Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
Date
2022
Type:
Article
item.page.extent
item.page.accessRights
item.contributor.advisor
ORCID:
Journal Title
Journal ISSN
Volume Title
Publisher
item.page.isbn
item.page.issn
item.page.issne
item.page.doiurl
item.page.other
item.page.references
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.
Description
item.page.coverage.spatial
item.page.sponsorship
Citation
Ayala-Altamirano, C.; Pinto, E.; Molina, M.; Cañadas, M.C. 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
Keywords
Arithmetic word problems, Early algebra, Indeterminate quantities, Elementary education, Problem posing, Translation