Abstract
In studies carried out in the 1980s the algebraic symbols and expressions are revealed through prealgebraic readers as non-independent texts, as texts that relate to other texts that in some cases belong to the reader’s native language or to the arithmetic sign system. Such outcomes suggest that the act of reading algebraic texts submerges the reader into a network of intertextual relations derived from that reader’s prior mathematics and linguistic experiences. In this article we propose an analytical perspective of algebraic activity that is based on intertextuality and that makes it possible to advance our knowledge concerning the production of sense in said activity. In particular, we resort to the notion of intertextuality as a means of theoretically describing and explaining sense production processes in the learning of two algebraic methods: the Cartesian Method (for the algebraic solution of word problems) and the Substitution Method (for the solution of systems of two linear equations with two unknowns). We support our arguments via a series of episodes of empirical study interviews with secondary school students, in order to demonstrate the pertinence and relevance of carrying out their analysis from the perspective proposed.
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Notes
MSSs are considered to be the product of a process of progressive abstraction (both in the history of mathematics and in the history of any individual). Hence the MSSs used are made up of strata that come from different points of time in that process, related to one another by the correspondences established by the process (Puig, 2003, p. 183; Filloy et al., 2008, pp. 125–126).
In the method of successive analytic inferences, the statement of the problem is conceived of as the description of “possible states of the world” and that text is transformed by analytical sentences, using “facts” that are valid in “any possible world”. These analytical sentences constitute logical inferences that act as logical descriptions of transformations of “possible situations”, until such time as the solver arrives at one that he/she recognizes as the solution to the problem (Filloy et al., 2008, p. 217).
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Acknowledgments
We want to thank Centro Escolar Revueltas in Mexico City for providing us with the facilities to carry out the empirical work of the long-term research project “Operating the unknown”. The preparation of this article was partially supported by Consejo Nacional de Ciencia y Tecnología (Conacyt), Mexico (Grant No. 168620).
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Rojano, T., Filloy, E. & Puig, L. Intertextuality and sense production in the learning of algebraic methods. Educ Stud Math 87, 389–407 (2014). https://doi.org/10.1007/s10649-014-9561-3
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DOI: https://doi.org/10.1007/s10649-014-9561-3