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# Estructuras en las formas directa e inversa de una función por estudiantes de 7-8 años Translated title: Structures in direct and inverse forms of a function evidenced by 7-8-year-old students Translated title: Estruturas nas formas direta e inversa de uma função por estudantes de 7-8 anos

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Uniciencia

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### Translated abstract

Abstract This study aimed to identify and compare the structures evidenced by primary school students in direct and inverse forms of a function, both working with particular cases and generalizing from an early algebra functional approach. The study was qualitative, exploratory, and descriptive. A contextualized task was designed involving the linear functiony=x+4 in direct and inverse variations. Six 2nd graders (7-8 years of age) from a school in Granada (Spain) participated in the study performing a designed task during semi-structured interviews conducted in the 2017-2018 school year. We described the structures evidenced in both variations with particular cases and the general case. All six students identified adequate structures in the direct variation of the function at least once during the interview. Adequate structures were also observed in the inverse variation. However, some students did not respond to this section or were not asked these questions. The majority of the structures that students generalized were produced when explicitly asked for generalization, in both direct and inverse variations of the function. When using the relationship between two variables, differences were found between structures identified by students in both direct and inverse variations. Most of the structures identified were adequate for the problem, which encourages work with both variations of linear functions in primary education.

### Most cited references36

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### Awareness of pattern and structure in early mathematical development

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### Early algebra and mathematical generalization

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### Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza

(2011)
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### Author and article information

###### Journal
uniciencia
Uniciencia
Uniciencia
Universidad Nacional, Costa Rica (Heredia, Costa Rica, Heredia, Costa Rica )
1011-0275
2215-3470
December 2021
: 35
: 2
: 237-252
###### Affiliations
[3] Andalucía orgnameUniversidad de Granada orgdiv1Departamento de Didáctica de la Matemática Spain amverdejo@ 123456ugr.es
[1] Andalucía orgnameUniversidad de Granada orgdiv1Departamento de Didáctica de la Matemática Spain mtorresg@ 123456ugr.es
[4] Bogotá Bogotá orgnameUniversidad de los Andes orgdiv1“Una empresa docente” Colombia argeifontes@ 123456uniandes.edu.co
[2] Andalucía orgnameUniversidad de Granada orgdiv1Departamento de Didáctica de la Matemática Spain mconsu@ 123456ugr.es
###### Article
S2215-34702021000200237 S2215-3470(21)03500200237
10.15359/ru.35-2.16
6587f29d-3dbb-41b2-8d4c-b082cd683690

###### History
: 18 March 2021
: 31 October 2020
###### Page count
Figures: 0, Tables: 0, Equations: 0, References: 37, Pages: 16
###### Product

SciELO Costa Rica

###### Categories
Artículo