: The author modified a course entitled Applied Probability and Statistics to engage students in performing their own hypothesis tests in a course-based undergraduate research experience (CURE). This paper discusses the structure of the course, what it does to encourage undergraduate research, and changes one could make to tailor this experience to their own institutional needs.
{"title":"Undergraduate Research in an Applied Probability & Statistics Course","authors":"Michael Smith","doi":"10.54870/1551-3440.1579","DOIUrl":"https://doi.org/10.54870/1551-3440.1579","url":null,"abstract":": The author modified a course entitled Applied Probability and Statistics to engage students in performing their own hypothesis tests in a course-based undergraduate research experience (CURE). This paper discusses the structure of the course, what it does to encourage undergraduate research, and changes one could make to tailor this experience to their own institutional needs.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48998534","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}
Efforts to expand the science, technology, engineering and mathematics (STEM) workforce have been topics of United States policy action for more than 50 years (Hira 2010). Unfortunately, among U.S. undergraduate curricula, STEM has one of the highest attrition rates (Tinto 1993) with less than half of students in the U.S. that enroll in an undergraduate STEM program ultimately receiving a degree in a STEM field (Hayes 2009). Naturally, the high rate of attrition is a topic of persisting concern. Many programs have been designed and implemented to model best practices in retaining students in STEM disciplines. One retention strategy is to engage STEM undergraduates in research experiences, and a number of programs have been implemented to provide such experiences. The Towson University Research Enhancement Program (TU REP) is one such program. This cohort-based program supports faculty in the development of course-based undergraduate research experiences (CUREs). In this note we describe a CURE in machine learning offered by the Towson University Department of Mathematics whose development was supported by TU REP. We categorize this course along the spectrum of traditional, inquiry, CURE and internship in each of the five dimensions characteristic of a CURE.
{"title":"Experimental Mathematics – A Course-Based Research Experience in Machine Learning","authors":"Mathew Gluck","doi":"10.54870/1551-3440.1580","DOIUrl":"https://doi.org/10.54870/1551-3440.1580","url":null,"abstract":"Efforts to expand the science, technology, engineering and mathematics (STEM) workforce have been topics of United States policy action for more than 50 years (Hira 2010). Unfortunately, among U.S. undergraduate curricula, STEM has one of the highest attrition rates (Tinto 1993) with less than half of students in the U.S. that enroll in an undergraduate STEM program ultimately receiving a degree in a STEM field (Hayes 2009). Naturally, the high rate of attrition is a topic of persisting concern. Many programs have been designed and implemented to model best practices in retaining students in STEM disciplines. One retention strategy is to engage STEM undergraduates in research experiences, and a number of programs have been implemented to provide such experiences. The Towson University Research Enhancement Program (TU REP) is one such program. This cohort-based program supports faculty in the development of course-based undergraduate research experiences (CUREs). In this note we describe a CURE in machine learning offered by the Towson University Department of Mathematics whose development was supported by TU REP. We categorize this course along the spectrum of traditional, inquiry, CURE and internship in each of the five dimensions characteristic of a CURE.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46196295","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}
We reconsider the classical equality 0.999. .. = 1 with the tool of circular words, that is: finite words whose last letter is assumed to be followed by the first one. Such circular words are naturally embedded with algebraic structures that enlight this problematic equality, allowing it to be considered in Q rather than in R. We comment early history of such structures, that involves English teachers and accountants of the first part of the xviii th century, who appear to be the firsts to assert the equality 0.999. .. = 1. Their level of understanding show links with Dubinsky et al.'s apos theory in mathematics education. Eventually, we rebuilt the field Q from circular words, and provide an original proof of the fact that an algebraic integer is either an integer or an irrational number.
