TY - GEN
T1 - Complementation Between Usage Schemes and Mental Actions in an Approach to the Definite Integral Using GeoGebra
AU - Martínez-Miraval, Mihály A.
AU - García-Rodríguez, Martha L.
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - In the process of approximating the area of a region by means of Riemann sums a relationship between different variables that change simultaneously takes place, and although digital technologies help to visualize the process, it is important to understand how an individual reasons with the software. This study aimed to analyze how the interaction between usage schemes and mental actions of an individual occurs when solving an assignment about the definite integral study using GeoGebra. Theoretical approaches of both covariational reasoning and instrumental approach were used in qualitative research using action research as a method. Students mobilized their usages schemes related to variation, summation, and limit notions, which were run using the GeoGebra commands slider and RectangleSum, these commands were used in order to represent and coordinate the changes in the values of the variables: number of rectangles and sum of their areas; this allowed identifying a complementation between these usage schemes and mental actions, strengthening the analysis of the information. Finally, it is concluded that the complementation of two theoretical approximations provides elements that are essential when analyzing the phenomenon studied, in order to understand how a student reasons covariationally when using GeoGebra during the learning process.
AB - In the process of approximating the area of a region by means of Riemann sums a relationship between different variables that change simultaneously takes place, and although digital technologies help to visualize the process, it is important to understand how an individual reasons with the software. This study aimed to analyze how the interaction between usage schemes and mental actions of an individual occurs when solving an assignment about the definite integral study using GeoGebra. Theoretical approaches of both covariational reasoning and instrumental approach were used in qualitative research using action research as a method. Students mobilized their usages schemes related to variation, summation, and limit notions, which were run using the GeoGebra commands slider and RectangleSum, these commands were used in order to represent and coordinate the changes in the values of the variables: number of rectangles and sum of their areas; this allowed identifying a complementation between these usage schemes and mental actions, strengthening the analysis of the information. Finally, it is concluded that the complementation of two theoretical approximations provides elements that are essential when analyzing the phenomenon studied, in order to understand how a student reasons covariationally when using GeoGebra during the learning process.
KW - Definite integral
KW - GeoGebra
KW - Mental action
KW - Usage scheme
UR - http://www.scopus.com/inward/record.url?scp=85186763219&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-45645-9_37
DO - 10.1007/978-3-031-45645-9_37
M3 - Conference contribution
AN - SCOPUS:85186763219
SN - 9783031456442
T3 - Lecture Notes in Networks and Systems
SP - 395
EP - 404
BT - Information Systems and Technologies - WorldCIST 2023
A2 - Rocha, Alvaro
A2 - Adeli, Hojjat
A2 - Dzemyda, Gintautas
A2 - Moreira, Fernando
A2 - Colla, Valentina
PB - Springer Science and Business Media Deutschland GmbH
T2 - 11th World Conference on Information Systems and Technologies, WorldCIST 2023
Y2 - 4 April 2023 through 6 April 2023
ER -