Research on textbooks has been carried out in different countries and with different purposes, including a set of studies that seek to know what those books convey in their texts. This type of investigation gives a view of the textbook as something that gives materiality to the proposed curriculum as a way to approach the knowledge taught and/or to identify elements that contribute to understanding reasons for some learning difficulties and persistent errors. Since the early 2000s, I have guided research studies that seeks to understand what kind of mathematics is proposed in textbooks intended for Brazilian basic education and how it is proposed. After a few years of this work, I outlined a model for textbook analysis based on elements of the anthropological theory of the didactic. This model consists of the following, not necessarily linear, steps: constituting the corpus for the analysis, the modellation of mathematical praxeologies present in the Course part of the material, doing the mathematical analysis of the Activities Proposed, the modellation of Didactic Praxeologies, and Triangulating data. This text presents this model, illustrating it with research studies I supervised, showing the relevance of the model of analysis developed.
{"title":"A METHODOLOGICAL PROPOSAL FOR TEXTBOOK ANALYSIS","authors":"Marilena Bittar","doi":"10.54870/1551-3440.1555","DOIUrl":"https://doi.org/10.54870/1551-3440.1555","url":null,"abstract":"Research on textbooks has been carried out in different countries and with different purposes, including a set of studies that seek to know what those books convey in their texts. This type of investigation gives a view of the textbook as something that gives materiality to the proposed curriculum as a way to approach the knowledge taught and/or to identify elements that contribute to understanding reasons for some learning difficulties and persistent errors. Since the early 2000s, I have guided research studies that seeks to understand what kind of mathematics is proposed in textbooks intended for Brazilian basic education and how it is proposed. After a few years of this work, I outlined a model for textbook analysis based on elements of the anthropological theory of the didactic. This model consists of the following, not necessarily linear, steps: constituting the corpus for the analysis, the modellation of mathematical praxeologies present in the Course part of the material, doing the mathematical analysis of the Activities Proposed, the modellation of Didactic Praxeologies, and Triangulating data. This text presents this model, illustrating it with research studies I supervised, showing the relevance of the model of analysis developed.","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":"70968380","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}
N. J. Spence, Rachel K. Anderson, Sherryse L. Corrow, Susan A. Dumais, L. Dierker
{"title":"Passion-Driven Statistics: A course-based undergraduate research experience (CURE)","authors":"N. J. Spence, Rachel K. Anderson, Sherryse L. Corrow, Susan A. Dumais, L. Dierker","doi":"10.54870/1551-3440.1575","DOIUrl":"https://doi.org/10.54870/1551-3440.1575","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":"70969027","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":"A tribute in honor of Ubiratan D’Ambrósio’s life and legacy","authors":"Jonei Cerqueira Barbosa","doi":"10.54870/1551-3440.1541","DOIUrl":"https://doi.org/10.54870/1551-3440.1541","url":null,"abstract":"","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":"46966037","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}
The objective of this article is to discuss actions of agency by analyzing the practices and conceptions of a mathematics teacher working in the municipal school system of Valinhos, state of São Paulo, while teaching statistics and probability to students in the final years of elementary school. The concept of agency is related to transformative capacity and refers to the power of the individual over the context in which they are inserted. The concept of agency is significant for teacher education and is linked to critical professional development, as criticality is essential for people’s transformation processes. This study adopted principles of (auto) biographical research, which view narratives as training and self-training practices. Through spoken and written narratives given by a teacher who participated in a collaborative study group, discussions about the way she develops her practices and the factors that most influence her decision-making are examined.
