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Educational Studies in Mathematics

, Volume 98, Issue 1, pp 19–37 | Cite as

Meanings given to algebraic symbolism in problem-posing

  • María C. Cañadas
  • Marta Molina
  • Aurora del Río
Article

Abstract

Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students’ capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic statements given. We designed a written questionnaire composed of eight closed algebraic statements expressed symbolically, which was administered to 55 students who had finished their compulsory education and who had some previous experience in problem-posing. In our analysis of the data, we examine both syntactic and semantic structures of the problem posed. We note that in most cases students posed problems with syntactic structures different to those given. They did not include computations within variables, and changed the kinds of relationships connecting variables. Students easily posed problems for statements with additive structures. Other differences in the type of problems posed depend on the characteristics of the given statements.

Keywords

Algebraic symbolism Problem-posing Semantic and syntactic structures 

Notes

Acknowledgements

This study was developed within the Spanish projects of Research and Development with reference codes EDU2013-41632-P and EDU2016-75771-P, financed by the Ministerio Español de Economía y Competitividad and FEDER funds.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • María C. Cañadas
    • 1
  • Marta Molina
    • 1
  • Aurora del Río
    • 1
  1. 1.Departamento de Didáctica de la Matemática, Facultad de Ciencias de la EducaciónUniversidad de GranadaGranadaSpain

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