{"title":"The Field Q and the Equality 0.999. . . = 1 from Combinatorics of Circular Words and History of Practical Arithmetics","authors":"Benoît Rittaud, L. Vivier","doi":"10.54870/1551-3440.1614","DOIUrl":"https://doi.org/10.54870/1551-3440.1614","url":null,"abstract":"We reconsider the classical equality 0.999. .. = 1 with the tool of circular words, that is: finite words whose last letter is assumed to be followed by the first one. Such circular words are naturally embedded with algebraic structures that enlight this problematic equality, allowing it to be considered in Q rather than in R. We comment early history of such structures, that involves English teachers and accountants of the first part of the xviii th century, who appear to be the firsts to assert the equality 0.999. .. = 1. Their level of understanding show links with Dubinsky et al.'s apos theory in mathematics education. Eventually, we rebuilt the field Q from circular words, and provide an original proof of the fact that an algebraic integer is either an integer or an irrational number.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42836999","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}
{"title":"Guest Editorial: Reflections on Course-Based Undergraduate Research","authors":"Diana S. Cheng, J. González","doi":"10.54870/1551-3440.1569","DOIUrl":"https://doi.org/10.54870/1551-3440.1569","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968759","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}
{"title":"Problem Solving for Teachers – Action Research in a Cross-Listed Undergraduate and Graduate Course","authors":"Diana S. Cheng","doi":"10.54870/1551-3440.1581","DOIUrl":"https://doi.org/10.54870/1551-3440.1581","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70969488","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}
Carlos Roberto Vianna, E. Godoy, Emerson Rolkouski
This article aims to present a public policy of large-scale literacy teachers continued training, the Pacto Nacional pela Alfabetizaçao na Idade Certa (PNAIC), making a summary of the Brazilian dissertations and theses results wich approached this public policy in the context of Mathematical Education. Initiated in 2012, the PNAIC involved more than three hundred thousand literacy teachers, from more than five thousand cities for five years. This article uses a qualitative research approach, in the descriptive modality, showing a status of the art of these researches. The set of works analyzed was divided into three groups, according to their declared research objectives: Objective 1: To analyzeinvestigate the meanings brought by the literacy teachers about the PNAIC (75.5%);Objective 2: To analyze-investigate the meanings brought by the other participants about the PNAIC (7.5%);and Objective 3: Unveil the PNAIC (17%). The analysis of the researches results associated with these objectives allowed us to reach four conclusions: 1) The trainings promoted by PNAIC supported changes in the pedagogical practices of the literacy teachers;2) the trainings promoted by PNAIC were necessary, but they wer not enough to combat illiteracy;3) the trainings promoted by the PNAIC induced the literacy teachers to reflections about the pedagogical practices and 4) the trainings promoted by the PNAIC showed weaknesses. In summary, this article presents an initial analysis of the scope from the manifested studies in dissertations and theses and supports the realization of new studies in order to deepen the analysis and evaluation of the varied aspects of one of the broadest training programs ever implemented in Brazil.
{"title":"A Look at the National Pact for Literacy at the Right Age in the Mathematics Education Context","authors":"Carlos Roberto Vianna, E. Godoy, Emerson Rolkouski","doi":"10.54870/1551-3440.1553","DOIUrl":"https://doi.org/10.54870/1551-3440.1553","url":null,"abstract":"This article aims to present a public policy of large-scale literacy teachers continued training, the Pacto Nacional pela Alfabetizaçao na Idade Certa (PNAIC), making a summary of the Brazilian dissertations and theses results wich approached this public policy in the context of Mathematical Education. Initiated in 2012, the PNAIC involved more than three hundred thousand literacy teachers, from more than five thousand cities for five years. This article uses a qualitative research approach, in the descriptive modality, showing a status of the art of these researches. The set of works analyzed was divided into three groups, according to their declared research objectives: Objective 1: To analyzeinvestigate the meanings brought by the literacy teachers about the PNAIC (75.5%);Objective 2: To analyze-investigate the meanings brought by the other participants about the PNAIC (7.5%);and Objective 3: Unveil the PNAIC (17%). The analysis of the researches results associated with these objectives allowed us to reach four conclusions: 1) The trainings promoted by PNAIC supported changes in the pedagogical practices of the literacy teachers;2) the trainings promoted by PNAIC were necessary, but they wer not enough to combat illiteracy;3) the trainings promoted by the PNAIC induced the literacy teachers to reflections about the pedagogical practices and 4) the trainings promoted by the PNAIC showed weaknesses. In summary, this article presents an initial analysis of the scope from the manifested studies in dissertations and theses and supports the realization of new studies in order to deepen the analysis and evaluation of the varied aspects of one of the broadest training programs ever implemented in Brazil.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44190563","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}