{"title":"Agency and criticality in statistics teaching practices: the account of a teacher","authors":"Celi Espasandin Lopes, Nathalia Tornisiello Scarlassari","doi":"10.54870/1551-3440.1558","DOIUrl":"https://doi.org/10.54870/1551-3440.1558","url":null,"abstract":"The objective of this article is to discuss actions of agency by analyzing the practices and conceptions of a mathematics teacher working in the municipal school system of Valinhos, state of São Paulo, while teaching statistics and probability to students in the final years of elementary school. The concept of agency is related to transformative capacity and refers to the power of the individual over the context in which they are inserted. The concept of agency is significant for teacher education and is linked to critical professional development, as criticality is essential for people’s transformation processes. This study adopted principles of (auto) biographical research, which view narratives as training and self-training practices. Through spoken and written narratives given by a teacher who participated in a collaborative study group, discussions about the way she develops her practices and the factors that most influence her decision-making are examined.","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":"70968681","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}
Kristin P. Bennett, John S. Erickson, Amy Svirsky, Josephine C. Seddon
This paper reports on Data Analytics Research (DAR), a course-based undergraduate research experience (CURE) in which undergraduate students conduct data analysis research on open real-world problems for industry, university, and community clients. We describe how DAR, offered by the Mathematical Sciences Department at Rensselaer Polytechnic Institute (RPI), is an essential part of an early low-barrier pipeline into data analytics studies and careers for diverse students. Students first take a foundational course, typically Introduction to Data Mathematics, that teaches linear algebra, data analytics, and R programming simultaneously using a project-based learning (PBL) approach. Then in DAR, students work in teams on open applied data analytics research problems provided by the clients. We describe the DAR organization which is inspired in part by agile software development practices. Students meet for coaching sessions with instructors multiple times a week and present to clients frequently. In a fully remote format during the pandemic, the students continued to be highly successful and engaged in COVID-19 research producing significant results as indicated by deployed online applications, refereed papers, and conference presentations. Formal evaluation shows that the pipeline of the single on-ramp course followed by DAR addressing real-world problems with societal benefits is highly effective at developing students' data analytics skills, advancing creative problem solvers who can work both independently and in teams, and attracting students to further studies and careers in data science.
{"title":"A Mathematics Pipeline to Student Success in Data Analytics through Course-Based Undergraduate Research","authors":"Kristin P. Bennett, John S. Erickson, Amy Svirsky, Josephine C. Seddon","doi":"10.54870/1551-3440.1573","DOIUrl":"https://doi.org/10.54870/1551-3440.1573","url":null,"abstract":"This paper reports on Data Analytics Research (DAR), a course-based undergraduate research experience (CURE) in which undergraduate students conduct data analysis research on open real-world problems for industry, university, and community clients. We describe how DAR, offered by the Mathematical Sciences Department at Rensselaer Polytechnic Institute (RPI), is an essential part of an early low-barrier pipeline into data analytics studies and careers for diverse students. Students first take a foundational course, typically Introduction to Data Mathematics, that teaches linear algebra, data analytics, and R programming simultaneously using a project-based learning (PBL) approach. Then in DAR, students work in teams on open applied data analytics research problems provided by the clients. We describe the DAR organization which is inspired in part by agile software development practices. Students meet for coaching sessions with instructors multiple times a week and present to clients frequently. In a fully remote format during the pandemic, the students continued to be highly successful and engaged in COVID-19 research producing significant results as indicated by deployed online applications, refereed papers, and conference presentations. Formal evaluation shows that the pipeline of the single on-ramp course followed by DAR addressing real-world problems with societal benefits is highly effective at developing students' data analytics skills, advancing creative problem solvers who can work both independently and in teams, and attracting students to further studies and careers in data science.","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":"70968876","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":"Employing College Geometry in Real-Life Settings","authors":"Tetyana Berezovski","doi":"10.54870/1551-3440.1582","DOIUrl":"https://doi.org/10.54870/1551-3440.1582","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":"70969088","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}
Lilian Aragão da Silva, Andréia Maria Pereira de Oliveira
This article aims to identify and analyze power relations in the negotiation of meanings in a Community of Practice, called the “Observatório da Educação Matemática” da Bahia (OEM-BA), formed by academics from the university and teachers of Basic Education, who came together to produce educational math curriculum materials. The research carried out was of a qualitative nature and the data were produced through observations of the activities carried out by OEM-BA. To support the analysis, we used Etienne Wenger's Social Theory of Learning and Basil Bernstein's Theory of Codes. By analyzing the data, we identify power relations between academic and non-academic discourses, as well as interdisciplinary and interdisciplinary discourses. This happened when members negotiated meanings relative to teaching and learning content operations with whole numbers and quantities directly and inversely proportional. The results of this research gave visibility to variations in the principles and hierarchies underlying the meeting between academics and scholars.
