Intertextuality and sense production in the learning of algebraic methods

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.     

Mathematical Modelling: the Interaction of Culture and Practice

Using a sociocultural approach we analyse the results of a Mexican/British project which investigated the ways in which mathematics is used in the practice of school science and the role of spreadsheets as a mathematical modelling tool. After discussing the different school cultures experienced by two groups of pre-university 16–18 year old students we analyse how these different cultures influenced their practice of mathematics, as well as their work with mathematical spreadsheet modelling activities. There were clear differences between the two groups of students in their preference for external representations, in their understanding of the kind of answers they were expected to produce and in the way they conceived the role of mathematics in the practice of science. Although students preferences for a particular representation were not significantly modified by the use of a spreadsheet as a modelling resource, at the end of the study the students recognised the value of using a more diverse set of representations. The results obtained suggest the possibility of enhancing students' capability to shift between a wider range of representations, including graphical, algebraic and numeric ones, using a modelling approach embedded in a computer environment such as a spreadsheet. This revised version was published online in July 2006 with corrections to the Cover Date.     

The learning and teaching of algebra. Ideas,insights, and activities: Abraham Arcavi,Paul Drjvers,and Kaye Stacey (2017)

Journal of Mathematics Teacher Education -