Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
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Materia
Arithmetic word problems Early algebra Indeterminate quantities Elementary education Problem posing Translation
Date
2022-06-25Referencia bibliográfica
Ayala-Altamirano, C... [et al.]. Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School. Mathematics 2022, 10, 2229. [https://doi.org/10.3390/math10132229]
Sponsorship
Universidad del Desarrollo (Chile) 23.400.173; State Research Agency (SRA) from Spain EDU2016-75771-P PID2020-113601GB-I00Abstract
In this study, we analyze how 9–10-year-old pupils work with equations, a central aspect of
algebraic thinking in early grades and a cornerstone for more formal learning of algebra. Specifically,
we seek: (a) to describe the main characteristics of the tasks that support algebraic thinking through a
translation process from arithmetic word problems to algebraic language and vice versa, and (b) to
identify how pupils refer to indeterminate quantities in these contexts and what meaning they give
to them. The analysis focuses on the semantic congruence of the expressions proposed by them and
on the dialogue they held during the translation process. We analyzed the oral discussion in the
pools and the written responses to the problem that pupils posed. The results show that arithmetic
word problems allow the indeterminate to become an object of thought for pupils, who represent
it in multiple ways and refer to it when proposing equations that represent the structure of each
problem. Another finding highlights that reflection on the interpretation of the equations supports
the identification of two meanings associated with indeterminate quantities, namely, unknown
and variable.