Pub Date : 2020-12-23DOI: 10.51272/pmena.42.2020-3
Ana Isabel Sacristán, José Carlos Cortés Zavala
{"title":"Preface / Prólogo","authors":"Ana Isabel Sacristán, José Carlos Cortés Zavala","doi":"10.51272/pmena.42.2020-3","DOIUrl":"https://doi.org/10.51272/pmena.42.2020-3","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":"85220551","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.42.2020-149
T. Mkhatshwa
This paper extends work in the area of quantitative reasoning at the undergraduate level. Task-based interviews were used to examine 16 calculus students’ difficulties when solving three related rates problems. Analysis of students’ verbal responses and written work revealed several difficulties, including dealing with several time-dependent quantities. The paper concludes with a recommendation for the teaching of related rates problems at the undergraduate level.
{"title":"A quantitative reasoning study of student-reported difficulties when solving related rates problems","authors":"T. Mkhatshwa","doi":"10.51272/PMENA.42.2020-149","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-149","url":null,"abstract":"This paper extends work in the area of quantitative reasoning at the undergraduate level. Task-based interviews were used to examine 16 calculus students’ difficulties when solving three related rates problems. Analysis of students’ verbal responses and written work revealed several difficulties, including dealing with several time-dependent quantities. The paper concludes with a recommendation for the teaching of related rates problems at the undergraduate level.","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":"76777685","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.42.2020-123
M. Troudt, Lindsay Reiten, Jodie D. Novak
We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence and connections of the mathematics. Despite similarities in the structure of the mathematical activities, differences existed in the ideas that emerged in the three teachers’ discussions regarding the relationship between the exponent value and the independent variable. We describe links between collections of teacher decisions to their influences on the mathematics discourse.
{"title":"Experienced secondary teachers’ decisions to attend to the independent variable in exponential functions","authors":"M. Troudt, Lindsay Reiten, Jodie D. Novak","doi":"10.51272/PMENA.42.2020-123","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-123","url":null,"abstract":"We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence and connections of the mathematics. Despite similarities in the structure of the mathematical activities, differences existed in the ideas that emerged in the three teachers’ discussions regarding the relationship between the exponent value and the independent variable. We describe links between collections of teacher decisions to their influences on the mathematics discourse.","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":"77112463","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.42.2020-127
G. Krause, Juanita M. Silva, Jair J. Aguilar
{"title":"Language: a hidden resource in preparing bilingual pre-service teachers","authors":"G. Krause, Juanita M. Silva, Jair J. Aguilar","doi":"10.51272/PMENA.42.2020-127","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-127","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":"83602022","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.42.2020-9
J. Newton, M. Cirillo, K. Kosko, Megan E. Staples, Keith Weber
Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. The inconsistencies in definitions and use of the terms argumentation, justification, and proof highlight the need for scholarly conversations addressing these (and other related) constructs. Collaboration is needed to move toward, not one-size-fits-all definitions, but rather a framework that highlights connections among them and exploits ways in which they may be used in tandem to address overarching research questions. Working group leaders aim to facilitate discussions and collaborations among researchers and to advance our collective understanding of argumentation, justification and proof, particularly the relationships among these important mathematical constructs. Working group sessions will provide opportunities to engage with a panel of researchers and other participants who approach these aspects of reasoning from different perspectives, as well as to: hear findings from a recent analysis of these constructs in research; reflect on one’s own work and position it with respect to the field; and contribute to moving the field forward in this area.
{"title":"Research Colloquia: Conceptions and consequences of what we call argumentation, justification and proof","authors":"J. Newton, M. Cirillo, K. Kosko, Megan E. Staples, Keith Weber","doi":"10.51272/PMENA.42.2020-9","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-9","url":null,"abstract":"Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. The inconsistencies in definitions and use of the terms argumentation, justification, and proof highlight the need for scholarly conversations addressing these (and other related) constructs. Collaboration is needed to move toward, not one-size-fits-all definitions, but rather a framework that highlights connections among them and exploits ways in which they may be used in tandem to address overarching research questions. Working group leaders aim to facilitate discussions and collaborations among researchers and to advance our collective understanding of argumentation, justification and proof, particularly the relationships among these important mathematical constructs. Working group sessions will provide opportunities to engage with a panel of researchers and other participants who approach these aspects of reasoning from different perspectives, as well as to: hear findings from a recent analysis of these constructs in research; reflect on one’s own work and position it with respect to the field; and contribute to moving the field forward in this area.","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":"80783329","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.42.2020-89
Francis Nzuki
One of the significant challenges facing higher education is narrowing the educational attainment gap between students who are academically prepared and those who are not. Although the intention of developmental education is to help support underprepared students in achieving academic success, there have been disagreements among researchers on the effectiveness of achieving this goal (Goudas & Boylan, 2012). On one hand, developmental mathematics has the capability of providing the impetus that can propel students to their overall academic success. On the other hand, the long road the students have to go through in completing mathematics requirements causes many to give up before they can finish the sequence of courses (Rosin, 2012). This study examines how developmental students’ general and mathematical experiences help to shape mathematical identities they develop and how these identities in turn hinder or enhance their successful participation in mathematics. Also examined are the factors that influence students’ mathematics identities after taking a developmental mathematics course. To this end, the following research questions guided this study of first year students taking a developmental mathematics course at a mid-sized, urban public university:
{"title":"Mathematics identity and sense of belonging of developmental mathematics students","authors":"Francis Nzuki","doi":"10.51272/PMENA.42.2020-89","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-89","url":null,"abstract":"One of the significant challenges facing higher education is narrowing the educational attainment gap between students who are academically prepared and those who are not. Although the intention of developmental education is to help support underprepared students in achieving academic success, there have been disagreements among researchers on the effectiveness of achieving this goal (Goudas & Boylan, 2012). On one hand, developmental mathematics has the capability of providing the impetus that can propel students to their overall academic success. On the other hand, the long road the students have to go through in completing mathematics requirements causes many to give up before they can finish the sequence of courses (Rosin, 2012). This study examines how developmental students’ general and mathematical experiences help to shape mathematical identities they develop and how these identities in turn hinder or enhance their successful participation in mathematics. Also examined are the factors that influence students’ mathematics identities after taking a developmental mathematics course. To this end, the following research questions guided this study of first year students taking a developmental mathematics course at a mid-sized, urban public university:","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":"84088245","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.42.2020-38
Genny Rocío Uicab Ballote, T. Rojano, Montserrat García Campos
Purpose of the Research We present preliminary results of a study focused on the analysis of expressions of mathematical generalization that arise in early ages, particularly among students ranging between 10 and 12 years of age when solving generalization mathematical tasks. It is expected that expressions of generalization shown by students in a natural and incipient way will be refined as they develop their capacity for generalization, which could contribute to development of algebraic thinking at later levels.
