El conocimiento didáctico-matemático para la enseñanza de la derivada de profesores colombianos activos

El estudio de los conocimientos del profesorado de matemáticas, es un tema de creciente interés. En esta investigación nos hemos interesado en caracterizar aspectos relevantes del conocimiento didáctico matemático sobre la derivada de profesores colombianos activos mediante una prueba que consta de 22 que explora diversos significados de la derivada. La investigación pretende responder a dos preguntas: ¿Cuál es el conocimiento del contenido que los profesores en activo tienen sobre la derivada?, ¿Cuál es el conocimiento para la enseñanza de la derivada que los profesores exhiben? Los resultados parciales obtenidos permiten señalar que los profesores tienen un conocimiento del contenido robusto sobre la derivada, y además, exhiben competencia para identificar conflictos de significado y para reconocer el conocimiento válido detrás de respuestas “erróneas” por parte de sus alumnos

Strategies proposed by preservice teachers to foster their students’ creativity

In this study, we aim to analyse the preservice teachers’ perspectives on creativity, in particular, if they consider that creativity can be developed, and their strategies to foster students’ creativity. The participants are 43 preservice teachers who were taking a master’s degree to become teachers of secondary school. The master’s program did not include a specific training in creativity. They answered a questionnaire about creativity and then three of them were interviewed. We did a content analysis of their answers. Most of the preservice teachers think that creativity can (and should) be developed in the mathematics classroom. They suggest different strategies to foster students’ creativity that agree with literature, but solving open-ended problems stands out among the rest of strategies.This work is part of the research project PGC2018-098603-B-I00 (MCIU/AEI/FEDER, UE), with the support of the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya and the European Social Fund (2020FI_B2 00017)

Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Background: The knowledge that a mathematics teacher should master has taken an increasing interest in recent years. Very few studies focused on comparing didactic-mathematic knowledge of in-service and pre-service teachers aimed at identifying features of the teachers’ didactic-mathematical knowledge on specific topics that can establish a line between pre-service and in-service teachers’ knowledge for teaching. Objective: The research aims to compare derivative knowledge of pre-service and in-service teachers to identify similarities and differences between teachers’ knowledge. Design: This research is a mixed and interpretative study. Settings and Participants: The participants were 22 pre-service teachers, and 11 in-service teachers enrolled in a pre-service teacher education programme and a master’s programme, respectively. Data collection and participants: Data were collected based on a questionnaire designed purposefully for the study. Results: The results show that pre-service teachers lack both epistemic derivative knowledge, while in-service teachers not only have this knowledge but relates it to its use in teaching. Pre-service teachers may not be making sense of the concept of derivative means, much less related to teaching. Conclusions: The insufficiencies found in pre-service teachers’ knowledge justify the pertinence to design specific formative cycles to develop prospective teachers’ epistemic facet of didactic-mathematical knowledge. It is recommended that both in-service and pre-service teachers discuss activities in which they can identify and reflect on possible mistakes and errors made by students. The development of these formative cycles should consider the complexity of the global meaning of the derivative

Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher's Management to Promote Them

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students' productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin's model for argumentation. The teacher's professional actions that promoted reiterative actions in students' mathematical practices were identified; we illustrate how these professional actions impelled students' actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process

Análisis didáctico en un trabajo de fin de máster de un futuro profesor

El objetivo de este trabajo es presentar cómo se utilizan los criterios de idoneidad didáctica propuestos por el Enfoque Ontosemiótico del conocimiento y la Instrucción Matemáticos en un proceso de formación de futuros profesores. Para ello, se realiza el estudio del trabajo de fin de máster de una futura profesora de secundaria de matemáticas. El análisis muestra que la futura profesora considera que mejoró su competencia de análisis e intervención didáctica como resultado de la reflexión sobre su propia práctica utilizando los criterios de idoneidad didáctica

Explorando aspectos relevantes del conocimiento didáctico-matemático sobre la derivada de profesores en formación inicial

En el presente trabajo se informa de los resultados obtenidos mediante la aplicación de un cuestionario que se ha diseñado para explorar algunos aspectos relevantes del conocimiento de futuros profesores de bachillerato sobre la derivada. El diseño del cuestionario se presenta en la primera parte de este trabajo. Los resultados del análisis de las respuestas de los estudiantes evidencian tanto una desconexión entre los distintos significados parciales de la derivada como la necesidad de potenciar el conocimiento especializado del contenido. Este aprendizaje puede hacerse mediante actividades que favorezcan el uso e identificación de objetos matemáticos, sus significados y los procesos involucrados en la solución de tareas matemáticas

El conocimiento didáctico-matemático: una propuesta de evaluación de tres de sus facetas

En esta comunicación se presentan algunos criterios tenidos en cuenta para el diseño de un cuestionario para evaluar tres facetas del conocimiento matemático para la enseñanza de la derivada: el conocimiento común del contenido, el conocimiento especializado y el conocimiento ampliado. Así mismo se presenta una tarea propuesta en el cuestionario aplicado a estudiantes de las licenciaturas en Básica Matemáticas y Matemáticas -Física de la Universidad de Antioquia, Colombia

Epistemic criteria for designing limit tasks on a real variable function

This article aims at presenting the results of a historical-epistemological study conducted to identify criteria for designing tasks that promote the understanding of the limit notion on a real variable function. As a theoretical framework, we used the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction, to identify the regulatory elements of mathematical practices developed throughout history, and that gave way to the emergence, evolution, and formalization of limit. As a result, we present a proposal of criteria that summarizes fundamental epistemic aspects, which could be considered when designing tasks that allow the promotion of each of the six meanings identified for the limit notion. The criteria presented allow us to highlight not only the mathematical complexity underlying the study of limit on a real variable function but also the richness of meanings that could be developed to help understand this notion

Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value function: two theoretical perspectives

This paper presents a study of networking of theories between the theory of registers of semiotic representation (TRSR) and the onto-semiotic approach of mathematical cognition and instruction (OSA). The results obtained show complementarities between these two theoretical perspectives, which might allow more detailed analysis of the students’ performance.Análisis de la actividad cognitiva subyacente en la resolución de una tarea sobre la derivabilidad de la función valor absoluto: dos perspectivas teóricas En este artículo se presenta un estudio de networking of theories, entre la teoría de los registros de representación semióticos (TRRS) y el enfoque onto-semiótico de la cognición e instrucción matemáticos (OSA). Los resultados obtenidos revelan complementariedades entre estas dos perspectivas teóricas cuya aplicación simultánea permitiría hacer análisis más pormenorizados de las producciones de los estudiantes.Handle: http://hdl.handle.net/10481/44148WOS-ESCIScopus record and citations

Towards a methodology for the characterization of teachers´ Didactic-Mathematical knowledge

ABSTARCT: This research study aims at exploring the useof some dimensions and theoretical-methodological tools suggested by the modelof Didactic-Mathematical Knowledge (DMK) for the analysis,characterization and development of knowledge that teachers should have inorder to efficiently develop within their practice. For this purpose, weanalyzed the activity performed by five high school teachers, in relation to anactivity about patterns suggested in the framework of the Master of MathematicsEducation Program at University of Los Lagos, Chile. As a result of theanalysis, it becomes evident that teachers can indeed solve items related tothe common content knowledge, but have certain difficulties when they faceitems that aim at exploring other dimensions of their knowledge, for example,about extended content knowledge, of resources and means, or of the affectivestate of students