathaphor as a Literary Tool","authors":"Sarah Voss","doi":"10.5642/jhummath.fhpm8098","DOIUrl":"https://doi.org/10.5642/jhummath.fhpm8098","url":null,"abstract":"Drawing from","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46842694","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.ytct4418
Erin Griesenauer
{"title":"Lessons from Human Experience: Teaching a Humanities Course Made Me a Better Math Teacher","authors":"Erin Griesenauer","doi":"10.5642/jhummath.ytct4418","DOIUrl":"https://doi.org/10.5642/jhummath.ytct4418","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48961982","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}
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