Banca de DEFESA: CESAR THIAGO JOSE DA SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : CESAR THIAGO JOSE DA SILVA
DATE: 24/02/2022
TIME: 17:00
LOCAL: Video conferência
TITLE:

Computational artifact use as support to the development of function covariational reasoning. 

KEY WORDS:

Teaching and learning functions. Computational technologies. Informatics Transposition. Instrumental Genesis. Geogebra.

PAGES: 327
BIG AREA: Ciências Humanas
AREA: Educação
SUMMARY:

Covariational reasoning in function involves thinking in terms of how one variable changes in relation to the change in the other variable. Covariation is linked to the historical development of the concept of function and it is important to conceptualize fundamental ideas of calculus. While research in area have pointed out students' difficulties to reason covariationally, computational technologies have been used to support covariational reasoning, however, little attention is paid to how aspects of mathematical representation in the computational environment (informatics transposition) result in new possibilities and constraints that influence activity and conceptual development. In this context, this study aimed to investigate the effects of using a computational artifact on students' covariational reasoning, and the relationship between these effects and the informatics transposition of covariation in this artifact. We used the Instrumental Approach lens, supported by Vergnaud's notion of schemes, to understand how subjects mobilized covariational reasoning in their instrumental genesis with the Geogebra software and, additionally, we analyzed the role that aspects of informatics transposition played in this process. Methodology consisted of a multiple case study of the instrumental genesis of three pre-service mathematics teachers who explored situations of covariation that were conceived in the Geogebra software. Study involved a teaching experiment structured by instrumental orchestrations, application of a questionnaire and task-based interviews. A microgenetic analysis was applied to the data focusingon instrumented use of Geogebra and also on mobilization of students' covariational reasoning, which was inferred in their schemes and descriptions of covariation. Results showed how aspects of computer transposition and its relationships with the students' instrumented use of the Geogebra software influenced the contributions and constraints to their covariational reasoning. Instrumental genesis of tools that support coordination of continuous covariation, and quantification of variation in y as x increases by constant increments in x, and dynamic-simultaneous connection across representations, supported a covariational interpretation of aspects of the graph, as well as variation in change and negative variation. On the other hand, schemes that were mobilized by students to explore situations of complex covariation, and to sketch the graph covariationally were limited. In this last aspect, it was revealed the influence of conventional schemes, which are developed in the paper and pencil environment, and based on the correspondence approach and on a static way of thinking. This result pointed out the need to develop schemes that articulate the possibilities of computational environments to the ways to represent covariation in the graph. Difficulties with interpretation of negative variation and the role that  representation of variation by dynamic segments played in this context, pointed out the need to take into account constraints and possibilities generated  in the creation of new objects and meanings in the process of design of didactic materials in the computational environment, which we proposed to characterize as a second-order informatic transposition.

BANKING MEMBERS:
Presidente - 2131772 - VERONICA GITIRANA GOMES FERREIRA
Interna - 2306894 - IRANETE MARIA DA SILVA LIMA
Externo ao Programa - 1285161 - ROGERIO DA SILVA IGNACIO
Externo à Instituição - JHONY ALEXANDER VILLA-OCHOA
Externo à Instituição - VICTOR AUGUSTO GIRALDO - UFRJ