{"title":"Mediadores verbales para la transferencia del aprendizaje en matemáticas","authors":"Elfriede Wenzelburguer","doi":"10.24844/em0101.03","DOIUrl":"https://doi.org/10.24844/em0101.03","url":null,"abstract":"","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123970895","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}
Miguel Rodríguez, Arturo Mena-Lorca, P. Gregori, Patricia Vásquez, María del Valle, Marcela Parraguez
: This article reports the Chilean high school and university students’ understanding of the Solution Set of a System of Linear Equations of Three Equations and Two Unknowns (CSSEL 3x2). The study is based on the theory of Modes of Thought, with a Case Study methodology and the use of Implicative Statistics. As a strategy, equivalent equations were used to investigate the influence of the concept of linear dependence on the path to the different ways of conceiv-ing its set of solutions. The use of the concept of slope and the idea of linear combination as mechanisms to transit between the synthetic-geometric and ana-lytical modes associated with the CSSEL3x2 stand out in the students’ responses. A disarticulation between the different ways of thinking the whole solution when parameters are incorporated to the coefficients of the equations was observed, which is particularly noticeable for students who had studied Linear Algebra. On the other hand, we show that the concept of linear dependence that is brought into play in the analysis is restricted to the case of scalar multiples.
{"title":"Comprensión del conjunto solución de un sistema de ecuaciones lineales de dos incógnitas: un estudio de casos","authors":"Miguel Rodríguez, Arturo Mena-Lorca, P. Gregori, Patricia Vásquez, María del Valle, Marcela Parraguez","doi":"10.24844/em3403.06","DOIUrl":"https://doi.org/10.24844/em3403.06","url":null,"abstract":": This article reports the Chilean high school and university students’ understanding of the Solution Set of a System of Linear Equations of Three Equations and Two Unknowns (CSSEL 3x2). The study is based on the theory of Modes of Thought, with a Case Study methodology and the use of Implicative Statistics. As a strategy, equivalent equations were used to investigate the influence of the concept of linear dependence on the path to the different ways of conceiv-ing its set of solutions. The use of the concept of slope and the idea of linear combination as mechanisms to transit between the synthetic-geometric and ana-lytical modes associated with the CSSEL3x2 stand out in the students’ responses. A disarticulation between the different ways of thinking the whole solution when parameters are incorporated to the coefficients of the equations was observed, which is particularly noticeable for students who had studied Linear Algebra. On the other hand, we show that the concept of linear dependence that is brought into play in the analysis is restricted to the case of scalar multiples.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"50 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120855771","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}
Jeannette Galleguillos, MIguel Ribeiro, Miguel Montes
: This paper focuses on the mathematical knowledge displayed and developed by a group of teachers when discussing a problem of maximization and some of its possible variations. The research was approached qualitatively by observing a group of mathematics teachers’ during the discussion involved in solving the problem. The analysis was carried out focusing on the teacher’s mathematical knowledge specificities, perceived in the Mathematics Teachers’ Specialized Knowledge (MTSK) perspective. The data reveal different in-depth levels of mathematical knowledge deployed and developed by teachers in problem-solving, which were associated with MTSK categories. The results show that, by solving the problem in different ways and observing different variants, the teacher’s mathematical knowledge was mobilized: in relation to the use of various geometric figures to design unusual pens; in the application and relationship of various mathematical notions in finding the resolution, and in the establishment of conjectures and possibilities of developing new knowledge. Thus, new indicators of teachers’ mathematical specialized knowledge are discussed.
