El objetivo de este artículo es investigar cómo la indagación puede promover la modelización. En particular, se presenta el análisis de los procesos de modelización que emergieron en la implementación de una secuencia didáctica de Enseñanza de las Matemáticas Basada en Indagación. Se trata de una experiencia co-disciplinar, realizada con 23 estudiantes de segundo ciclo de educación primaria de una escuela pública de Badalona en la que, a partir de una situación inicial, el descubrimiento de un tesoro en una casa romana de Baetulo, se intenta responder a quién pudo pertenecer ese tesoro. La metodología consiste, básicamente, en encontrar, en la implementación de dicha secuencia didáctica, evidencias que permitan inferir la aparición de alguno de los subprocesos del modelo del proceso de modelización que se toma como referencia teórica a priori. El principal resultado es que, efectivamente, el proceso de indagación propicia la emergencia de subprocesos de modelización matemática.
{"title":"Papel de la modelización en una experiencia de enseñanza de matemáticas basada en indagación","authors":"Gemma Sala, V. Font","doi":"10.35763/aiem.v0i16.283","DOIUrl":"https://doi.org/10.35763/aiem.v0i16.283","url":null,"abstract":"El objetivo de este artículo es investigar cómo la indagación puede promover la modelización. En particular, se presenta el análisis de los procesos de modelización que emergieron en la implementación de una secuencia didáctica de Enseñanza de las Matemáticas Basada en Indagación. Se trata de una experiencia co-disciplinar, realizada con 23 estudiantes de segundo ciclo de educación primaria de una escuela pública de Badalona en la que, a partir de una situación inicial, el descubrimiento de un tesoro en una casa romana de Baetulo, se intenta responder a quién pudo pertenecer ese tesoro. La metodología consiste, básicamente, en encontrar, en la implementación de dicha secuencia didáctica, evidencias que permitan inferir la aparición de alguno de los subprocesos del modelo del proceso de modelización que se toma como referencia teórica a priori. El principal resultado es que, efectivamente, el proceso de indagación propicia la emergencia de subprocesos de modelización matemática.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46639877","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}
Problem solving is often considered to be an essential part of learning mathematics. In this paper we examine the whole class interactions around problems and problem solving as they naturally occur in mathematics classrooms. Thus, we are examining students’ ordinary experiences of problem solving in their everyday mathematics lessons. Our analysis shows how students’ participate in a very narrow range of problem solving actions and that the actions that they do participate in are controlled by the teacher. This raises implications for what students perceive and interpret problem solving to be in mathematics.
{"title":"Experiences of problem solving in whole class interactions","authors":"J. Ingram, P. Riser","doi":"10.35763/aiem.v0i16.279","DOIUrl":"https://doi.org/10.35763/aiem.v0i16.279","url":null,"abstract":"Problem solving is often considered to be an essential part of learning mathematics. In this paper we examine the whole class interactions around problems and problem solving as they naturally occur in mathematics classrooms. Thus, we are examining students’ ordinary experiences of problem solving in their everyday mathematics lessons. Our analysis shows how students’ participate in a very narrow range of problem solving actions and that the actions that they do participate in are controlled by the teacher. This raises implications for what students perceive and interpret problem solving to be in mathematics.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46529716","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}
Nuestra revista está viviendo tres transiciones conectadas en las direcciones de: (i) llegar a ser más internacional, (ii) llegar a ser más influyente y (iii) llegar a ser más formativa. Como mecanismo al servicio de la comunidad de investigación en educación matemática, AIEM es un proyecto de contribución al desarrollo de esta comunidad mediante acciones dirigidas a situarse e impactar en el estado del arte de mayor nivel – que es necesariamente internacional – y a apoyar a los investigadores para que sus artículos sean útiles a estos dos fines. Este editorial problematiza ciertas interpretaciones de ‘internacional’, ‘influyente’ y ‘formativa’ y apuesta por la priorización de significados científicos.
