Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School

Cristina Ayala-Altamirano, Eder Pinto, Marta Molina and María C. Cañadas
Additional contact information
Cristina Ayala-Altamirano: Department of Education, University of Almeria, Carretera San Urbano, La Cañada, 04120 Almería, Spain
Eder Pinto: Faculty of Education, Universidad del Desarrollo, Av. Plaza 680, Santiago 7610658, Chile
Marta Molina: Departamento de Didáctica de las Matemáticas y de las Ciencias Experimentales, Escuela de Educación y Turismo de Ávila, Universidad de Salamanca, Madrigal de las Altas Torres, 3, 05003 Ávila, Spain
María C. Cañadas: Department of Mathematics Didactics, Faculty of Education Sciences, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 13, 1-18

Abstract: 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.

Keywords: arithmetic word problems; early algebra; indeterminate quantities; elementary education; problem posing; translation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/13/2229/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/13/2229/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:13:p:2229-:d:847933

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().