Autores - Editores Ureña, Jason

Descripción

In this study we analyze the generalization levels shown by eight 4th grade Spanish students while working, during an interview, on a task based on the functional relationship x+2. The task had an inductive structure and asked about the relation between the hours of stay of a car in a parking lot and the money to be paid. At the same time we study how the stimuli made by the interviewer (e.g. suggest, summarize information, redirect, etc.) influence the manifestation of generalizations.

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Ureña, Jason, Molina, Marta y Ramírez, Rafael

Fecha

2018

Autores

Descripción

Este trabajo forma parte de una investigación más amplia centrada en la capacidad de generalización de estudiantes de primaria en contextos funcionales. En este estudio descriptivo se analizan los niveles de generalización que manifiestan ocho estudiantes de cuarto de primaria durante una entrevista en la que se les propone una tarea que involucra una relación funcional. De los resultados se aprecia la capacidad de los alumnos de primaria para expresar la relación funcional y manifestar generalización en diferentes grados, incluso a un nivel simbólico.

Lista de autores

Ureña, Jason, Molina, Marta y Ramírez, Rafael

Fecha

2018

Autores

Descripción

The ability to generalize and represent the generalization exhibited by eight fourth-grade students was analyzed in this descriptive study, designed around a semi-structured interview involving a task based on the linear functional relationship y=x+2. The relation of the interviewer’s mediation on students’ representations of generalization was determined on the grounds of students’ interaction with her. Four forms to represent the generalization of a functional relationship were defined. The findings confirm the importance of mediation in helping students strengthen their ability to recognize, represent and generalize functional relationships.

Lista de autores

Ureña, Jason, Ramírez, Rafael y Molina, Marta

Fecha

2019

Autores

Descripción

Describimos las representaciones de la generalización que manifiestan estudiantes de sexto curso de educación primaria (11 años) sin conocimientos formales de álgebra y alumnos de primero (12 años) y segundo curso de secundaria (13 años) que inician su formación algebraica. Participan 313 estudiantes que resuelven una tarea de generalización en el contexto funcional del álgebra escolar. Los resultados muestran que los estudiantes representan la generalización de las relaciones funcionales verbal o simbólicamente, encontrándose en secundaria la representación de relaciones funcionales con estructuras más complejas. Los resultados aportan información sobre el efecto de la experiencia educativa y la formación algebraica recibida en las expresiones de generalización de los estudiantes. We describe the representations of generalization used by elementary school sixth graders (12 years old), without formal knowledge of algebra, and first and second graders in high school (13 and 14 years old, respectively), who begin their algebraic training A total of 313 students participated to solve a generalization task in the functional context of school algebra. The results inform that students represent the generalization of the functional relationships verbally and symbolically in all grades. The functional relationships represented in high school are more complex. The results inform about the effect of the educative experience and the algebraic instruction received on students’ expressions of generalization.

Lista de autores

Ureña, Jason, Ramírez, Rafael, Molina, Marta y Cañadas, María C.

Fecha

2021

Autores

Descripción

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, and also the strategies used by students and their connection with generalization. This paper jointly describes the strategies and representations of generalisation used by a group of 33 sixth-year elementary school students, with no former algebraic training, in two generalisation tasks involving a functional relationship. The strategies applied by the students differed depending on whether they were working on specific or general cases. To answer questions on near specific cases they resorted to counting or additive operational strategies. As higher values or indeterminate quantities were considered, the strategies diversified. The correspondence strategy was the most used and the common approach when students generalised. Students were able to generalise verbally as well as symbolically and varied their strategies flexibly when changing from specific to general cases, showing a clear preference for a functional approach in the latter.

Lista de autores

Ureña, Jason, Ramírez, Rafael, Molina, Marta y Cañadas, María C.

Fecha

2022

Autores

Descripción

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students’ answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to identify the types of representation used to express their generalizations. We integrated how regularities are produced, evidenced in structures and represented by students. One of the most prominent findings was that functional strategy was used by almost all the students who generalized. They expressed the generalization using verbal, symbolical or multiple representations. Ways of expressing regularities that are not restricted to algebraic symbolism are also shown. Although the potential to identify functional relationships was observed in sixth graders, seventh and eighth school students were able to represent more varied and structurally complex relationships. However, no relevant differences in generalization strategies were found between students of different ages with and without previous algebraic training.

Lista de autores

Ureña, Jason, Ramírez, Rafael, Molina, Marta y Cañadas, María C.

Fecha

2023

Autores

Descripción

Se presenta un estudio descriptivo y exploratorio en el que se analizan los diferentes niveles de generalización que manifiestan ocho estudiantes de cuarto curso de primaria en una entrevista semiestructurada, a la vez que se reconoce la influencia, en tales manifestaciones, de los estímulos efectuados a los alumnos por parte de la entrevistadora.

Lista de autores

Ureña, Jason

Fecha

2017

Autores