Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-236
Ian Whitacre, K. Findley, Ş. Atabaş
Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers’ (PSTs) knowledge of fractions and has given little attention to the productive resources that PSTs bring to teacher education. We surveyed 26 PSTs using a set of 9 fraction-comparison tasks. We report the frequency of complete strategyarguments and the perspectives (ways of reasoning) used for each item. We further examine incomplete strategy-arguments, noting substantial evidence for productive seeds of reasoning. Using data from interviews with 10 of these PSTs, we identify evidence suggesting these seeds are, in fact, productive in that they provide foundations for further development. We argue that this type of research is needed in order to further mathematics teacher education.
{"title":"Productive seeds in preservice teachers’ reasoning about fraction comparisons","authors":"Ian Whitacre, K. Findley, Ş. Atabaş","doi":"10.51272/PMENA.42.2020-236","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-236","url":null,"abstract":"Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers’ (PSTs) knowledge of fractions and has given little attention to the productive resources that PSTs bring to teacher education. We surveyed 26 PSTs using a set of 9 fraction-comparison tasks. We report the frequency of complete strategyarguments and the perspectives (ways of reasoning) used for each item. We further examine incomplete strategy-arguments, noting substantial evidence for productive seeds of reasoning. Using data from interviews with 10 of these PSTs, we identify evidence suggesting these seeds are, in fact, productive in that they provide foundations for further development. We argue that this type of research is needed in order to further mathematics teacher education.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90686503","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-85
Sean P. Freeland
{"title":"Blackness and whiteness in Appalachian mathematics classrooms","authors":"Sean P. Freeland","doi":"10.51272/PMENA.42.2020-85","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-85","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90719254","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-15
Katrina Piatek-Jimenez, Brent Jackson, A. Dias, Weverton Ataide Pinheiro, Harryson Júnio Lessa Gonçalves, Jennifer Hall, E. Kersey, Angie Hodge-Zickerman
The Gender and Sexuality in Mathematics Education Working Group convened in 2018 and 2019. Over the past two working group sessions, working group members have (1) shared historical and contemporary research related to the topics of the working group; (2) clarified language related to gender and sexuality; (3) developed understandings related to language and its influence on methods, results, and interpretations; (4) explored how gender and sexuality are experienced by students and teachers, and studied by researchers, in international contexts; and (5) developed research relationships among participants to explore relevant ideas. Based on the discussions from past working groups, during the 2020 Working Group, we will strengthen our understanding of these topics by examining underlying theories of gender and sexuality and the affordances of these theories on both research and practice.
{"title":"Working group on gender and sexuality in mathematics education: Informing methodology with theory","authors":"Katrina Piatek-Jimenez, Brent Jackson, A. Dias, Weverton Ataide Pinheiro, Harryson Júnio Lessa Gonçalves, Jennifer Hall, E. Kersey, Angie Hodge-Zickerman","doi":"10.51272/PMENA.42.2020-15","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-15","url":null,"abstract":"The Gender and Sexuality in Mathematics Education Working Group convened in 2018 and 2019. Over the past two working group sessions, working group members have (1) shared historical and contemporary research related to the topics of the working group; (2) clarified language related to gender and sexuality; (3) developed understandings related to language and its influence on methods, results, and interpretations; (4) explored how gender and sexuality are experienced by students and teachers, and studied by researchers, in international contexts; and (5) developed research relationships among participants to explore relevant ideas. Based on the discussions from past working groups, during the 2020 Working Group, we will strengthen our understanding of these topics by examining underlying theories of gender and sexuality and the affordances of these theories on both research and practice.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90810634","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-268
A. Stoltz, Imani Goffney, Kelly K. Ivy, Tarik Buli, Ebony Terrell Shockley
In this multiple-case study, we track the diverging paths of two teacher candidates enrolled in an undergraduate elementary mathematics methods course as they developed their understanding of equitable teaching practices that were central to their course learning objectives. The cases were purposefully selected based upon our previous finding that, by the end of the course, Mary and Rose were extreme opposites in terms of their implementation of equitable mathematics teaching practices they attributed to the course. Teacher preparation programs are designed to help beginning teachers develop the skills to teach content equitably to diverse learners. Thus, methods instructors must consider the ways that teacher candidates use their knowledge and skills in their teaching.
