Books by Guadalupe Cabañas-Sánchez
Cabañas, G., Cantoral, R., Castañeda, A., Farfán, R. M. (Directora), Lezama, J., Martínez, G., Molina, G., Montiel, G. y Sánchez, M. (2006). Matemáticas 1. Serie para la educación secundaria: Desarrollo del Pensamiento Matemático. México: McGraw Hill
Cabañas, G., Cantoral, R., Castañeda, A., Farfán, R. M. (Directora), Ferrari, M., Lezama, J., Martínez, G. y Montiel, G. (2008). Matemáticas 3. Serie para la educación secundaria: Desarrollo del Pensamiento Matemático. México: McGraw Hill.
Papers by Guadalupe Cabañas-Sánchez
A study on the teacher ́s speech in the mathematics classroom, when trying to teach concepts and ... more A study on the teacher ́s speech in the mathematics classroom, when trying to teach concepts and mathematical processes linked to the notion of similarity is presented. The main objective is to identify the interaction patterns that rule behaviors that must be valid to create consensus in the classroom. The theoretical framework adopted included the principles and strategies developed by the interactionism perspective and discourse analysis. A qualitative research model based in the ethnographic method was considered. Data for the study were taken from the Math lessons in a high school course (ages 16-18). The results demonstrate that appropriate speech simplifies the identification of interaction patterns between the professor and the students.
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
A study on the teacher ́s speech in the mathematics classroom, when trying to teach concepts and ... more A study on the teacher ́s speech in the mathematics classroom, when trying to teach concepts and mathematical processes linked to the notion of similarity is presented. The main objective is to identify the interaction patterns that rule behaviors that must be valid to create consensus in the classroom. The theoretical framework adopted included the principles and strategies developed by the interactionism perspective and discourse analysis. A qualitative research model based in the ethnographic method was considered. Data for the study were taken from the Math lessons in a high school course (ages 16-18). The results demonstrate that appropriate speech simplifies the identification of interaction patterns between the professor and the students.
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
Authors: José Rafael Couoh Noh; Guadalupe Cabañas-Sánchez; Eddie Aparicio.
Presentamos los ava... more Authors: José Rafael Couoh Noh; Guadalupe Cabañas-Sánchez; Eddie Aparicio.
Presentamos los avances de una investigación que se interesa por caracterizar la práctica profesional del profesor de matemáticas mientras desarrolla una propuesta didáctica sobre los límites infinitos que está basada en situaciones contextuales. Interesan dos cuestiones: a) comprender y a partir de ello caracterizar el tipo de ayudas, dificultades y formas de comunicación que establece con sus estudiantes en ese proceso, y b) reconocer de la propuesta didáctica, aquella(s) que posibilita(n) el aprendizaje de este tipo de límites. El estudio se realizará con estudiantes de Cálculo Diferencial de una licenciatura en Matemáticas, al momento en que este tópico es objeto de estudio. En este reporte, describimos principalmente la propuesta didáctica que será el instrumento para observar la clase del profesor universitario de Cálculo y en consecuencia caracterizar su práctica.
Capítulo 2 Propuestas para la enseñanza de las matemáticas C o m i t é L a t i n o a m e r i c a ... more Capítulo 2 Propuestas para la enseñanza de las matemáticas C o m i t é L a t i n o a m e r i c a n o d e M a t e m á t i c a E d u c a t i v a A . C. 661 Resu Resu Resu Resumen men men men. . .
Capítulo 4. El pensamiento del profesor, sus prácticas y elementos para su formación inicial C o ... more Capítulo 4. El pensamiento del profesor, sus prácticas y elementos para su formación inicial C o m i t é L a t i n o a m e r i c a n o d e M a t e m á t i c a E d u c a t i v a A . C.
El artículo discute aspectos teórico-metodológicos de una investigación en desarrollo, que busca ... more El artículo discute aspectos teórico-metodológicos de una investigación en desarrollo, que busca caracterizar las prácticas matemáticas que emergen en el salón de clases, durante la explicación escolar del concepto de integral definida desde una perspectiva que articula usos del área en la matemática, con la conservación del área en transformaciones analíticas. La noción de práctica es fundamental en este trabajo y se discute desde la teoría socioepistemología. Por cuanto a las prácticas matemáticas, nos sustentamos de un modelo estratégico, que distingue las prácticas de un profesor y los estudiantes a nivel macro, meso y micro. En el primero se localizan a nivel de proyecto de una lección, en el segundo, de la configuración de una situación de aprendizaje, formas de organización, comunicación e interacción en el aula, y en el último, de la gestión que el profesor hace del objeto de saber y de las interacciones de sus estudiantes.
Este artículo describe los resultados de un diseño experimental realizado en un salón de clases d... more Este artículo describe los resultados de un diseño experimental realizado en un salón de clases de cálculo integral al momento en que la integral definida es objeto de estudio. El propósito es presentar un análisis desde las prácticas del salón de clases, cómo se resignifica por estudiantes de matemáticas el concepto de integral definida, desde una perspectiva que articula usos, contextos y procedimientos, con la conservación del área de regiones planas, limitadas por la gráfica de una función polinómica, continua y positiva en un intervalo cerrado. El estudio de la integral definida bajo este enfoque, ubica las explicaciones y argumentos de los estudiantes en aspectos como: forma, tamaño y posición relativa de una región de área respecto del plano cartesiano, resultado de conservar la medida de un área en regiones planas; en lugar de situar su discurso únicamente hacia conceptos, símbolos y fórmulas matemáticas.
