Why Paquito does not know how to add? ... forty years later: He already adds but does not multiply and less divide

Abstract

The numerical manipulation is essential for daily existence, that is a reason why the work focuses attention on the sources and origins of the errors associated with the basic operations (addition subtraction multiplication and division) of the students of the secondary school (children between 12 and 15 years old), is striking the generality of the existence of such errors in a population that has spent at least six years in contact with the topic. To outline the possible reasons for this, a brief description is made (it cannot be otherwise for the extension), on historical textbooks, training programs for students of the degree in primary education, political situations - of the conditions of teachers' work and the inadequate responses of students in the first year of secondary school, of course, others are pending: the beliefs of teachers, the attitudes of students and family members towards school mathematics, the reasons why Results of research in mathematics education have not been installed in teaching (otherwise the central theme of this paper would not exist) and others that surely exist but are not yet explicit (at least for those who sign this document).