Noemí Ruiz Munzón | Tecnocampus de Mataro (original) (raw)

Papers by Noemí Ruiz Munzón

Research paper thumbnail of Actividades de estudio e investigación para introducir los números negativos en un entorno algebraico

Research paper thumbnail of El portafolio electrónico mediante moodle para el seguimiento y evaluación del trabajo final de grado

Research paper thumbnail of El problema del álgebra elemental en la teoría antropológica de lo didáctico

Los primeros trabajos sobre la transposición didáctica del álgebra, llevados a cabo por Yves Chev... more Los primeros trabajos sobre la transposición didáctica del álgebra, llevados a cabo por Yves Chevallard en la década de los 80 del siglo pasado, pusieron de manifiesto que, en primera instancia, el álgebra es un instrumento-el instrumento algebraico-que culmina en la modelización algebraica y transforma completamente las condiciones del trabajo matemático. En coherencia con esta posición epistemológica, las investigaciones desarrolladas a lo largo de los últimos 25 años sobre el álgebra elemental en el ámbito de la teoría antropológica de lo didáctico proponen considerar este dominio como un proceso de algebrización, ampliando así el ámbito de la actividad matemática escolar en el que se suele situar el problema didáctico correspondiente. Hemos estudiado, como componentes de dicho problema, la relación entre «lo numérico» y «lo algebraico», la algebrización de la proporcionalidad, la construcción de los números enteros como objetos algebraicos y el desarrollo de la modelización algebraica hacia la modelización funcional. Palabras clave: teoría antropológica de lo didáctico, modelización algebraica, proceso de algebrización, problema didáctico.

Research paper thumbnail of Comparing Approaches Through a Reference Epistemological Model: The Case of School Algebra

Luis Radford and Yves Chevallard, whose last two research programmes in mathematics education wer... more Luis Radford and Yves Chevallard, whose last two research programmes in mathematics education were awarded with the Hans Freudenthal medal, have both given a prime place to the problem of teaching and learning elementary algebra. However, their approaches are far from being similar. Are they comparable? We are starting a dialogue considering how each approach, in a more or less explicit way, defines what algebra is, that is, how it characterises ‘algebraic thinking’ or ‘algebraic activities’ with what we call a reference epistemological model (REM) of elementary algebra. The dialogue starts by assuming the point of view of the Anthropological Theory of the Didactic (ATD), presenting our own REM, and the kind of questions addressed by this approach, in relation to the Theory of Knowledge Objectification developed by Radford.

Research paper thumbnail of El problema del álgebra elemental en la teoría antropológicade lo didáctico

Los primeros trabajos sobre la transposicion didactica del algebra, llevados a cabo por Yves Chev... more Los primeros trabajos sobre la transposicion didactica del algebra, llevados a cabo por Yves Chevallard en la decada de los 80 del siglo pasado, pusieron de manifiesto que, en primera instancia, el algebra es un instrumento —el instrumento algebraico— que culmina en la modelizacion algebraica y transforma completamente las condiciones del trabajo matematico. En coherencia con esta posicion epistemologica, las investigaciones desarrolladas a lo largo de los ultimos 25 anos sobre el algebra elemental en el ambito de la teoria antropologica de lo didactico proponen considerar este dominio como un proceso de algebrizacion, ampliando asi el ambito de la actividad matematica escolar en el que se suele situar el problema didactico correspondiente. Hemos estudiado, como componentes de dicho problema, la relacion entre «lo numerico» y «lo algebraico», la algebrizacion de la proporcionalidad, la construccion de los numeros enteros como objetos algebraicos y el desarrollo de la modelizacion al...

Research paper thumbnail of Un modelo epistemológico de referencia del álgebra como instrumento de modelización

The aim of this work is to coordinate and complete the papers we presented at the first two confe... more The aim of this work is to coordinate and complete the papers we presented at the first two conferences on the ATD. We propose a reference epistemRORJLFDOPRGHOWKDWLV�≥JOREDO¥�HQRXJKWRSURYLGHDEDVLVIRUW KHVFKRRO� genesis of algebra as a modelling tool and to support a progressive development of the algebraisation process of school mathematics leading to functional modelling.