{"title":"Teachers candidates’ implementations of equitable mathematics teaching practices: An examination of divergent paths","authors":"A. Stoltz, Imani Goffney, Kelly K. Ivy, Tarik Buli, Ebony Terrell Shockley","doi":"10.51272/PMENA.42.2020-268","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-268","url":null,"abstract":"In this multiple-case study, we track the diverging paths of two teacher candidates enrolled in an undergraduate elementary mathematics methods course as they developed their understanding of equitable teaching practices that were central to their course learning objectives. The cases were purposefully selected based upon our previous finding that, by the end of the course, Mary and Rose were extreme opposites in terms of their implementation of equitable mathematics teaching practices they attributed to the course. Teacher preparation programs are designed to help beginning teachers develop the skills to teach content equitably to diverse learners. Thus, methods instructors must consider the ways that teacher candidates use their knowledge and skills in their teaching.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90670632","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-172
José N. Contreras
{"title":"Posing problems about geometric situations: A study of prospective secondary mathematics teachers","authors":"José N. Contreras","doi":"10.51272/PMENA.42.2020-172","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-172","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85080298","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-132
Jose Saul Barbosa, C. Duffer
When studying mathematics education and student success, most research tends to study the inclassroom teaching aspect. Another important aspect of mathematics education occurs outside the traditional classroom with tutors. While it has been shown that tutoring leads to student success (Xu, Hartman, Uribe, & Mencke, 2001), research has not necessarily focused on what tutoring is or what makes it effective. In recent years, efforts have been made to expand research in this field. Two major themes are the study of the types of knowledge necessary for effective tutoring and the interplay between these domains of knowledge to better understand the tutoring process.
{"title":"A study on the relationship between tutor’s content knowledge and their tutoring decisions","authors":"Jose Saul Barbosa, C. Duffer","doi":"10.51272/PMENA.42.2020-132","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-132","url":null,"abstract":"When studying mathematics education and student success, most research tends to study the inclassroom teaching aspect. Another important aspect of mathematics education occurs outside the traditional classroom with tutors. While it has been shown that tutoring leads to student success (Xu, Hartman, Uribe, & Mencke, 2001), research has not necessarily focused on what tutoring is or what makes it effective. In recent years, efforts have been made to expand research in this field. Two major themes are the study of the types of knowledge necessary for effective tutoring and the interplay between these domains of knowledge to better understand the tutoring process.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85609054","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-47
Sofía Vázquez-Gómez, Francisco Sepúlveda-Vega
{"title":"Student’s strategies to solve ratio comparison problems in elementary school / Estrategias de los estudiantes para resolver problemas de comparación de razones en primaria","authors":"Sofía Vázquez-Gómez, Francisco Sepúlveda-Vega","doi":"10.51272/PMENA.42.2020-47","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-47","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"163 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83227755","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-293
Jeffrey Choppin, Julie M. Amador, Cynthia Callard, Cynthia Carson
We studied two iterations of an online course provided to rural mathematics teachers. The online courses, which involved primarily synchronous activity, emphasized high-leverage discourse practices. We applied a community of inquiry framework, which emphasizes deep intellectual work, and its three tenets: cognitive presence, social presence, and teaching presence. We adapted the framework by creating a category on content-related interactions and by using mediating processes from our conjecture maps (e.g., Sandoval, 2014) to characterize cognitive presence. The adapted framework allowed us to notice substantive differences between the course iterations, especially in relation to teaching presence and cognitive presence. The implications of the study are that the framework helps us gauge the efficacy of synchronous online interactions and to better gauge goals for future iterations of the course.
{"title":"Studying a synchronous online course using a community of inquiry framework","authors":"Jeffrey Choppin, Julie M. Amador, Cynthia Callard, Cynthia Carson","doi":"10.51272/PMENA.42.2020-293","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-293","url":null,"abstract":"We studied two iterations of an online course provided to rural mathematics teachers. The online courses, which involved primarily synchronous activity, emphasized high-leverage discourse practices. We applied a community of inquiry framework, which emphasizes deep intellectual work, and its three tenets: cognitive presence, social presence, and teaching presence. We adapted the framework by creating a category on content-related interactions and by using mediating processes from our conjecture maps (e.g., Sandoval, 2014) to characterize cognitive presence. The adapted framework allowed us to notice substantive differences between the course iterations, especially in relation to teaching presence and cognitive presence. The implications of the study are that the framework helps us gauge the efficacy of synchronous online interactions and to better gauge goals for future iterations of the course.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75397851","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-322
Carola Manolino
{"title":"The semiosphere: A lens to look at lesson study practices in their cultural context","authors":"Carola Manolino","doi":"10.51272/PMENA.42.2020-322","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-322","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91020119","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 : 2020-12-23DOI: 10.51272/PMENA.42.2020-370
Marisol Santacruz-Rodríguez, A. I. Sacristán, C. Buteau, Joyce Mgombelo, E. Muller
{"title":"A university instructor’s orchestration for supporting his students’ programming for mathematics","authors":"Marisol Santacruz-Rodríguez, A. I. Sacristán, C. Buteau, Joyce Mgombelo, E. Muller","doi":"10.51272/PMENA.42.2020-370","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-370","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73440025","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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