{"title":"Avances de Investigación en Educación Matemática: Tres transiciones cualitativas en proceso","authors":"Núria Planas","doi":"10.35763/aiem.v0i16.285","DOIUrl":"https://doi.org/10.35763/aiem.v0i16.285","url":null,"abstract":"Nuestra revista está viviendo tres transiciones conectadas en las direcciones de: (i) llegar a ser más internacional, (ii) llegar a ser más influyente y (iii) llegar a ser más formativa. Como mecanismo al servicio de la comunidad de investigación en educación matemática, AIEM es un proyecto de contribución al desarrollo de esta comunidad mediante acciones dirigidas a situarse e impactar en el estado del arte de mayor nivel – que es necesariamente internacional – y a apoyar a los investigadores para que sus artículos sean útiles a estos dos fines. Este editorial problematiza ciertas interpretaciones de ‘internacional’, ‘influyente’ y ‘formativa’ y apuesta por la priorización de significados científicos.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42903091","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}
Esta investigación establece el significado institucional de referencia del máximo común divisor para estudiantes del Grado en Ingeniería Informática a través de un estudio epistemológico. Ello nos ha permitido crear una herramienta de análisis didáctico que posibilita el estudio de las características del significado pretendido en manuales representativos, a pesar de la diversidad curricular propia de la etapa universitaria. La comparativa entre manuales muestra una importante diferencia entre un texto que trabaja en entornos computacionales, donde son relevantes las aplicaciones informáticas y los procedimientos; frente a otro, en el que se realizan fuertes procesos de generalización, pero no se consideran aplicaciones. Son destacadas las restricciones en los dominios de definición y la ausencia de demostraciones en el libro más recomendado. Esto permite extraer carencias de significado y mostrar una tendencia en la enseñanza hacia la preeminencia de lo particular frente a lo general, fuente de conflictos semióticos potenciales.
{"title":"Enseñanza del mcd en el Grado en Ingeniería Informática mediada por un entorno computacional","authors":"Carmen Ordóñez, L. Ordóñez, Ángel Contreras","doi":"10.35763/aiem.v0i16.236","DOIUrl":"https://doi.org/10.35763/aiem.v0i16.236","url":null,"abstract":"Esta investigación establece el significado institucional de referencia del máximo común divisor para estudiantes del Grado en Ingeniería Informática a través de un estudio epistemológico. Ello nos ha permitido crear una herramienta de análisis didáctico que posibilita el estudio de las características del significado pretendido en manuales representativos, a pesar de la diversidad curricular propia de la etapa universitaria. La comparativa entre manuales muestra una importante diferencia entre un texto que trabaja en entornos computacionales, donde son relevantes las aplicaciones informáticas y los procedimientos; frente a otro, en el que se realizan fuertes procesos de generalización, pero no se consideran aplicaciones. Son destacadas las restricciones en los dominios de definición y la ausencia de demostraciones en el libro más recomendado. Esto permite extraer carencias de significado y mostrar una tendencia en la enseñanza hacia la preeminencia de lo particular frente a lo general, fuente de conflictos semióticos potenciales.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805612","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}
As society continues to progress, it is becoming more and more important to deal with issues mathematically, take risks and uncertainty into consideration, clarify the grounds in participating in judgements or decision-making, and make critical deliberations. This competence is defined as "decision-making”. We present the design of a task about saving more lives with automatic external defibrillators (AEDs), aimed at fostering this competency in mathematics lessons. In methodological terms, we use Lesson Study to carefully anticipate the process of students’ finding and solving problems. We review the design from different viewpoint, such as “What times and how should all the students in the class study?” or “When and what kind of materials should be presented?”
{"title":"Task design to foster the competence in social decision-making on mathematics education","authors":"Keiichi Nishimura, Chiharu Honda","doi":"10.35763/AIEM.V0I15.261","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.261","url":null,"abstract":"As society continues to progress, it is becoming more and more important to deal with issues mathematically, take risks and uncertainty into consideration, clarify the grounds in participating in judgements or decision-making, and make critical deliberations. This competence is defined as \"decision-making”. We present the design of a task about saving more lives with automatic external defibrillators (AEDs), aimed at fostering this competency in mathematics lessons. In methodological terms, we use Lesson Study to carefully anticipate the process of students’ finding and solving problems. We review the design from different viewpoint, such as “What times and how should all the students in the class study?” or “When and what kind of materials should be presented?”","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47208326","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}
Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the development of the basic principles of the mathematics of change. The study combines design and research in three successive phases. In the first phase a hypothetical learning trajectory and instructional activities are designed, in the teaching experiment phase the trajectory is acted out, and in the phase of the retrospective analysis the articulated hypotheses are reflected upon. In this way, a cyclic process of (re)design and development of innovative teaching is structured. The resulting local instruction theory is expected to create opportunities for teachers, textbook authors and researchers to consider contextual factors and to adapt results for their research or teaching.
