: 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":" ","pages":""},"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":" ","pages":""},"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":"1 1","pages":""},"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":"1 1","pages":""},"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":"1 1","pages":""},"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}
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":"1 1","pages":""},"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}
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":" ","pages":""},"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}
Sueli dos Prazeres Santos, Luiz Márcio Santos Farias
In the present article, we undertook a systematic study of bibliographic review based on the discussions, in the academic scope, about the contribution of the Anthropological Theory of Didactic – ATD (Chevallard, 1992) linked to Mathematics teaching and learning processes. The purpose was to investigate the current appropriation of ATD in Stricto sensu researches in Brazil. It is worth mentioning that the present study refers to a part of a PhD thesis. Thus, we aim to present an overview of thesis and dissertations answering the following question: "What are the main programs, institutions and researchers in Brazil that have been working on ATD?" In addition, we developed a study on the investigation axes of the researches, classified as: I) Teaching: focusing on the teacher, II) Learning: the object being the student's learning and III) Analysis of documents: books, lesson plans, course projects. For this purpose, we selected as a corpus 69 dissertations and 37 thesis defended in the period from 2005 to 2017.
{"title":"The Anthropological Theory of the Didactic in Brazilian researches","authors":"Sueli dos Prazeres Santos, Luiz Márcio Santos Farias","doi":"10.54870/1551-3440.1562","DOIUrl":"https://doi.org/10.54870/1551-3440.1562","url":null,"abstract":"In the present article, we undertook a systematic study of bibliographic review based on the discussions, in the academic scope, about the contribution of the Anthropological Theory of Didactic – ATD (Chevallard, 1992) linked to Mathematics teaching and learning processes. The purpose was to investigate the current appropriation of ATD in Stricto sensu researches in Brazil. It is worth mentioning that the present study refers to a part of a PhD thesis. Thus, we aim to present an overview of thesis and dissertations answering the following question: \"What are the main programs, institutions and researchers in Brazil that have been working on ATD?\" In addition, we developed a study on the investigation axes of the researches, classified as: I) Teaching: focusing on the teacher, II) Learning: the object being the student's learning and III) Analysis of documents: books, lesson plans, course projects. For this purpose, we selected as a corpus 69 dissertations and 37 thesis defended in the period from 2005 to 2017.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968896","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}
Verônica Gitirana, Rosilângela Lucena, R. Ignácio, Roberto Araújo Filho, José Wilson Pereira, César Thiago da Silva
Recommended Citation Gitirana, Verônica; Lucena, Rosilângela; Ignácio, Rogério; Araújo Filho, Roberto; Wilson Pereira, José; and Thiago da Silva, César (2022) "The Man Creates Instruments that Transform Himself: An Overview of GERE Research within Mathematics Education," The Mathematics Enthusiast: Vol. 19 : No. 2 , Article 10. DOI: https://doi.org/10.54870/1551-3440.1563 Available at: https://scholarworks.umt.edu/tme/vol19/iss2/10
{"title":"The Man Creates Instruments that Transform Himself: An Overview of GERE Research within Mathematics Education","authors":"Verônica Gitirana, Rosilângela Lucena, R. Ignácio, Roberto Araújo Filho, José Wilson Pereira, César Thiago da Silva","doi":"10.54870/1551-3440.1563","DOIUrl":"https://doi.org/10.54870/1551-3440.1563","url":null,"abstract":"Recommended Citation Gitirana, Verônica; Lucena, Rosilângela; Ignácio, Rogério; Araújo Filho, Roberto; Wilson Pereira, José; and Thiago da Silva, César (2022) \"The Man Creates Instruments that Transform Himself: An Overview of GERE Research within Mathematics Education,\" The Mathematics Enthusiast: Vol. 19 : No. 2 , Article 10. DOI: https://doi.org/10.54870/1551-3440.1563 Available at: https://scholarworks.umt.edu/tme/vol19/iss2/10","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70968905","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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