Banca de DEFESA: CHEICK OUMAR DOUMBIA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : CHEICK OUMAR DOUMBIA
DATA : 06/12/2019
HORA: 14:00
LOCAL: Instituto de física UFBA
TÍTULO:

A DIDACTIC REFERENCE MODEL FOR THE CONSTRUCTION OF KNOWING AND THE UPDATING OF KNOWLEDGE ON THE CONCEPT OF LIMIT IN MALI

PALAVRAS-CHAVES:

Limit Concept, Formal Definition, Teaching-Learning, Algebraic Frame and Geometric Framework.

PÁGINAS: 231
GRANDE ÁREA: Ciências Humanas
ÁREA: Educação
SUBÁREA: Ensino-Aprendizagem
ESPECIALIDADE: Métodos e Técnicas de Ensino
RESUMO:

We are interested in the study of the concept of limit of function, more particularly to the epistemological and didactic aspects of this mathematical concept. His teaching is essentially based on algebraic and numerical frameworks. Much research has shown that the notion of limit is a complex notion for learners. Draft solutions have been developed, but still, the difficulties persist for learners. The notion of limit is a fundamental notion of analysis. The purpose of our study is to help future teachers participating in our research project to build teaching situations allowing students to give a mathematical meaning to the notion of limit of a numerical function of a variable real at a point and use it to show that a given real is the limit of a function at a given point. We propose more specifically to answer the following questions: What knowing / knowledge about the concept of limit, are built by students, during articulations and interactions, in the case of a Reference Didactic Model built in relying on the epistemological, eco-logical and economic-institutional dimensions of the mathematical object under study? And sub-questions such as: Does this model make it possible to reduce the gap between scholarly knowledge and the knowledge taught? Does it allow the formalized definition to work? Is there no confusion between calculating the limit at one point and studying continuity at this point? How has the notion of limit evolved in the Malian education system? And why? What understanding do students and teachers currently have of the definition of the limit? What knowledge is needed to understand the formal definition of the limit? What are the different techniques used? What is the importance of taking into account the domain of definition in the calculation of the limit? At what levels of education should the formalized definition emerge? How important is the formal definition? Many studies have shown the profound difficulties of students (and students) in the conceptualization of the notion of limit. Some of them attribute some of these difficulties to epistemological obstacles (conception of the limit as impassable and unreachable or conception of the limit as a "finite" algebraic process, for example) Cornu (1983), d. others point to the dual operational and structural status of the notion or the problems associated with its progressive formalization Artigue (1996) and Bkouche (1997). The results show that it is the intuitive definition that emerges and stands as an obstacle to the understanding of the precise formal definition, the teachers who were the subject of our survey have a dynamic conception of the limit, it is necessary to include the history of mathematics in the curriculum of future teachers, the formalized definition of the limit is not inaccessible to students, its manipulation allows students to update a lot of knowledge-it is related such as the notion of interval, inequalities with absolute value, distance, composition, decomposition of order function in R etc. the precise formal definition makes it possible to correct obstacles such as the limit reached or not reached, the elimination of quantifiers, the confusion between the limit and the continuity, the taking into account of the set-definition in the calculating the limit, it marks the passage from algebra to analysis.

MEMBROS DA BANCA:
Interno - 1808015 - ANDRE LUIS MATTEDI DIAS
Externo à Instituição - HAMID CHAACHOUA
Externo à Instituição - JOSÉ LUIZ MAGALHÃES DE FREITAS - UFMS
Externo à Instituição - JOSÉ MESSILDO VIANA NUNES - UFPA
Presidente - 2138504 - LUIZ MARCIO SANTOS FARIAS
Interno - 1148606 - ROSILEIA OLIVEIRA DE ALMEIDA
Externo à Instituição - SADDO AG ALMOULOUD - PUC - SP