Pub Date : 2020-12-23DOI: 10.51272/PMENA.42.2020-332
Christine Taylor, Jean S. Lee
Professional developments (PD) play a central role in efforts to improve teachers’ mathematical content knowledge, pedagogical content knowledge, and beliefs about what it means to ‘do mathematics’ (Ball, 1990; Hill, 2007). Creating Algebra Teaching Communities for Hoosiers was the result of a Math-Science Partnership grant from Indiana’s Department of Education in 2015. The study involved 15 middle and high school urban teachers, with a focus on enriching teachers’ knowledge and skills for teaching algebra. This study examines: How do teacher portraits help facilitate the activities in the PD experience? This study focuses on exploring how PD facilitators used facilitation techniques to support participants based on character portraits (Sztajn, Borko, & Smith (2017), and contributes to an area of research needed on skillful facilitation techniques (e.g., Bobis, 2011; van es, 2014) to prepare and support PD facilitators. Findings culminated in five teacher portraits. Highly Skeptical Teacher (HST) is an experienced teacher but is uncomfortable being observed by colleagues. HST doubts students can be successful with the PD tasks. Others followed the skepticism because of HST’s experience in the classroom. Facilitators probed questions to interrupt preconceived perceptions of students. Cautiously Receptive Teacher (CRT) is eager to apply the theories into practice but struggles to bring ideas into reality in the classroom. CRT is hesitant to try new things, but gradually over time buys into the vision of the PD. Trying out activities with students was the best technique to convince CRT of novel teaching practices. Highly Receptive Teacher (HRT) is highly reflective and collaborative. HRT sees the potential of all students to be mathematical learners and makes connections between teaching, the PD, and everyday life experiences. PD facilitators would ask HRT to point out students’ mathematical thinking. BoxChecker Teacher (BCT) is extremely organized, thrives on explicit directions and timeline, and most comfortable with direct instruction. BCT’s intense focus on clear tasks and schedules, and high anxiety made the group dynamics tense. PD facilitators solicited input from BCT on the clarity of expectations. Lopsided Engager Teacher (LET) has great relationships with all students, even the most disruptive, and is deeply troubled when other teachers do not believe that all students can learn mathematics. LET displays turns of both low engagement and intense engagement. PD facilitators stoked this passion to engage in rich discussions, and showed empathy to situations where relationships take priority over learning. This study begins a conversation about mathematics teaching facilitation and how best to support and facilitate with a wide range of participants.
{"title":"From highly receptive to highly skeptical: Engaging all teachers through responsive PD facilitation","authors":"Christine Taylor, Jean S. Lee","doi":"10.51272/PMENA.42.2020-332","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-332","url":null,"abstract":"Professional developments (PD) play a central role in efforts to improve teachers’ mathematical content knowledge, pedagogical content knowledge, and beliefs about what it means to ‘do mathematics’ (Ball, 1990; Hill, 2007). Creating Algebra Teaching Communities for Hoosiers was the result of a Math-Science Partnership grant from Indiana’s Department of Education in 2015. The study involved 15 middle and high school urban teachers, with a focus on enriching teachers’ knowledge and skills for teaching algebra. This study examines: How do teacher portraits help facilitate the activities in the PD experience? This study focuses on exploring how PD facilitators used facilitation techniques to support participants based on character portraits (Sztajn, Borko, & Smith (2017), and contributes to an area of research needed on skillful facilitation techniques (e.g., Bobis, 2011; van es, 2014) to prepare and support PD facilitators. Findings culminated in five teacher portraits. Highly Skeptical Teacher (HST) is an experienced teacher but is uncomfortable being observed by colleagues. HST doubts students can be successful with the PD tasks. Others followed the skepticism because of HST’s experience in the classroom. Facilitators probed questions to interrupt preconceived perceptions of students. Cautiously Receptive Teacher (CRT) is eager to apply the theories into practice but struggles to bring ideas into reality in the classroom. CRT is hesitant to try new things, but gradually over time buys into the vision of the PD. Trying out activities with students was the best technique to convince CRT of novel teaching practices. Highly Receptive Teacher (HRT) is highly reflective and collaborative. HRT sees the potential of all students to be mathematical learners and makes connections between teaching, the PD, and everyday life experiences. PD facilitators would ask HRT to point out students’ mathematical thinking. BoxChecker Teacher (BCT) is extremely organized, thrives on explicit directions and timeline, and most comfortable with direct instruction. BCT’s intense focus on clear tasks and schedules, and high anxiety made the group dynamics tense. PD facilitators solicited input from BCT on the clarity of expectations. Lopsided Engager Teacher (LET) has great relationships with all students, even the most disruptive, and is deeply troubled when other teachers do not believe that all students can learn mathematics. LET displays turns of both low engagement and intense engagement. PD facilitators stoked this passion to engage in rich discussions, and showed empathy to situations where relationships take priority over learning. This study begins a conversation about mathematics teaching facilitation and how best to support and facilitate with a wide range of participants.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76958597","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.42.2020-148
Gulden Karakok, M. Savić, Gail Tang, Emily Cilli-Turner, Paul R. Regier
{"title":"Creativity-in-progress rubric on problem solving at the post-secondary level","authors":"Gulden Karakok, M. Savić, Gail Tang, Emily Cilli-Turner, Paul R. Regier","doi":"10.51272/PMENA.42.2020-148","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-148","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73398857","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.42.2020-124
Viana Nallely García Salmerón, F. Rodríguez-Vásquez
{"title":"A classroom experience: vector concept / Una experiencia de clase: concepto vector","authors":"Viana Nallely García Salmerón, F. Rodríguez-Vásquez","doi":"10.51272/PMENA.42.2020-124","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-124","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73920750","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":null,"pages":null},"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.42.2020-375
H. Enriquez, A. I. Sacristán
Resources play an important role in how subjects act and think. Teachers, throughout their professional career, develop ways of teaching mathematics —articulated by the organization and type of activities that guide their class, the resources they use and their forms of intervention; these are modified when a new resource is integrated. In this paper we present evidence of this phenomenon using the case study of a teacher who, as a result of her participation in a professional development course that we implemented, integrated digital resources into her documentation work, destabilizing her previous forms of teaching.
