Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing

Elena Fernández-Millán; Marta Molina

doi:10.29333/iejme/649

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Elena Fernández-Millán, Marta Molina

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Abstract

Through the task of problem posing, we inquire into students’ conceptual knowledge of algebraic symbolism developed in compulsory secondary education. We focus on identifying the characteristics of equations and systems of equations that made the problem posing task difficult for the students and analyzing the meanings that they gave to the operations contained in the expressions. To collect the data we used two questionnaires in which students were asked to pose problems that could be solved by using given equations or system of equations. In the second questionnaire a specific meaning for the unknowns in the given expression was suggested. The results complement those of a previous study. Students evidence a good conceptual knowledge of algebraic symbolism when meanings for the unknowns are suggested. Decimal numbers and an equation including parenthesis and multiplication of unknowns are the main elements that made some weaknesses in students’ knowledge to surface. The results are more promising. They suggest the potential for compulsory algebra instruction to develop students’ conceptual knowledge, although greater attention should be paid to the semantic aspects of algebra if students are to access such knowledge unaided.

Keywords

Algebraic symbolism
conceptual knowledge
equations
Problem posing
unknown

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2017, Volume 12, Issue 3, 799-826

https://doi.org/10.29333/iejme/649

Publication date: 27 Nov 2017

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How to cite this article

APA

Fernández-Millán, E., & Molina, M. (2017). Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing. International Electronic Journal of Mathematics Education, 12(3), 799-826. https://doi.org/10.29333/iejme/649

Vancouver

Fernández-Millán E, Molina M. Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing. INT ELECT J MATH ED. 2017;12(3):799-826. https://doi.org/10.29333/iejme/649

AMA

Fernández-Millán E, Molina M. Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing. INT ELECT J MATH ED. 2017;12(3), 799-826. https://doi.org/10.29333/iejme/649

Chicago

Fernández-Millán, Elena, and Marta Molina. "Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing". International Electronic Journal of Mathematics Education 2017 12 no. 3 (2017): 799-826. https://doi.org/10.29333/iejme/649

Harvard

Fernández-Millán, E., and Molina, M. (2017). Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing. International Electronic Journal of Mathematics Education, 12(3), pp. 799-826. https://doi.org/10.29333/iejme/649

MLA

Fernández-Millán, Elena et al. "Secondary Students’ Implicit Conceptual Knowledge of Algebraic Symbolism. An Exploratory Study through Problem Posing". International Electronic Journal of Mathematics Education, vol. 12, no. 3, 2017, pp. 799-826. https://doi.org/10.29333/iejme/649