{"title":"El conocimiento matemático que despliega y desarrolla un grupo de profesores en la resolución del problema del corral","authors":"Jeannette Galleguillos, MIguel Ribeiro, Miguel Montes","doi":"10.24844/em3403.07","DOIUrl":"https://doi.org/10.24844/em3403.07","url":null,"abstract":": This paper focuses on the mathematical knowledge displayed and developed by a group of teachers when discussing a problem of maximization and some of its possible variations. The research was approached qualitatively by observing a group of mathematics teachers’ during the discussion involved in solving the problem. The analysis was carried out focusing on the teacher’s mathematical knowledge specificities, perceived in the Mathematics Teachers’ Specialized Knowledge (MTSK) perspective. The data reveal different in-depth levels of mathematical knowledge deployed and developed by teachers in problem-solving, which were associated with MTSK categories. The results show that, by solving the problem in different ways and observing different variants, the teacher’s mathematical knowledge was mobilized: in relation to the use of various geometric figures to design unusual pens; in the application and relationship of various mathematical notions in finding the resolution, and in the establishment of conjectures and possibilities of developing new knowledge. Thus, new indicators of teachers’ mathematical specialized knowledge are discussed.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114233085","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}
Horacio Solar Bezmalinovic, Manuel Goizueta, Sebastián Howard Montaner
: The article draws on the assumption that interaction patterns emerge from and are associated with situations that participants are able to recognize. As part of an exploratory case study, we analyze interaction patterns that emerge in two mathematics secondary classrooms characterized by the teachers’ support of students’ argumentation. Results account for relationships between teachers’ support of argumentation and focus interaction patterns, where the teacher avoids assessment of students’ statements. We discuss the relevance of argumentation and teacher’s actions to support it as elements to foster educatively significant interactions in the mathematics classroom.
{"title":"Emergencia de patrones de interacción al promover la argumentación en el aula de matemáticas","authors":"Horacio Solar Bezmalinovic, Manuel Goizueta, Sebastián Howard Montaner","doi":"10.24844/em3403.05","DOIUrl":"https://doi.org/10.24844/em3403.05","url":null,"abstract":": The article draws on the assumption that interaction patterns emerge from and are associated with situations that participants are able to recognize. As part of an exploratory case study, we analyze interaction patterns that emerge in two mathematics secondary classrooms characterized by the teachers’ support of students’ argumentation. Results account for relationships between teachers’ support of argumentation and focus interaction patterns, where the teacher avoids assessment of students’ statements. We discuss the relevance of argumentation and teacher’s actions to support it as elements to foster educatively significant interactions in the mathematics classroom.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126746138","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":"Conocimiento especializado del profesorado de Educación Primaria para enseñar estadística y probabilidad","authors":"Joan Franco Seguí, Á. Alsina","doi":"10.24844/em3403.03","DOIUrl":"https://doi.org/10.24844/em3403.03","url":null,"abstract":"","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122797440","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}
: In this study, we analysed the topics taught in probability in 57 countries. We made a conceptual structure in which we present the concepts, representations and phenomena that give meaning to this topic at this educational level. Based on that information, we reviewed the curricular information on probability up to the fourth grade in the 56 countries that participated in the international TIMSS 2015 study and in Colombia. Then, we compared the curricular information of the countries analyzed with the information found in Colombia. We found that approximately 45% of the countries that participated in TIMSS still do not include information for teaching probability in their curricula or only include the term probability. In the other countries and in Colombia, we identified that the most common topics are related to determining the possibility of the occurrence of events (possible, impossible, certain) in everyday life contexts that involve uncertainty or chance. We concluded that, although the literature shows the importance of including probability in the curriculum, its teaching still requires higher attention at this educational level.
{"title":"Probabilidad en diferentes países del mundo: enseñanza de la probabilidad en educación primaria","authors":"Camilo López, P. Gómez","doi":"10.24844/em3403.02","DOIUrl":"https://doi.org/10.24844/em3403.02","url":null,"abstract":": In this study, we analysed the topics taught in probability in 57 countries. We made a conceptual structure in which we present the concepts, representations and phenomena that give meaning to this topic at this educational level. Based on that information, we reviewed the curricular information on probability up to the fourth grade in the 56 countries that participated in the international TIMSS 2015 study and in Colombia. Then, we compared the curricular information of the countries analyzed with the information found in Colombia. We found that approximately 45% of the countries that participated in TIMSS still do not include information for teaching probability in their curricula or only include the term probability. In the other countries and in Colombia, we identified that the most common topics are related to determining the possibility of the occurrence of events (possible, impossible, certain) in everyday life contexts that involve uncertainty or chance. We concluded that, although the literature shows the importance of including probability in the curriculum, its teaching still requires higher attention at this educational level.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134115818","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}
Ana E. Madrid, Silvia M. Valenzuela-Ruiz, Carmen Batanero
: The box plot was developed by Tukey as a tool in exploratory data analysis and is used to summarise and compare distributions in terms of their extreme values, median and quartiles. Although its teaching is included in various curricular guidelines for secondary education, research related to its understanding is still scarce. In order to identify semiotic conflicts in its interpretation, we present the results of a study to evaluate the understanding of this graph in 148 university students of Physical Activity and Sport Sciences after studying the subject. The open responses to a task with four questions related to the identification of the median and outliers in the graph and the interpretation of the quartiles and whiskers are analysed, looking at the reading level achieved. The results show ease of identification of the elements of the graph, although we observe semiotic conflicts related to the definition and computation of median and confusion of other concepts.
