Ontological complexity and mathematical problem statements

Abstract

The common context, which conditions the school practice of solving mathematical problems, contemplates the passage from verbal enunciation (oral, written or pictographic), that is, from the general enunciation (usually linguistic) of the problem to its resolution in mathematical language , and this process is not at all automatic, immediate or transparent, since it is determined by what we call the degree of ontological complexity -process that conditions the understanding (interpretation) in mathematical terms of what is posed- from colloquial language. Ontological complexity refers to the grammatical sentence as its logical structure. This theoretical proposal postulates the formula - which we call the ontological complexity index (CO) -, as a quotient to the number that refers to the total number of variables that the predicate or predicates of the propositions contain, and the denominator to the total number of relationships between the variables of the predicates. This formula can be used to qualify the exercises in terms of the number of referents and their relationships –ontological content-, thus providing a tool that provides another perspective for the pedagogical work in the classroom. This research, is meta-analytic, the databases of the Third Regional Comparative and Explanatory Study TERCE (of the United Nations Educational, Scientific and Cultural Organization - UNESCO - Regional Office of Education for Latin America and the Caribbean) with regard to the results of children in the third grade of Basic School Education in Paraguay, finding that 73% of these, grouped in levels IV and III of mathematical competence, also reached Level IV in Reading, this leads to think that higher levels of mathematical competence are associated with higher levels of reading (language) competence.