Research paper thumbnail of “Think Global, Act Local”: un método de diálogo epistemológico para reducir la brecha entre universidad-empresa en el ámbito del marketing

Research paper thumbnail of La introducción del álgebra elemental y su desarrollo hacia la modelización funcional

Resumen: Nuestra investigación parte de los trabajos en torno al problema didáctico del álgebra e... more Resumen: Nuestra investigación parte de los trabajos en torno al problema didáctico del álgebra elemental realizados por el investigador francés Yves Chevallard (1984, 1986, 1989a, 1989b, 1990a y 1990b). En estos trabajos se puso de manifiesto que la función ...

Research paper thumbnail of Una visión innovadora de los cursos cero de matemáticas enfocada al grado de Administración y Dirección de Empresas

Una de las medidas, adoptadas por algunas universidades para frenar el fracaso de los estudiantes... more Una de las medidas, adoptadas por algunas universidades para frenar el fracaso de los estudiantes en el aprendizaje de las matemáticas del grado de administración y dirección de empresas, es ofrecer unos cursos preparatorios o "cursos de matemáticas cero" en verano, unas semanas antes del inicio del año académico. En este trabajo describiremos dos de estos cursos que se han experimentado en las semanas previas al curso académico 2010-11 en

Research paper thumbnail of The Didactical Problem of Elementary Algebra: A Macro- Ecological Analysis Based on the Anthropological Theory of Didactics

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of Central dialectics for mathematical modelling in the experience of a study and research path at university level

HAL (Le Centre pour la Communication Scientifique Directe), Apr 5, 2018

This paper presents the a posteriori analysis of a study and research path (SRP) on comparing rea... more This paper presents the a posteriori analysis of a study and research path (SRP) on comparing reality and forecasts of the number of users of certain social networks, which appears as a teaching and learning proposal for mathematical modelling. We analyse the main elements of the SRP that have been experienced with a first-year course at university in management sciences degrees in two consecutive courses, 2015/16 and 2016/17. We focus our analysis on two essential dialectics for mathematical modelling to be developed: the questions-answers and the mediamilieu dialectics. In particular, we take empirical results from the two successive implementation of the SRP to outline through which mechanism these two dialectics could be prompted.

Research paper thumbnail of The Didactical Problem of Elementary Algebra: A Macro- Ecological Analysis Based on the Anthropological Theory of Didactics

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of El problema didáctico del álgebra elemental: Un análisis macro-ecológico desde la teoría antropológica de lo didáctico

Journal of Research in Mathematics Education, 2015

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of Un modelo epistemológico de referencia del algebra como instrumento de modelización

The aim of this work is to coordinate and complete the papers we presented at the first two confe... more The aim of this work is to coordinate and complete the papers we presented at the first two conferences on the ATD. We propose a reference epistemRORJLFDOPRGHOWKDWLV�≥JOREDO¥�HQRXJKWRSURYLGHDEDVLVIRUW KHVFKRRO� genesis of algebra as a modelling tool and to support a progressive development of the algebraisation process of school mathematics leading to functional modelling.

Research paper thumbnail of Real or Fake Inquiries? Study and Research Paths in Statistics and Engineering Education

Advances in mathematics education, 2022

Research paper thumbnail of Levels of analysis of a mathematical modelling activity: Beyond the questions-answers dialectic

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

This paper presents the a posteriori analysis of an study and research path (SRP) on comparing re... more This paper presents the a posteriori analysis of an study and research path (SRP) on comparing reality versus forecasts of Facebook users, which appears as a teaching and learning proposal for mathematical modelling. We present the main elements of the SRP that have been designed through a virtual platform developed in the frame of the European project MCSquared and experienced in a first-year course at university in management sciences degrees. The three-layer analysis we present is based on three main study dialectics: the questions-answers, media-milieu and individualcollective dialectics, which are central for an SRP and for mathematical modelling. In particular, we focus our a posteriori analysis on how these three dialectics were fostered and which are the main weaknesses as well as strengths of the SRP experienced.

