Categorías en la traducción del lenguaje natural al algebraico de la matemática en contexto.

The translation constitutes a fundamental stage in the posing and solution of contextualized math problems; this is because in order to establish the mathematical model –central element in the process of mathematics in context [Camarena, 1999]- it is necessary to successfully make the transition from the natural language, in which problems are communicated to us, into the algebraic language, in which they are mathematically represented. Therefore, this work studies the phenomenon of the contextualized math problems under the translation approach. In such a way, texts of Algebra and Differential Calculus of the upper-middle and upper levels are analyzed, with the purpose of finding mathematical and linguistic elements common to the elements of different problems from these texts, which may allow classifying them into categories according to the translation they demand. Resulting from this analysis, we created three categories of problems according to the characteristics of their statements, which in turn involve the knowledge of the translator at different levels. The first category corresponds to the problems with literal statement where, from the same statement, it is possible to literally obtain the model of the problem, for which the translator must know the vocabulary and its mathematical symbols. The second category corresponds to the problems having statements with evocation, where the statement evokes the problem model by mentioning it, describing it or referring to it, and where the translator must know its meaning. In the third category, the one corresponding to problems with complex statements, the statement doesn’t literally express or evoke the model to be used in the problem, but the individual must deduce it, so he/she must have a cognitive structure prepared for such task. This classification is subject to a qualitative research in order to analyze the hypothesis that the translation is a basic skill in the understanding and posing of contextualized math problems, as well as the hypothesis that the number of students solving the problems is reduced as the category rises. After applying a problem solving activity from each category to a group of students from the first semester studying their bachelor’s degree, and who had recently finished the course of Differential and Integral Calculus, it was possible to confirm the first research hypothesis, whereas the hierarchy proposed for the classification was not fulfilled, as it is observed that success levels for the understanding and posing of contextualized math problems have a variable behavior with regard to the category to which they belong. It is suspected that these levels are at the mercy of different factors that came to light during the research, such as the translation key elements appearing in each particular problem and the knowledge the translator may have about them, the number and type of translations being involved, the syntax of the sentences making up the statements, or the experience in solving similar problems. It is recommended to broaden this research to be able to define the role that each of these elements play on the understanding and posing of contextualized math problems