本文旨在识别和分析实践共同体中意义谈判中的权力关系，该共同体被称为“Observatório da educa o Matemática”da Bahia (OEM-BA)，由大学的学者和基础教育教师组成，他们聚集在一起制作教育数学课程材料。所进行的研究是定性的，数据是通过观察OEM-BA所进行的活动而产生的。为了支持这一分析，我们使用了Etienne Wenger的社会学习理论和Basil Bernstein的符码理论。通过对数据的分析，我们确定了学术话语与非学术话语、跨学科话语与跨学科话语之间的权力关系。当成员们讨论与教学内容操作相关的意义时，就会出现这种情况，这些操作与整数和数量成正比或成反比。这项研究的结果揭示了学者和学者之间会面的原则和等级制度的变化。
{"title":"Power relations and the negotiation of meanings in a Community of Practice in the field of Mathematics Education","authors":"Lilian Aragão da Silva, Andréia Maria Pereira de Oliveira","doi":"10.54870/1551-3440.1556","DOIUrl":"https://doi.org/10.54870/1551-3440.1556","url":null,"abstract":"This article aims to identify and analyze power relations in the negotiation of meanings in a Community of Practice, called the “Observatório da Educação Matemática” da Bahia (OEM-BA), formed by academics from the university and teachers of Basic Education, who came together to produce educational math curriculum materials. The research carried out was of a qualitative nature and the data were produced through observations of the activities carried out by OEM-BA. To support the analysis, we used Etienne Wenger's Social Theory of Learning and Basil Bernstein's Theory of Codes. By analyzing the data, we identify power relations between academic and non-academic discourses, as well as interdisciplinary and interdisciplinary discourses. This happened when members negotiated meanings relative to teaching and learning content operations with whole numbers and quantities directly and inversely proportional. The results of this research gave visibility to variations in the principles and hierarchies underlying the meeting between academics and scholars.","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":"70968555","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 investigates 48 preservice middle school teachers’ formal textbook definitions, formulas, and graphs of the directly and inversely proportional relationships. The connections among these three types of representations and how preservice teachers’ representations differ according to the two relationships are also examined. The data of the study included the preservice teachers’ responses to a paper-and-pencil test with two items. An explanatory research design model was followed when developing this study. The study findings indicated the preservice teachers’ over-attention to the simultaneous increases and/or decreases when representing the directly and inversely proportional relationships. Only four preservice teachers stated in their definitions that the ratio was constant in the directly proportional relationship. Whereas none of them stated constant product in their inversely proportional definition. Although the preservice teachers were slightly better at writing the direct proportion formula than the inverse proportion formula, this difference was much greater in terms of drawing the direct and inverse proportion graphs. Sixty percent of the preservice teachers drew their inverse proportion graphs as linear with negative slopes. Moreover, the analysis showed that the preservice teachers’ definitions were not well-linked with their graphs and formulas. On the other hand, the preservice teachers who were better at providing correct formulas were also better at drawing the correct graphs. Implications for teaching and future study suggestions are discussed.