Capítulo 3. Aspectos socioepistemológicos en el análisis y el rediseño del discurso matemático es... more Capítulo 3. Aspectos socioepistemológicos en el análisis y el rediseño del discurso matemático escolar Comité Latinoamericano de Matemática Educativa A. C.
ABSTRACT. This contribution presents a study of argumentation schemes developed by mathematics st... more ABSTRACT. This contribution presents a study of argumentation schemes developed by mathematics students during an integral calculus lesson and the role of the professor in the
classroom interactions. The study was based on the adaptation of a design used in Cabañas and Cantoral (2006) whose activities center on the use of notions of comparison,
conservation, measure and quantification of area at different levels. The arguments were analyzed whenever the students justified an answer, made transformations, built representations or determined magnitudes. It was also interesting to see whether, through characterized argumentation schemes, the students perceived that the area is compared, conserved, measured and quantified and the role of the professor in this process.
Practices associated to the mathematics classroom situation
Abstract. This paper discusses the ... more Practices associated to the mathematics classroom situation
Abstract. This paper discusses the notion of practice based on the relational activity that is established in the classroom practice at the moment the mathematical knowledge is constructed. It is explanation, we tray to relate the three components of the didactical system, without ignoring the social contexts, institutional, historical and cultural. This notion is analyzed from the Socioepistemology theory and is conceived as an organized group of activities or objective and intentional actions to solve a given problem. Placed in the school context, the practice is inherent to the specific actions that there develop the actors of the didactic system, each one in the performance of his own role, so it is attributed to activities or actions which are evident in objective observable for behaviors humans. In the analysis of practices we distinguish three levels: macro, meso and micro. Through them it was set a strategical model, to derive explanations of the relational activity in the classroom.
Key word: Classroom practice, relational activity, construction of the mathematical knowledge.
This article presents the central aspects of a doctoral research project in which we will study t... more This article presents the central aspects of a doctoral research project in which we will study the didactic phenomenon known as reproductibility using the socioepistemological approach to research in Educational Mathematics (Cantoral & Farfán, 2003), taking as a starting point the treatment of the notion of area in relation to activities such as sharing, comparing and reproducing, measuring, quantifying and conserving. The background to the study can be found in the results of the research carried out by Piaget, J., Inhelder, B. & Szeminska, A. (1970) and Kordaky, Potari (2002).
KEY WORDS: socioepistemology, reproductibility of didactic situations, definite integral, comparison, measurement and conservation of area.
This contribution presents a study about how university students perceive that the area is compar... more This contribution presents a study about how university students perceive that the area is compared, conserved and measured. The study is based on Toulmin’s argumentation scheme to reconstruct students’ arguments and analyze their mathematical logical reasons. The findings show that the students perceived: a) area conservation when they alluded both the parallelism relation and the elements of the formula to calculate the area of triangles or simulated movements on figures; b) area comparison when they became conscious on the relationship between the areas of the polygons and; c) area measurement when they managed to use the formula to calculate the area of the triangles or realized that the area had to be conserved.
This study examines university students’ perceptions of how the area on plane regions is conserve... more This study examines university students’ perceptions of how the area on plane regions is conserved, compared and measured and also the role of the teacher in this process. The data analysis comes from classroom interactions during the solution of a learning situation which involves geometrical transformations –convex polygons– and includes a semi-structured interview. The
analysis is supported by the argumentation scheme proposed by Toulmin (1958) to reconstruct
students’ argumentation schemes. The findings show that the students perceive: a) area conservation when they refer both the parallelism relation and the elements of the formula to calculate the area of triangles or simulate movements on figures; b) area comparison when they realize the relationship between the areas of the three polygons (triangles), and; c) area measurement when they manage to use the formula to calculate the area of the triangles. The teacher’s role becomes complex when he confronts students’ arguments. The study of the interactions in the mathematics classroom provides evidence of the importance of communication. Finally, the examination of the arguments show how students build their justifications, give reasons, argue,
think about knowledge, share knowledge and the methods they use to argue.
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Books by Guadalupe Cabañas-Sánchez
Papers by Guadalupe Cabañas-Sánchez
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
Presentamos los avances de una investigación que se interesa por caracterizar la práctica profesional del profesor de matemáticas mientras desarrolla una propuesta didáctica sobre los límites infinitos que está basada en situaciones contextuales. Interesan dos cuestiones: a) comprender y a partir de ello caracterizar el tipo de ayudas, dificultades y formas de comunicación que establece con sus estudiantes en ese proceso, y b) reconocer de la propuesta didáctica, aquella(s) que posibilita(n) el aprendizaje de este tipo de límites. El estudio se realizará con estudiantes de Cálculo Diferencial de una licenciatura en Matemáticas, al momento en que este tópico es objeto de estudio. En este reporte, describimos principalmente la propuesta didáctica que será el instrumento para observar la clase del profesor universitario de Cálculo y en consecuencia caracterizar su práctica.
classroom interactions. The study was based on the adaptation of a design used in Cabañas and Cantoral (2006) whose activities center on the use of notions of comparison,
conservation, measure and quantification of area at different levels. The arguments were analyzed whenever the students justified an answer, made transformations, built representations or determined magnitudes. It was also interesting to see whether, through characterized argumentation schemes, the students perceived that the area is compared, conserved, measured and quantified and the role of the professor in this process.
