Construcción social de los procesos de definir y demostrar
Social construction of define and demonstrate processes

Angelina Alvarado Monroy, Maria Teresa González Astudillo

Resumo


Resumen

Dado que los procesos de definir y demostrar en matemáticas no están considerados como objeto de estudio en los diferentes niveles educativos, realizamos una investigación en la educación inicial universitaria con el propósito de mostrar la importancia y el papel de las definiciones dentro del proceso de demostrar. Tratamos de mejorar su comprensión por parte de los estudiantes a través de una secuencia didáctica centrada en el análisis de los procesos de construcción social de tal conocimiento.  A la luz del modelo Abstracción en Contexto, analizamos el flujo de conocimiento de un estudiante a otro mediante las interacciones producidas. Finalmente documentamos que la secuencia contribuye a su aprendizaje, dado que el conocimiento base compartido les permite incorporar habilidades y sutilezas para deconstruir definiciones y utilizarlas para realizar demostraciones y comunicarlas.

Palabras clave: Demostración y Definición; Construcción social de conocimiento; Abstracción en Contexto.

 

Resumo

Embora os processos de definir e de demonstrar em matemática não sejam considerados um objeto de estudo nos diferentes níveis de ensino, realizámos uma pesquisa sobre o seu ensino e aprendizagem na formação inicial universitária com a finalidade de mostrar o papel fundamental das definições em os processo de demonstração. Tentamos melhorar a compreensão do aluno através de uma sequência didática centrada na análise dos construção social daquele conhecimento. À luz do modelo Abstração em Contexto, analisámos o fluxo de conhecimento de um aluno para outro através interações que ocorreram. Por fim, chegamos evidência de que a sequência contribui para a aprendizagem, uma vez que o conhecimento base compartilhado permitiu-lhes incorporar capacidades e subtilezas para desconstruir definições, quer para a realização de demonstrações matemáticas, quer para comuncá-las.

Palavras-chave: Demonstração e definição; Construção social do conhecimento; Abstração em Contexto.

 

 

Abstract

The processes of defining and proving in mathematics aren’t considered as object for studying them in the different educative levels so we have made a research about the teaching and learning of these processes during the university education of mathematicians. We try to improve its understanding through a didactical session centered on the social construction of this knowledege. Through the light of the Abstraction in Context model, we analyze the knowledge flow between students during the interactions when they are solving different questions. As a result of these interactions the base knowledge shared, allow them to incorporate skills and subtleties to deconstruct the definitions and use them to construct correct mathematics proofs and to communicate them.

Keywords: Proof and definition; Social Construction of Knowledge, Abstraction  in Context.


Palavras-chave


Demostración y Definición; Construcción social de conocimiento; Abstracción en Contexto.

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Referências


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