Romaro Antonio Silva, Pedro Manuel Baptista Palhares, José Roberto Linhares de Mattos
In this article, we bring forward a research with ethnomathematical aspects that shows the sociocultural relations experienced in a quilombola community registered as Santa Luzia do Maruanum, in the rural region of the capital Macapá, in the state of Amapá, Brazil. Such research was based on the activities developed by 12 ceramic craftswomen in the community, members of the Ceramic Craftswomen Association of Maruanum ALOMA (Associação de Louceiras do Maruanum in portuguese). It was possible, through field research, with a qualitative approach, to understand the social context of ceramic craftswomen, to verify the spoken mathematical knowledge learned out of school in the production of ceramic tableware, in family farming, and consequently in daily habits, such as Marabaixo culture. Through participant observation, it was possible to verify aspects in the relationship between the contents of school mathematics and the activities developed by the ceramic craftswomen, which brings us possibilities of a bridge for teaching mathematics in quilombola schools. The results presented here point to the importance of a school education focused on valuing local culture, which strengthens ethnic relations in the search for equity and establishes an artistic-cultural rescue. In this sense, the presence of women as maintainers of household income and in the political leadership of the community stands out. This leads us to reinforce the understanding of the representativeness of the practices of ceramic craftswomen in the teaching of school mathematics, in which the concepts approached in the classroom are exemplified with everyday reality from the communities. Thus, we hope that this article will contribute to reflections at the most diverse levels and educational modalities. We also hope to contribute with other research in Ethnomathematics and to disseminate the quilombola culture present in the state of Amapá, which is currently under constant attacks on its rights by the state policy that has been installed in Brazil since 2016.
在本文中，我们提出了一项民族数学方面的研究，该研究显示了在巴西阿马apap州首府马卡帕农村地区注册为Santa Luzia do Maruanum的一个quilombola社区所经历的社会文化关系。这项研究是基于社区中12名陶瓷女工匠所开展的活动，她们是Maruanum ALOMA(葡萄牙语associa o de Louceiras do Maruanum)陶瓷女工匠协会的成员。通过实地研究，可以用定性的方法了解陶瓷工匠的社会背景，验证在陶瓷餐具生产、家庭农业以及日常习惯(如Marabaixo文化)中从学校学到的口头数学知识。通过参与观察，可以验证学校数学内容与陶艺妇女开展的活动之间关系的某些方面，这为我们提供了在quilombola学校进行数学教学的桥梁的可能性。这里提出的结果指出了重视当地文化的学校教育的重要性，这在寻求公平的过程中加强了民族关系，并建立了艺术文化拯救。从这个意义上说，妇女作为维持家庭收入和社区政治领导的存在是突出的。这使我们加强了对学校数学教学中陶瓷女工匠实践的代表性的理解，其中课堂上的概念以社区的日常现实为例。因此，我们希望这篇文章将有助于在最不同的层次和教育方式上进行反思。我们也希望为民族数学的其他研究做出贡献，并传播amapap州存在的quilombola文化，该文化目前正受到巴西自2016年以来实施的国家政策对其权利的不断攻击。
{"title":"Ethnomathematics Approach as a Tool for Cultural Valuation and Social Representativity: Possibilities in a Quilombola Community in the State of Amapá - Brazil","authors":"Romaro Antonio Silva, Pedro Manuel Baptista Palhares, José Roberto Linhares de Mattos","doi":"10.54870/1551-3440.1557","DOIUrl":"https://doi.org/10.54870/1551-3440.1557","url":null,"abstract":"In this article, we bring forward a research with ethnomathematical aspects that shows the sociocultural relations experienced in a quilombola community registered as Santa Luzia do Maruanum, in the rural region of the capital Macapá, in the state of Amapá, Brazil. Such research was based on the activities developed by 12 ceramic craftswomen in the community, members of the Ceramic Craftswomen Association of Maruanum ALOMA (Associação de Louceiras do Maruanum in portuguese). It was possible, through field research, with a qualitative approach, to understand the social context of ceramic craftswomen, to verify the spoken mathematical knowledge learned out of school in the production of ceramic tableware, in family farming, and consequently in daily habits, such as Marabaixo culture. Through participant observation, it was possible to verify aspects in the relationship between the contents of school mathematics and the activities developed by the ceramic craftswomen, which brings us possibilities of a bridge for teaching mathematics in quilombola schools. The results presented here point to the importance of a school education focused on valuing local culture, which strengthens ethnic relations in the search for equity and establishes an artistic-cultural rescue. In this sense, the presence of women as maintainers of household income and in the political leadership of the community stands out. This leads us to reinforce the understanding of the representativeness of the practices of ceramic craftswomen in the teaching of school mathematics, in which the concepts approached in the classroom are exemplified with everyday reality from the communities. Thus, we hope that this article will contribute to reflections at the most diverse levels and educational modalities. We also hope to contribute with other research in Ethnomathematics and to disseminate the quilombola culture present in the state of Amapá, which is currently under constant attacks on its rights by the state policy that has been installed in Brazil since 2016.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968634","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}
