# Functional relationships evidenced and representations used by third graders within a functional approach to early algebra

Pinto, Eder; Cañadas, María C.; Moreno, Antonio (2021). Functional relationships evidenced and representations used by third graders within a functional approach to early algebra. International Journal of Science and Mathematics Education, in press, pp. 1-20 .

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URL Oficial: https://doi.org/10.1007/s10763-021-10183-0

## Resumen

This study describes how 24 third-graders (8-9 years old) relate and represent the relationships between variables when working with a functional thinking problem. This aspect contributes to providing insights about how elementary school students attend properties and relationships between covarying quantities rather than isolated computations. From a functional approach to early algebra, we describe written students’ answers when working with a problem that involves a function, which includes questions for specific values and to generalize. Design research guidelines, specifically those set out for Classroom Teaching Experiment were followed. This study addresses the fourth and last Classroom Teaching Experiment session, which involved a function of the type y=ax+b and students had not previously worked it. Students primarily evidenced correspondence relationship, using natural language and numerical representation to express this functional relationship. Our findings let us to state that: (a) although students were not used to working with these types of problems, eleven of them go beyond arithmetic computations, finding relationships that relate the variables; and (b) three students generalized using natural language as a useful vehicle, while there are other students who perceived the same regularity for different specific values but they are unable to represent generalization clearly.

Tipo de Registro: Artículo 13. Matemáticas escolares > Álgebra > Funciones10. Otras nociones de Educación Matemática > Enfoques de las matemáticas escolares > Funcional10. Otras nociones de Educación Matemática > Resolución de problemas > Resolución y estrategias13. Matemáticas escolares > Álgebra Educación Primaria (7-12 años) 23272 Eder Pinto 09 Jul 2021 16:13 09 Jul 2021 16:13

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