{"title":"Interpretación del diagrama de caja por estudiantes universitarios de ciencias de la actividad física y deporte","authors":"Ana E. Madrid, Silvia M. Valenzuela-Ruiz, Carmen Batanero","doi":"10.24844/em3403.10","DOIUrl":"https://doi.org/10.24844/em3403.10","url":null,"abstract":": The box plot was developed by Tukey as a tool in exploratory data analysis and is used to summarise and compare distributions in terms of their extreme values, median and quartiles. Although its teaching is included in various curricular guidelines for secondary education, research related to its understanding is still scarce. In order to identify semiotic conflicts in its interpretation, we present the results of a study to evaluate the understanding of this graph in 148 university students of Physical Activity and Sport Sciences after studying the subject. The open responses to a task with four questions related to the identification of the median and outliers in the graph and the interpretation of the quartiles and whiskers are analysed, looking at the reading level achieved. The results show ease of identification of the elements of the graph, although we observe semiotic conflicts related to the definition and computation of median and confusion of other concepts.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121892548","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 study of external representations in early algebra usually focuses on formal symbolic aspects. Therefore, little is known about the role those other representations might play in the development of algebraic thinking. This article analyses representations like drawings, schemes, and idiosyncratic sym-bols spontaneously produced by third-grade elementary students ( n =27) during an early algebra program with generalized arithmetic and functional thinking components. The program was evaluated through a pre-test, posttest design. There was a significant increase in the students’ generalized arithmetic and functional thinking performance. The sophistication of the representations produced by the students increased for the functional problems but not for the generalized arithmetic problems. During the program, the levels of representations remained stable. It was found that the production of more sophisticated representations was associated with a better performance in functional problems but not on generalized arithmetic problems. The notion of how the production of external representations can support the acquisition of algebraic ideas is discussed. Conclusions are drawn by highlighting some theoretical and prac-tical implications of the study.
{"title":"Un análisis de la producción de representaciones al solucionar problemas de álgebra temprana en estudiantes de primaria","authors":"Ana Medrano, Ulises Xolocotzin, R. Flores-Macías","doi":"10.24844/em3403.01","DOIUrl":"https://doi.org/10.24844/em3403.01","url":null,"abstract":": The study of external representations in early algebra usually focuses on formal symbolic aspects. Therefore, little is known about the role those other representations might play in the development of algebraic thinking. This article analyses representations like drawings, schemes, and idiosyncratic sym-bols spontaneously produced by third-grade elementary students ( n =27) during an early algebra program with generalized arithmetic and functional thinking components. The program was evaluated through a pre-test, posttest design. There was a significant increase in the students’ generalized arithmetic and functional thinking performance. The sophistication of the representations produced by the students increased for the functional problems but not for the generalized arithmetic problems. During the program, the levels of representations remained stable. It was found that the production of more sophisticated representations was associated with a better performance in functional problems but not on generalized arithmetic problems. The notion of how the production of external representations can support the acquisition of algebraic ideas is discussed. Conclusions are drawn by highlighting some theoretical and prac-tical implications of the study.","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121998988","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 Valenzuela García, María del Socorro García, Judith Alejandra Hernández, Humberto Gutiérrez Pulido
{"title":"Promoción de redes académicas para el área de matemática educativa en el 55 Congreso Nacional de la Sociedad Matemática Mexicana","authors":"Carlos Valenzuela García, María del Socorro García, Judith Alejandra Hernández, Humberto Gutiérrez Pulido","doi":"10.24844/em3403.16","DOIUrl":"https://doi.org/10.24844/em3403.16","url":null,"abstract":"","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134157345","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":"Jeremy Kilpatrick: un caballero y un profesional","authors":"Douglas B. McLeod, M. S. G. García González","doi":"10.24844/em3403.17","DOIUrl":"https://doi.org/10.24844/em3403.17","url":null,"abstract":"","PeriodicalId":438012,"journal":{"name":"Educación matemática","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134536477","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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