This study aims to analyze the perceptions of undergraduates in Mathematics Teaching on the evaluation practices of their teachers of specific content subjects and the possible implications of this practice in their training as teachers. It is a qualitative research, expositive and explicative, developed in a Mathematics Teaching degree in a Brazilian Federal University. We used random non-probabilistic sample to select the course and the students. To produce the data, we used: documental analysis, class observation, interviews, group talks, and social networks – Facebook and WhatsApp groups, followed by content analysis. The main intervening which emerged from the data were indications of possible dispositions composing the habitus of mathematics teachers. From these dispositions, undergraduates indicated, directly and indirectly, the legitimizing role of the evaluation practices in the subjects of mathematics content as a way of symbolic violence, when mentioning the tension between the bachelor’s and the teaching degrees, and criticizing or defending the expositive classes with demonstrations, the rigor of classificatory tests, and the relationship teacher-student with little dialogue. The analysis shows that the students do not clearly see the implications of these evaluation practices on their training as teachers. In this context, they have shown a propensity to incorporate the habitus of the mathematics teacher, becoming possible reproducers of a pedagogical practice focused on transmission and traditional evaluation in their future.
{"title":"Learning Evaluation in Mathematics Teaching Degree and the Possible Implications for Teacher Training","authors":"Niusarte Virginia Pinheiro, Samira Zaidan","doi":"10.54870/1551-3440.1560","DOIUrl":"https://doi.org/10.54870/1551-3440.1560","url":null,"abstract":"This study aims to analyze the perceptions of undergraduates in Mathematics Teaching on the evaluation practices of their teachers of specific content subjects and the possible implications of this practice in their training as teachers. It is a qualitative research, expositive and explicative, developed in a Mathematics Teaching degree in a Brazilian Federal University. We used random non-probabilistic sample to select the course and the students. To produce the data, we used: documental analysis, class observation, interviews, group talks, and social networks – Facebook and WhatsApp groups, followed by content analysis. The main intervening which emerged from the data were indications of possible dispositions composing the habitus of mathematics teachers. From these dispositions, undergraduates indicated, directly and indirectly, the legitimizing role of the evaluation practices in the subjects of mathematics content as a way of symbolic violence, when mentioning the tension between the bachelor’s and the teaching degrees, and criticizing or defending the expositive classes with demonstrations, the rigor of classificatory tests, and the relationship teacher-student with little dialogue. The analysis shows that the students do not clearly see the implications of these evaluation practices on their training as teachers. In this context, they have shown a propensity to incorporate the habitus of the mathematics teacher, becoming possible reproducers of a pedagogical practice focused on transmission and traditional evaluation in their future.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968744","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}
This paper outlines a mathematics course centered around the interdisciplinary topic of modeling self-assembling DNA which was used as a venue for a mathematics course-based undergraduate research experience (CURE). The structure and logistics of designing and teaching such a course in addition to suggestions and student feedback from the course are also included.
{"title":"Graph Theoretical Modeling of DNA as a Vehicle for a Course-Based Undergraduate Research Experience","authors":"Amanda Harsy","doi":"10.54870/1551-3440.1572","DOIUrl":"https://doi.org/10.54870/1551-3440.1572","url":null,"abstract":"This paper outlines a mathematics course centered around the interdisciplinary topic of modeling self-assembling DNA which was used as a venue for a mathematics course-based undergraduate research experience (CURE). The structure and logistics of designing and teaching such a course in addition to suggestions and student feedback from the course are also included.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968863","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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