Research paper thumbnail of Teaching didactics to lecturers: A challenging field

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

Lecturers' professional activity is, at least, twofold: research and teaching. However, their pro... more Lecturers' professional activity is, at least, twofold: research and teaching. However, their professional development is generally mostly based on research achievements and little effort is made to empower lecturers overcome the difficulties experienced during their teaching activities. We postulate that didactics of mathematics can be a powerful tool to help lecturers question and reorganize the knowledge to be taught, and to make them aware of the conditions enabling and the constraints hindering new modalities of teaching mathematics, more based on its use as a modelling tool to approach open questions. We present in this paper a first edition of a professional development course for lecturers designed for and experienced in an Engineering School in Barcelona. The results obtained are then used for a subsequent course redesign to be conducted with lecturers of a similar university school.

Research paper thumbnail of Points of contact between the ATD and the TDS: questions raised by the implementation of study and research paths

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

Research paper thumbnail of A new approach to the pre-courses of mathematics at the degree of Business Administration

Una de les mesures, adoptades per algunes universitats, per frenar el fracàs dels estudiants en l... more Una de les mesures, adoptades per algunes universitats, per frenar el fracàs dels estudiants en l’aprenentatge de les matemàtiques del grau d’administració i direcció d’empresa, és oferir cursos preparatoris o “cursos de matemàques zero”a l’estiu, unes setmanes abans de l’inici del curs acadèmic. En aquest treball descriurem dos d’aquests cursos que s’han experimentat en les setmanes prèvies al curs acadèmic 2010-11 a les facultats d’Economia i Empresa (Universitat Pompeu Fabra) i la d’Economia IQS (Universitat Ramon Lllul). El curs zero de la UPF proposa donar una major cohesió a les matemàtiques bàsiques de Secundaria així com proposar una ampliació controlada del tipus d’activitat matemàtica més habitual del alumnes. El curs zero d’IQS proposa un canvi dràstic en el tipus d’activitat matemàtica que els alumnes han realitzat en el batxillerat, centrant-se en l’estudi d’una única situació problemàtica contextualitzada en el món empresarial. Un cop descrits aquest dos casos, conclui...

Research paper thumbnail of Study and research paths in the frontier between paradigms

International Journal of Mathematical Education in Science and Technology

Research paper thumbnail of Actividades de estudio e investigación para introducir los números negativos en un entorno algebraico

Research paper thumbnail of El portafolio electrónico mediante moodle para el seguimiento y evaluación del trabajo final de grado

Research paper thumbnail of El problema del álgebra elemental en la teoría antropológica de lo didáctico

Los primeros trabajos sobre la transposición didáctica del álgebra, llevados a cabo por Yves Chev... more Los primeros trabajos sobre la transposición didáctica del álgebra, llevados a cabo por Yves Chevallard en la década de los 80 del siglo pasado, pusieron de manifiesto que, en primera instancia, el álgebra es un instrumento-el instrumento algebraico-que culmina en la modelización algebraica y transforma completamente las condiciones del trabajo matemático. En coherencia con esta posición epistemológica, las investigaciones desarrolladas a lo largo de los últimos 25 años sobre el álgebra elemental en el ámbito de la teoría antropológica de lo didáctico proponen considerar este dominio como un proceso de algebrización, ampliando así el ámbito de la actividad matemática escolar en el que se suele situar el problema didáctico correspondiente. Hemos estudiado, como componentes de dicho problema, la relación entre «lo numérico» y «lo algebraico», la algebrización de la proporcionalidad, la construcción de los números enteros como objetos algebraicos y el desarrollo de la modelización algebraica hacia la modelización funcional. Palabras clave: teoría antropológica de lo didáctico, modelización algebraica, proceso de algebrización, problema didáctico.

Research paper thumbnail of Comparing Approaches Through a Reference Epistemological Model: The Case of School Algebra

Luis Radford and Yves Chevallard, whose last two research programmes in mathematics education wer... more Luis Radford and Yves Chevallard, whose last two research programmes in mathematics education were awarded with the Hans Freudenthal medal, have both given a prime place to the problem of teaching and learning elementary algebra. However, their approaches are far from being similar. Are they comparable? We are starting a dialogue considering how each approach, in a more or less explicit way, defines what algebra is, that is, how it characterises ‘algebraic thinking’ or ‘algebraic activities’ with what we call a reference epistemological model (REM) of elementary algebra. The dialogue starts by assuming the point of view of the Anthropological Theory of the Didactic (ATD), presenting our own REM, and the kind of questions addressed by this approach, in relation to the Theory of Knowledge Objectification developed by Radford.