{"title":"Integrating digital resources to the documentation system of a mathematics teacher in a Mexican rural primary-school / Integración de recursos digitales al sistema documental de una profesora de matemáticas en una primaria rural de méxico","authors":"H. Enriquez, A. I. Sacristán","doi":"10.51272/PMENA.42.2020-375","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-375","url":null,"abstract":"Resources play an important role in how subjects act and think. Teachers, throughout their professional career, develop ways of teaching mathematics —articulated by the organization and type of activities that guide their class, the resources they use and their forms of intervention; these are modified when a new resource is integrated. In this paper we present evidence of this phenomenon using the case study of a teacher who, as a result of her participation in a professional development course that we implemented, integrated digital resources into her documentation work, destabilizing her previous forms of teaching.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73237320","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.42.2020-250
Anna F. DeJarnette, Casey Hord
This study documented changes in the types of questions posed by pre-service teachers (PSTs) who participated in a semester-long professional development (PD) program focused on questioning in algebra. PSTs who participated in the PD—who were conducting 1-1 tutoring for students with learning disabilities during the same time—showed positive changes in the types of questions they posed. PSTs reduced their frequency of closed, leading questions to lead students through solution methods, and they increased their frequency of questions to probe students’ thinking, to focus attention on important mathematical ideas, and to establish mathematical relationships.
{"title":"Pre-service teachers’ patterns of questioning while tutoring students with learning disabilities in Algebra 1","authors":"Anna F. DeJarnette, Casey Hord","doi":"10.51272/PMENA.42.2020-250","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-250","url":null,"abstract":"This study documented changes in the types of questions posed by pre-service teachers (PSTs) who participated in a semester-long professional development (PD) program focused on questioning in algebra. PSTs who participated in the PD—who were conducting 1-1 tutoring for students with learning disabilities during the same time—showed positive changes in the types of questions they posed. PSTs reduced their frequency of closed, leading questions to lead students through solution methods, and they increased their frequency of questions to probe students’ thinking, to focus attention on important mathematical ideas, and to establish mathematical relationships.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73634914","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.42.2020-392
Nicole L. Fonger, Amy B. Ellis
In this theoretical report we focus on the issue of communicating learning trajectories (LTs) to researchers. There is great variation in the body of work on LTs including how researchers communicate what a LT entails, and the kinds of metaphors employed for making meaning of LTs. We elaborate possible affordances and limitations of different metaphors for LTs including “a garden path” and “growing flowers.” This work has implications for how LTs are taken up by researchers, and also how LTs are leveraged to inform student-centered teaching practices.
{"title":"Making meaning of learning trajectories amidst multiple metaphors","authors":"Nicole L. Fonger, Amy B. Ellis","doi":"10.51272/PMENA.42.2020-392","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-392","url":null,"abstract":"In this theoretical report we focus on the issue of communicating learning trajectories (LTs) to researchers. There is great variation in the body of work on LTs including how researchers communicate what a LT entails, and the kinds of metaphors employed for making meaning of LTs. We elaborate possible affordances and limitations of different metaphors for LTs including “a garden path” and “growing flowers.” This work has implications for how LTs are taken up by researchers, and also how LTs are leveraged to inform student-centered teaching practices.","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73635286","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.42.2020-102
Luz Graciela Orozco Vaca
{"title":"Self-instructions for applying writing in geometry problem resolution / Autoinstrucciones para aplicar la escritura en la resolución de problemas de geometría","authors":"Luz Graciela Orozco Vaca","doi":"10.51272/pmena.42.2020-102","DOIUrl":"https://doi.org/10.51272/pmena.42.2020-102","url":null,"abstract":"","PeriodicalId":68089,"journal":{"name":"数学教学通讯","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83103644","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":null,"pages":null},"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.42.2020-370
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":null,"pages":null},"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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