{"title":"Investigating Preservice Mathematics Teachers’ Definitions, Formulas, and Graphs of Directly and Inversely Proportional Relationships","authors":"Muhammet Arıcan, Yasemin Kiymaz","doi":"10.54870/1551-3440.1566","DOIUrl":"https://doi.org/10.54870/1551-3440.1566","url":null,"abstract":"This study investigates 48 preservice middle school teachers’ formal textbook definitions, formulas, and graphs of the directly and inversely proportional relationships. The connections among these three types of representations and how preservice teachers’ representations differ according to the two relationships are also examined. The data of the study included the preservice teachers’ responses to a paper-and-pencil test with two items. An explanatory research design model was followed when developing this study. The study findings indicated the preservice teachers’ over-attention to the simultaneous increases and/or decreases when representing the directly and inversely proportional relationships. Only four preservice teachers stated in their definitions that the ratio was constant in the directly proportional relationship. Whereas none of them stated constant product in their inversely proportional definition. Although the preservice teachers were slightly better at writing the direct proportion formula than the inverse proportion formula, this difference was much greater in terms of drawing the direct and inverse proportion graphs. Sixty percent of the preservice teachers drew their inverse proportion graphs as linear with negative slopes. Moreover, the analysis showed that the preservice teachers’ definitions were not well-linked with their graphs and formulas. On the other hand, the preservice teachers who were better at providing correct formulas were also better at drawing the correct graphs. Implications for teaching and future study suggestions are discussed.","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":"70968603","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}
Jaqueline de Souza Pereira Grilo, Jonei Cerqueira Barbosa
{"title":"It is necessary to know a specific mathematics to teach mathematics","authors":"Jaqueline de Souza Pereira Grilo, Jonei Cerqueira Barbosa","doi":"10.54870/1551-3440.1547","DOIUrl":"https://doi.org/10.54870/1551-3440.1547","url":null,"abstract":"","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":"47867972","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}
The present work presents some examples of data originated from a set of investigations developed in Brazil, at the Federal Institute of Education, Science and Technology of the State of Ceará IFCE, in the context of teacher education, and the consideration of elements of a historical, mathematical, and evolutionary nature. Thus, from a perspective of theoretical complementarity involving the research elements derived from the notion of the didactic engineering for development and some assumptions of the French aspect of the professional didactics, two sets of data are discussed. The first set involved research carried out between 2017 and 2020. The second set considered involved studies still under development in Brazil, considering the period of 2020 2023. The historical landscape of investigation rests on considering the recurring number sequences of Fibonacci, Lucas, Pell, Jacobsthal, Coordonier or Padovan, Perrin, Mersenne, Oresme, Naraynna, and Leonardo. Furthermore, in a broad sense, the study aims to provide a learning scenario for the teacher, affected by a perspective of mathematical knowledge evolution, including the repercussions and applications with current technology.
{"title":"Didactic Engineering (DE) and Professional Didactics (PD): A Proposal for Historical Eesearch in Brazil on Recurring Number Sequences","authors":"Francisco Régis Vieira Alves","doi":"10.54870/1551-3440.1551","DOIUrl":"https://doi.org/10.54870/1551-3440.1551","url":null,"abstract":"The present work presents some examples of data originated from a set of investigations developed in Brazil, at the Federal Institute of Education, Science and Technology of the State of Ceará IFCE, in the context of teacher education, and the consideration of elements of a historical, mathematical, and evolutionary nature. Thus, from a perspective of theoretical complementarity involving the research elements derived from the notion of the didactic engineering for development and some assumptions of the French aspect of the professional didactics, two sets of data are discussed. The first set involved research carried out between 2017 and 2020. The second set considered involved studies still under development in Brazil, considering the period of 2020 2023. The historical landscape of investigation rests on considering the recurring number sequences of Fibonacci, Lucas, Pell, Jacobsthal, Coordonier or Padovan, Perrin, Mersenne, Oresme, Naraynna, and Leonardo. Furthermore, in a broad sense, the study aims to provide a learning scenario for the teacher, affected by a perspective of mathematical knowledge evolution, including the repercussions and applications with current technology.","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":"44458010","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：