Research paper thumbnail of El problema del álgebra elemental en la teoría antropológicade lo didáctico

Los primeros trabajos sobre la transposicion didactica del algebra, llevados a cabo por Yves Chev... more Los primeros trabajos sobre la transposicion didactica del algebra, llevados a cabo por Yves Chevallard en la decada de los 80 del siglo pasado, pusieron de manifiesto que, en primera instancia, el algebra es un instrumento —el instrumento algebraico— que culmina en la modelizacion algebraica y transforma completamente las condiciones del trabajo matematico. En coherencia con esta posicion epistemologica, las investigaciones desarrolladas a lo largo de los ultimos 25 anos sobre el algebra elemental en el ambito de la teoria antropologica de lo didactico proponen considerar este dominio como un proceso de algebrizacion, ampliando asi el ambito de la actividad matematica escolar en el que se suele situar el problema didactico correspondiente. Hemos estudiado, como componentes de dicho problema, la relacion entre «lo numerico» y «lo algebraico», la algebrizacion de la proporcionalidad, la construccion de los numeros enteros como objetos algebraicos y el desarrollo de la modelizacion al...

Research paper thumbnail of Un modelo epistemológico de referencia del álgebra como instrumento de modelización

The aim of this work is to coordinate and complete the papers we presented at the first two confe... more The aim of this work is to coordinate and complete the papers we presented at the first two conferences on the ATD. We propose a reference epistemRORJLFDOPRGHOWKDWLV�≥JOREDO¥�HQRXJKWRSURYLGHDEDVLVIRUW KHVFKRRO� genesis of algebra as a modelling tool and to support a progressive development of the algebraisation process of school mathematics leading to functional modelling.

Research paper thumbnail of “Think Global, Act Local”: un método de diálogo epistemológico para reducir la brecha entre universidad-empresa en el ámbito del marketing

Research paper thumbnail of La introducción del álgebra elemental y su desarrollo hacia la modelización funcional

Resumen: Nuestra investigación parte de los trabajos en torno al problema didáctico del álgebra e... more Resumen: Nuestra investigación parte de los trabajos en torno al problema didáctico del álgebra elemental realizados por el investigador francés Yves Chevallard (1984, 1986, 1989a, 1989b, 1990a y 1990b). En estos trabajos se puso de manifiesto que la función ...

Research paper thumbnail of Una visión innovadora de los cursos cero de matemáticas enfocada al grado de Administración y Dirección de Empresas

Una de las medidas, adoptadas por algunas universidades para frenar el fracaso de los estudiantes... more Una de las medidas, adoptadas por algunas universidades para frenar el fracaso de los estudiantes en el aprendizaje de las matemáticas del grado de administración y dirección de empresas, es ofrecer unos cursos preparatorios o "cursos de matemáticas cero" en verano, unas semanas antes del inicio del año académico. En este trabajo describiremos dos de estos cursos que se han experimentado en las semanas previas al curso académico 2010-11 en

Research paper thumbnail of The Didactical Problem of Elementary Algebra: A Macro- Ecological Analysis Based on the Anthropological Theory of Didactics

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of Central dialectics for mathematical modelling in the experience of a study and research path at university level

HAL (Le Centre pour la Communication Scientifique Directe), Apr 5, 2018

This paper presents the a posteriori analysis of a study and research path (SRP) on comparing rea... more This paper presents the a posteriori analysis of a study and research path (SRP) on comparing reality and forecasts of the number of users of certain social networks, which appears as a teaching and learning proposal for mathematical modelling. We analyse the main elements of the SRP that have been experienced with a first-year course at university in management sciences degrees in two consecutive courses, 2015/16 and 2016/17. We focus our analysis on two essential dialectics for mathematical modelling to be developed: the questions-answers and the mediamilieu dialectics. In particular, we take empirical results from the two successive implementation of the SRP to outline through which mechanism these two dialectics could be prompted.