Abstract. This paper discusses the notion of practice based on the relational activity that is established in the classroom practice at the moment the mathematical knowledge is constructed. It is explanation, we tray to relate the three components of the didactical system, without ignoring the social contexts, institutional, historical and cultural. This notion is analyzed from the Socioepistemology theory and is conceived as an organized group of activities or objective and intentional actions to solve a given problem. Placed in the school context, the practice is inherent to the specific actions that there develop the actors of the didactic system, each one in the performance of his own role, so it is attributed to activities or actions which are evident in objective observable for behaviors humans. In the analysis of practices we distinguish three levels: macro, meso and micro. Through them it was set a strategical model, to derive explanations of the relational activity in the classroom.
Key word: Classroom practice, relational activity, construction of the mathematical knowledge.
KEY WORDS: socioepistemology, reproductibility of didactic situations, definite integral, comparison, measurement and conservation of area.
analysis is supported by the argumentation scheme proposed by Toulmin (1958) to reconstruct
students’ argumentation schemes. The findings show that the students perceive: a) area conservation when they refer both the parallelism relation and the elements of the formula to calculate the area of triangles or simulate movements on figures; b) area comparison when they realize the relationship between the areas of the three polygons (triangles), and; c) area measurement when they manage to use the formula to calculate the area of the triangles. The teacher’s role becomes complex when he confronts students’ arguments. The study of the interactions in the mathematics classroom provides evidence of the importance of communication. Finally, the examination of the arguments show how students build their justifications, give reasons, argue,
think about knowledge, share knowledge and the methods they use to argue.
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
Keywords: interaction patters, discourse analysis, interactionism, similarity, ethnographic method
Presentamos los avances de una investigación que se interesa por caracterizar la práctica profesional del profesor de matemáticas mientras desarrolla una propuesta didáctica sobre los límites infinitos que está basada en situaciones contextuales. Interesan dos cuestiones: a) comprender y a partir de ello caracterizar el tipo de ayudas, dificultades y formas de comunicación que establece con sus estudiantes en ese proceso, y b) reconocer de la propuesta didáctica, aquella(s) que posibilita(n) el aprendizaje de este tipo de límites. El estudio se realizará con estudiantes de Cálculo Diferencial de una licenciatura en Matemáticas, al momento en que este tópico es objeto de estudio. En este reporte, describimos principalmente la propuesta didáctica que será el instrumento para observar la clase del profesor universitario de Cálculo y en consecuencia caracterizar su práctica.
classroom interactions. The study was based on the adaptation of a design used in Cabañas and Cantoral (2006) whose activities center on the use of notions of comparison,
conservation, measure and quantification of area at different levels. The arguments were analyzed whenever the students justified an answer, made transformations, built representations or determined magnitudes. It was also interesting to see whether, through characterized argumentation schemes, the students perceived that the area is compared, conserved, measured and quantified and the role of the professor in this process.
Abstract. This paper discusses the notion of practice based on the relational activity that is established in the classroom practice at the moment the mathematical knowledge is constructed. It is explanation, we tray to relate the three components of the didactical system, without ignoring the social contexts, institutional, historical and cultural. This notion is analyzed from the Socioepistemology theory and is conceived as an organized group of activities or objective and intentional actions to solve a given problem. Placed in the school context, the practice is inherent to the specific actions that there develop the actors of the didactic system, each one in the performance of his own role, so it is attributed to activities or actions which are evident in objective observable for behaviors humans. In the analysis of practices we distinguish three levels: macro, meso and micro. Through them it was set a strategical model, to derive explanations of the relational activity in the classroom.
Key word: Classroom practice, relational activity, construction of the mathematical knowledge.
KEY WORDS: socioepistemology, reproductibility of didactic situations, definite integral, comparison, measurement and conservation of area.
analysis is supported by the argumentation scheme proposed by Toulmin (1958) to reconstruct
students’ argumentation schemes. The findings show that the students perceive: a) area conservation when they refer both the parallelism relation and the elements of the formula to calculate the area of triangles or simulate movements on figures; b) area comparison when they realize the relationship between the areas of the three polygons (triangles), and; c) area measurement when they manage to use the formula to calculate the area of the triangles. The teacher’s role becomes complex when he confronts students’ arguments. The study of the interactions in the mathematics classroom provides evidence of the importance of communication. Finally, the examination of the arguments show how students build their justifications, give reasons, argue,
think about knowledge, share knowledge and the methods they use to argue.