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

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...

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Main Authors: Ayala Altamirano, Cristina Alejandra, Pinto, Eder, Molina, Marta, Cañadas, María C.
Format: info:eu-repo/semantics/article
Language:English
Published: MDPI 2022
Subjects:
Online Access:http://hdl.handle.net/10835/13868
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author Ayala Altamirano, Cristina Alejandra
Pinto, Eder
Molina, Marta
Cañadas, María C.
author_facet Ayala Altamirano, Cristina Alejandra
Pinto, Eder
Molina, Marta
Cañadas, María C.
author_sort Ayala Altamirano, Cristina Alejandra
collection DSpace
description 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.
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spelling oai:repositorio.ual.es:10835-138682023-04-12T19:11:12Z Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School Ayala Altamirano, Cristina Alejandra Pinto, Eder Molina, Marta Cañadas, María C. arithmetic word problems early algebra indeterminate quantities elementary education problem posing translation 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. 2022-06-29T15:56:09Z 2022-06-29T15:56:09Z 2022-06-25 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/13868 10.3390/math10132229 en https://www.mdpi.com/2227-7390/10/13/2229 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI
spellingShingle arithmetic word problems
early algebra
indeterminate quantities
elementary education
problem posing
translation
Ayala Altamirano, Cristina Alejandra
Pinto, Eder
Molina, Marta
Cañadas, María C.
Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title_full Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title_fullStr Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title_full_unstemmed Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title_short Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
title_sort interacting with indeterminate quantities through arithmetic word problems: tasks to promote algebraic thinking at elementary school
topic arithmetic word problems
early algebra
indeterminate quantities
elementary education
problem posing
translation
url http://hdl.handle.net/10835/13868
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