{"title":"Expressions of mathematical generalization among children in grade five of primary school / Expresiones de generalización matemática en niños de quinto grado de primaria","authors":"Genny Rocío Uicab Ballote, T. Rojano, Montserrat García Campos","doi":"10.51272/PMENA.42.2020-38","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-38","url":null,"abstract":"Purpose of the Research We present preliminary results of a study focused on the analysis of expressions of mathematical generalization that arise in early ages, particularly among students ranging between 10 and 12 years of age when solving generalization mathematical tasks. It is expected that expressions of generalization shown by students in a natural and incipient way will be refined as they develop their capacity for generalization, which could contribute to development of algebraic thinking at later levels.","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":"82391153","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.42.2020-96
C. A. Pena, Mirela Rigo-Lemini
The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons a central theme in school mathematics and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called ‘Interpretive Model of the Conceptualization of Polygon Congruence’ (MICP). This model emerged from the interpretive analysis of empirical data recollected during the investigation. The MICP categories can be used by teachers or researchers to cover different didactic objectives (e.g., interpret the resolution of tasks with congruence content; prepare student profiles or identify their difficulties. See Peña, 2019) and it is relevant because it does not seem to exist in the literature a similar model that covers the previously stated objectives.
{"title":"Interpretive model of the conceptualization of the congruence of polygons (MICP) / Modelo Interpretativo de la Conceptualización de la Congruencia de Polígonos (MICP)","authors":"C. A. Pena, Mirela Rigo-Lemini","doi":"10.51272/PMENA.42.2020-96","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-96","url":null,"abstract":"The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons a central theme in school mathematics and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called ‘Interpretive Model of the Conceptualization of Polygon Congruence’ (MICP). This model emerged from the interpretive analysis of empirical data recollected during the investigation. The MICP categories can be used by teachers or researchers to cover different didactic objectives (e.g., interpret the resolution of tasks with congruence content; prepare student profiles or identify their difficulties. See Peña, 2019) and it is relevant because it does not seem to exist in the literature a similar model that covers the previously stated objectives.","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":"82436910","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.42.2020-95
Yudi Andrea Ortiz Rocha, Ivonne Twiggy Sandoval Cáceres, A. Sacristán
Spatial reasoning skills are necessary to perform activities at school, at work and in everyday life, in general. Different studies indicate the importance of its development at an early age, since it allows the reading of a three-dimensional world and its interpretation in two-dimensional representations. Our research focuses on the design of activities, using the Theory of Variation, to enhance spatial reasoning skills in seven to eight year-old students. In this document, we present characteristics of the design of an activity based on the use of pentominoes (two-dimensional puzzles). The results show that spatial reasoning skills develop when the following actions are favored: comparing, overlapping, rotating, moving, visualizing, and imagining movements, positions and locations of the pentomino pieces.
{"title":"Development of space reasoning in early ages through variation activities / Diseño de actividades para el desarrollo de razonamiento espacial en edades tempranas a través de manipulativos","authors":"Yudi Andrea Ortiz Rocha, Ivonne Twiggy Sandoval Cáceres, A. Sacristán","doi":"10.51272/PMENA.42.2020-95","DOIUrl":"https://doi.org/10.51272/PMENA.42.2020-95","url":null,"abstract":"Spatial reasoning skills are necessary to perform activities at school, at work and in everyday life, in general. Different studies indicate the importance of its development at an early age, since it allows the reading of a three-dimensional world and its interpretation in two-dimensional representations. Our research focuses on the design of activities, using the Theory of Variation, to enhance spatial reasoning skills in seven to eight year-old students. In this document, we present characteristics of the design of an activity based on the use of pentominoes (two-dimensional puzzles). The results show that spatial reasoning skills develop when the following actions are favored: comparing, overlapping, rotating, moving, visualizing, and imagining movements, positions and locations of the pentomino pieces.","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":"82306508","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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