{"title":"Design and research for developing local instruction theories","authors":"M. Doorman","doi":"10.35763/AIEM.V0I15.266","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.266","url":null,"abstract":"Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the development of the basic principles of the mathematics of change. The study combines design and research in three successive phases. In the first phase a hypothetical learning trajectory and instructional activities are designed, in the teaching experiment phase the trajectory is acted out, and in the phase of the retrospective analysis the articulated hypotheses are reflected upon. In this way, a cyclic process of (re)design and development of innovative teaching is structured. The resulting local instruction theory is expected to create opportunities for teachers, textbook authors and researchers to consider contextual factors and to adapt results for their research or teaching.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42095264","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}
Francisco García, Berta Barquero, Ignasi Florensa, Marianna Bosch
En la Teoría Antropológica de lo Didáctico (TAD), el diseño de tareas se integra dentro de su metodología experimental planteada en términos de ingeniería didáctica. La implementación de nuevas organizaciones de enseñanza y aprendizaje, basadas en nuevas formas de concebir las actividades matemáticas escolares, se inscribe en una problemática epistemológica e institucional. En este artículo, presentamos una reflexión sobre los objetivos, los principios, la metodología y el alcance que atribuimos a este trabajo experimental. La reflexión se complementa con la descripción de tres casos, que sirven para ejemplificar cómo estos objetivos, principios y metodología han sido implementados en procesos didácticos concretos. Concluimos con una reflexión sobre la necesaria dialéctica y articulación entre investigación, diseño y prácticas de aula a fin de profundizar en el análisis de la ecología de estas propuestas, es decir, de las condiciones que permiten que ciertas tareas puedan vivir en las instituciones docentes, así como las restricciones que impiden su desarrollo como actividades normalizadas en el aula, desde una visión no normativa de la investigación didáctica.
{"title":"Diseño de tareas en el marco de la Teoría Antropológica de lo Didáctico","authors":"Francisco García, Berta Barquero, Ignasi Florensa, Marianna Bosch","doi":"10.35763/AIEM.V0I15.267","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.267","url":null,"abstract":"En la Teoría Antropológica de lo Didáctico (TAD), el diseño de tareas se integra dentro de su metodología experimental planteada en términos de ingeniería didáctica. La implementación de nuevas organizaciones de enseñanza y aprendizaje, basadas en nuevas formas de concebir las actividades matemáticas escolares, se inscribe en una problemática epistemológica e institucional. En este artículo, presentamos una reflexión sobre los objetivos, los principios, la metodología y el alcance que atribuimos a este trabajo experimental. La reflexión se complementa con la descripción de tres casos, que sirven para ejemplificar cómo estos objetivos, principios y metodología han sido implementados en procesos didácticos concretos. Concluimos con una reflexión sobre la necesaria dialéctica y articulación entre investigación, diseño y prácticas de aula a fin de profundizar en el análisis de la ecología de estas propuestas, es decir, de las condiciones que permiten que ciertas tareas puedan vivir en las instituciones docentes, así como las restricciones que impiden su desarrollo como actividades normalizadas en el aula, desde una visión no normativa de la investigación didáctica.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42093116","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}
Topic-specific Didactical Design Research is a research methodology with two aims, 1) designing and improving teaching-learning arrangements and 2) generating theoretical contributions for understanding the initiated teaching-learning processes for a certain topic. The article provides methodological reflections and examples for elaborating the meaning of theorizing within this methodology. Starting from a distinction of categorial, descriptive, explanatory, normative and predictive theory elements with their functions and logical structures, the examples show that theorizing in Design Research studies can be conceived as a process of successively developing and connecting theory elements, for the how-questions (the rationales for the arrangements) and the what-questions (the structuring of the learning content). The considerations are illustrated for the case of topic-specific Didactical Design Research for language-responsive classrooms, particularly in relation to language learners’ conceptual understanding of fractions, variables, and percentages.
