Main area of research: didactics of mathematics or mathematics education, in the framework of the Anthropological theory of the didactic (ATD), mainly focusing on secondary, tertiary and lifelong education.
Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics
We present the design and implementation of an inquiry-based activity based on a general proposal... more We present the design and implementation of an inquiry-based activity based on a general proposal of the Anthropological Theory of the Didactic called “study and research path for teacher education” (SRP-TE) as a tool to reflect, develop, analyze, and experience proposals for teaching statistics at lower secondary school. Our proposal of SRP-TE starts from a textbook activity based on a statistical graph about water distribution in Brazil and turns it into an open activity that fosters different dimensions of statistical work (searching, collecting, cleaning, organizing, and exploring data), including interdisciplinary interaction. After its implementation, when asked about the content inherent in the inquiry, pre-service teachers seem to disregard many dimensions of the statistical work, especially those related to data handling.
Nuestra investigación se centra en la implementación de propuestas de enseñanza a nivel universit... more Nuestra investigación se centra en la implementación de propuestas de enseñanza a nivel universitario que promuevan un cambio del paradigma pedagógico. Partimos del paradigma dominante en estas instituciones, principalmente basado en la visita de los saberes como si fueran monumentos, para avanzar hacia un paradigma más centrado en el estudio de cuestiones. En el marco de teoría antropológica de lo didáctico, hemos trabajado en el diseño de los recorridos de estudio e investigación (REI) como dispositivos de enseñanza en la transición entre paradigmas, los cuales se han desarrollado en distintas modalidades. En este trabajo, nos centramos en la formación universitaria del profesorado como agente crucial en este cambio, y nos centramos en la adaptación de los REI al caso de la formación del profesorado (REI-FP). Veremos en qué sentido los REI-FP permiten avanzar en el estudio de las condiciones y restricciones que emergen en la difusión de los REI.
This paper focuses on the role of combinatorics as a modelling tool to inquire about different si... more This paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks' problem situation. We consider students' construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the rel...
En este trabajo se propone y se analiza, desde la Teoria Antropologica de lo Didactico (TAD), un ... more En este trabajo se propone y se analiza, desde la Teoria Antropologica de lo Didactico (TAD), un ejemplo de organizacion didactica en torno a la Numeracion que se experimento durante 11 sesiones en una clase de 3o de ESO de un instituto de Madrid. El diseno del proceso se basa en los ultimos desarrollos de la TAD (Chevallard 2002), que pretenden contribuir a una ensenanza renovada de las Matematicas. Para ello, se propone, por un lado, que el profesor pase de ser “ensenante” a asumir el papel de director de estudio, guiando y animando el estudio e investigacion de los alumnos, sobre una cuestion problematica a la que intentan aportar una respuesta; y, por otro, que las razones de ser, que han motivado la creacion y el desarrollo del conocimiento matematico, esto es, las cuestiones a las que dicho conocimiento responde, formen parte del programa de estudios.
I analyze the interplay of theories within a study on computer-based mathematics teaching. I will... more I analyze the interplay of theories within a study on computer-based mathematics teaching. I will address divergences in their conceptualization of the empirical realities, influences on the interpretation of data, characteristics of my linking strategies, and issues of compatibility.
One of the main research gestures within the Anthropological Theory of the Didactic (ATD) consist... more One of the main research gestures within the Anthropological Theory of the Didactic (ATD) consists in questioning the mathematical knowledge that is at the core of teaching and learning processes. In the case of university education, and because the knowledge at stake is closely related to scholar knowledge, this questioning might seem less necessary and the tendency is to focus on the possible different ways of organizing its teaching. Through the example of Group Theory we illustrate the methodology of questioning proposed by ATD in two different moments of the evolution of this framework: a first one centred on the structure and dynamics of the different components of mathematical praxeologies; a second one more focused on the raison d'etre and functionality of what is taught and learnt.
Esta investigacion se propone estudiar las respuestas de alumnos de primer curso de secundaria (1... more Esta investigacion se propone estudiar las respuestas de alumnos de primer curso de secundaria (12-13 anos) a una actividad de estudio e investigacion sobre las relaciones entre area y perimetro de figuras planas estructurada en base a los momentos didacticos (Chevallard 1999). Presentamos una primera fase de la actividad experimentada en tres sesiones, donde aparecen los momentos del primer encuentro y el exploratorio, junto con una actividad de evaluacion. El analisis de las respuestas permite establecer los resultados sobre las estrategias de comparaciones de magnitudes y de medida, su apropiacion y su posible explotacion en momentos posteriores de la experimentacion.
We present the design process of a Study and Research Path (SRP) in a course of General Elasticit... more We present the design process of a Study and Research Path (SRP) in a course of General Elasticity, belonging to a degree of Mechanical Engineering. General elasticity is a field with a high presence of mathematical modelling, and in fact, it cannot be conceived without mathematics. We take as a starting point the observation of several didactic facts associated to the actual pedagogical and didactical organization of the course. The SRP design tries to overcome these didactical facts by proposing a possible new rationale for teaching General Elasticity. We have carried out an a priori analysis of the SRP in order to evaluate to what extent the generating question is rich enough to act as the main motivation of the community of study. A systematic plan to collect data during experimentation is also presented.
Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics
We present the design and implementation of an inquiry-based activity based on a general proposal... more We present the design and implementation of an inquiry-based activity based on a general proposal of the Anthropological Theory of the Didactic called “study and research path for teacher education” (SRP-TE) as a tool to reflect, develop, analyze, and experience proposals for teaching statistics at lower secondary school. Our proposal of SRP-TE starts from a textbook activity based on a statistical graph about water distribution in Brazil and turns it into an open activity that fosters different dimensions of statistical work (searching, collecting, cleaning, organizing, and exploring data), including interdisciplinary interaction. After its implementation, when asked about the content inherent in the inquiry, pre-service teachers seem to disregard many dimensions of the statistical work, especially those related to data handling.
Nuestra investigación se centra en la implementación de propuestas de enseñanza a nivel universit... more Nuestra investigación se centra en la implementación de propuestas de enseñanza a nivel universitario que promuevan un cambio del paradigma pedagógico. Partimos del paradigma dominante en estas instituciones, principalmente basado en la visita de los saberes como si fueran monumentos, para avanzar hacia un paradigma más centrado en el estudio de cuestiones. En el marco de teoría antropológica de lo didáctico, hemos trabajado en el diseño de los recorridos de estudio e investigación (REI) como dispositivos de enseñanza en la transición entre paradigmas, los cuales se han desarrollado en distintas modalidades. En este trabajo, nos centramos en la formación universitaria del profesorado como agente crucial en este cambio, y nos centramos en la adaptación de los REI al caso de la formación del profesorado (REI-FP). Veremos en qué sentido los REI-FP permiten avanzar en el estudio de las condiciones y restricciones que emergen en la difusión de los REI.
This paper focuses on the role of combinatorics as a modelling tool to inquire about different si... more This paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks' problem situation. We consider students' construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the rel...
En este trabajo se propone y se analiza, desde la Teoria Antropologica de lo Didactico (TAD), un ... more En este trabajo se propone y se analiza, desde la Teoria Antropologica de lo Didactico (TAD), un ejemplo de organizacion didactica en torno a la Numeracion que se experimento durante 11 sesiones en una clase de 3o de ESO de un instituto de Madrid. El diseno del proceso se basa en los ultimos desarrollos de la TAD (Chevallard 2002), que pretenden contribuir a una ensenanza renovada de las Matematicas. Para ello, se propone, por un lado, que el profesor pase de ser “ensenante” a asumir el papel de director de estudio, guiando y animando el estudio e investigacion de los alumnos, sobre una cuestion problematica a la que intentan aportar una respuesta; y, por otro, que las razones de ser, que han motivado la creacion y el desarrollo del conocimiento matematico, esto es, las cuestiones a las que dicho conocimiento responde, formen parte del programa de estudios.
I analyze the interplay of theories within a study on computer-based mathematics teaching. I will... more I analyze the interplay of theories within a study on computer-based mathematics teaching. I will address divergences in their conceptualization of the empirical realities, influences on the interpretation of data, characteristics of my linking strategies, and issues of compatibility.
One of the main research gestures within the Anthropological Theory of the Didactic (ATD) consist... more One of the main research gestures within the Anthropological Theory of the Didactic (ATD) consists in questioning the mathematical knowledge that is at the core of teaching and learning processes. In the case of university education, and because the knowledge at stake is closely related to scholar knowledge, this questioning might seem less necessary and the tendency is to focus on the possible different ways of organizing its teaching. Through the example of Group Theory we illustrate the methodology of questioning proposed by ATD in two different moments of the evolution of this framework: a first one centred on the structure and dynamics of the different components of mathematical praxeologies; a second one more focused on the raison d'etre and functionality of what is taught and learnt.
Esta investigacion se propone estudiar las respuestas de alumnos de primer curso de secundaria (1... more Esta investigacion se propone estudiar las respuestas de alumnos de primer curso de secundaria (12-13 anos) a una actividad de estudio e investigacion sobre las relaciones entre area y perimetro de figuras planas estructurada en base a los momentos didacticos (Chevallard 1999). Presentamos una primera fase de la actividad experimentada en tres sesiones, donde aparecen los momentos del primer encuentro y el exploratorio, junto con una actividad de evaluacion. El analisis de las respuestas permite establecer los resultados sobre las estrategias de comparaciones de magnitudes y de medida, su apropiacion y su posible explotacion en momentos posteriores de la experimentacion.
We present the design process of a Study and Research Path (SRP) in a course of General Elasticit... more We present the design process of a Study and Research Path (SRP) in a course of General Elasticity, belonging to a degree of Mechanical Engineering. General elasticity is a field with a high presence of mathematical modelling, and in fact, it cannot be conceived without mathematics. We take as a starting point the observation of several didactic facts associated to the actual pedagogical and didactical organization of the course. The SRP design tries to overcome these didactical facts by proposing a possible new rationale for teaching General Elasticity. We have carried out an a priori analysis of the SRP in order to evaluate to what extent the generating question is rich enough to act as the main motivation of the community of study. A systematic plan to collect data during experimentation is also presented.
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Papers by Marianna Bosch