Research paper thumbnail of The Didactical Problem of Elementary Algebra: A Macro- Ecological Analysis Based on the Anthropological Theory of Didactics

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of El problema didáctico del álgebra elemental: Un análisis macro-ecológico desde la teoría antropológica de lo didáctico

Journal of Research in Mathematics Education, 2015

We present a global, synthetic and updated vision of the contributions made by the anthropologica... more We present a global, synthetic and updated vision of the contributions made by the anthropological theory of the didactic to the problem of teaching elementary algebra. We start by summarising the first results obtained by Yves Chevallard in the 80s that have marked the trend of research on elementary algebra in the anthropological approach. A reference epistemological model of elementary algebra is then proposed. This model provides a new interpretation of the role of elementary algebra in current school mathematics and guides the study of its ecology, that is, the constraints which partially explain the current situation and the conditions that could modify it in a given direction.

Research paper thumbnail of Un modelo epistemológico de referencia del algebra como instrumento de modelización

The aim of this work is to coordinate and complete the papers we presented at the first two confe... more The aim of this work is to coordinate and complete the papers we presented at the first two conferences on the ATD. We propose a reference epistemRORJLFDOPRGHOWKDWLV�≥JOREDO¥�HQRXJKWRSURYLGHDEDVLVIRUW KHVFKRRO� genesis of algebra as a modelling tool and to support a progressive development of the algebraisation process of school mathematics leading to functional modelling.

Research paper thumbnail of Real or Fake Inquiries? Study and Research Paths in Statistics and Engineering Education

Advances in mathematics education, 2022

Research paper thumbnail of Levels of analysis of a mathematical modelling activity: Beyond the questions-answers dialectic

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

This paper presents the a posteriori analysis of an study and research path (SRP) on comparing re... more This paper presents the a posteriori analysis of an study and research path (SRP) on comparing reality versus forecasts of Facebook users, which appears as a teaching and learning proposal for mathematical modelling. We present the main elements of the SRP that have been designed through a virtual platform developed in the frame of the European project MCSquared and experienced in a first-year course at university in management sciences degrees. The three-layer analysis we present is based on three main study dialectics: the questions-answers, media-milieu and individualcollective dialectics, which are central for an SRP and for mathematical modelling. In particular, we focus our a posteriori analysis on how these three dialectics were fostered and which are the main weaknesses as well as strengths of the SRP experienced.

Research paper thumbnail of Teaching didactics to lecturers: A challenging field

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

Lecturers' professional activity is, at least, twofold: research and teaching. However, their pro... more Lecturers' professional activity is, at least, twofold: research and teaching. However, their professional development is generally mostly based on research achievements and little effort is made to empower lecturers overcome the difficulties experienced during their teaching activities. We postulate that didactics of mathematics can be a powerful tool to help lecturers question and reorganize the knowledge to be taught, and to make them aware of the conditions enabling and the constraints hindering new modalities of teaching mathematics, more based on its use as a modelling tool to approach open questions. We present in this paper a first edition of a professional development course for lecturers designed for and experienced in an Engineering School in Barcelona. The results obtained are then used for a subsequent course redesign to be conducted with lecturers of a similar university school.

Research paper thumbnail of Points of contact between the ATD and the TDS: questions raised by the implementation of study and research paths

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

Research paper thumbnail of A new approach to the pre-courses of mathematics at the degree of Business Administration

Una de les mesures, adoptades per algunes universitats, per frenar el fracàs dels estudiants en l... more Una de les mesures, adoptades per algunes universitats, per frenar el fracàs dels estudiants en l’aprenentatge de les matemàtiques del grau d’administració i direcció d’empresa, és oferir cursos preparatoris o “cursos de matemàques zero”a l’estiu, unes setmanes abans de l’inici del curs acadèmic. En aquest treball descriurem dos d’aquests cursos que s’han experimentat en les setmanes prèvies al curs acadèmic 2010-11 a les facultats d’Economia i Empresa (Universitat Pompeu Fabra) i la d’Economia IQS (Universitat Ramon Lllul). El curs zero de la UPF proposa donar una major cohesió a les matemàtiques bàsiques de Secundaria així com proposar una ampliació controlada del tipus d’activitat matemàtica més habitual del alumnes. El curs zero d’IQS proposa un canvi dràstic en el tipus d’activitat matemàtica que els alumnes han realitzat en el batxillerat, centrant-se en l’estudi d’una única situació problemàtica contextualitzada en el món empresarial. Un cop descrits aquest dos casos, conclui...

Research paper thumbnail of Study and research paths in the frontier between paradigms

International Journal of Mathematical Education in Science and Technology