{"title":"Theorizing in Design Research","authors":"Susanne Prediger","doi":"10.35763/AIEM.V0I15.265","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.265","url":null,"abstract":"Topic-specific Didactical Design Research is a research methodology with two aims, 1) designing and improving teaching-learning arrangements and 2) generating theoretical contributions for understanding the initiated teaching-learning processes for a certain topic. The article provides methodological reflections and examples for elaborating the meaning of theorizing within this methodology. Starting from a distinction of categorial, descriptive, explanatory, normative and predictive theory elements with their functions and logical structures, the examples show that theorizing in Design Research studies can be conceived as a process of successively developing and connecting theory elements, for the how-questions (the rationales for the arrangements) and the what-questions (the structuring of the learning content). The considerations are illustrated for the case of topic-specific Didactical Design Research for language-responsive classrooms, particularly in relation to language learners’ conceptual understanding of fractions, variables, and percentages.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46067246","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 paper discusses the role of task design in APOS Theory. The role played by the genetic decomposition in the theory and in task design is discussed. An example of a genetic decomposition for the concepts of inverse matrix transformation and inverse matrix is given. Tasks designed using this tool as a guide are exemplified and a description of their relationship to the genetic decomposition accompanies them. This provides insights about each task and the specific detailed construction it has as its aim. The role of the tasks in the classroom is discussed since the combination of collaborative work of students in sequences of tasks and in group discussions are the foundation of APOS theory’s potential to promote essential constructions needed for a deep learning of mathematical concepts.
{"title":"Task design in APOS Theory","authors":"M. Trigueros, Asuman Oktaç","doi":"10.35763/AIEM.V0I15.256","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.256","url":null,"abstract":"This paper discusses the role of task design in APOS Theory. The role played by the genetic decomposition in the theory and in task design is discussed. An example of a genetic decomposition for the concepts of inverse matrix transformation and inverse matrix is given. Tasks designed using this tool as a guide are exemplified and a description of their relationship to the genetic decomposition accompanies them. This provides insights about each task and the specific detailed construction it has as its aim. The role of the tasks in the classroom is discussed since the combination of collaborative work of students in sequences of tasks and in group discussions are the foundation of APOS theory’s potential to promote essential constructions needed for a deep learning of mathematical concepts.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44687133","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}
El diseno de actividades, de tareas, de secuencias o, en general, de algun tipo de material curricular para la ensenanza, es una parte crucial del trabajo de investigacion en didactica de las matematicas. Como senalan Watson y Ohtani (2015), ya sea desde una perspectiva cognitiva, cultural o practica, las tareas son el fundamento del aprendizaje matematico. Por unificar terminologia, uso el termino tarea, deliberadamente, en un sentido amplio e indefinido en cierta forma. Cada contribucion dara un sentido mas preciso a este termino a lo largo del actual monografico.
{"title":"Introducción a 'Diseño de tareas en educación matemática: Una diversidad de marcos teóricos'","authors":"F. García","doi":"10.35763/AIEM.V0I15.264","DOIUrl":"https://doi.org/10.35763/AIEM.V0I15.264","url":null,"abstract":"El diseno de actividades, de tareas, de secuencias o, en general, de algun tipo de material curricular para la ensenanza, es una parte crucial del trabajo de investigacion en didactica de las matematicas. Como senalan Watson y Ohtani (2015), ya sea desde una perspectiva cognitiva, cultural o practica, las tareas son el fundamento del aprendizaje matematico. Por unificar terminologia, uso el termino tarea, deliberadamente, en un sentido amplio e indefinido en cierta forma. Cada contribucion dara un sentido mas preciso a este termino a lo largo del actual monografico.","PeriodicalId":52046,"journal":{"name":"Avances de Investigacion en Educacion Matematica","volume":null,"pages":null},"PeriodicalIF":0.1,"publicationDate":"2019-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42176471","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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