Algebra vs arithmetic. A didactic proposal that allows the problematized construction of a mathematical space of constructivist work in the classroom

Abstract

At the moment (end of the second decade of the 21st century), it is observed that, in the didactic proposals of teaching practices of secondary education, the school arithmetic activity has been displaced to give greater exclusivity to the mathematical teaching through the Algebra. This process has been described as algebrization of school mathematics education, which even extends beyond the activity of Arithmetic itself, and also covers the didactics of Geometry, Mathematical Analysis, and Statistics. The following work constitutes a reflexive contribution about possible didactic proposals that do without the work with procedural generalizations, or algorithms, and of the use of different languages and representations corresponding to the Algebra. To overcome the described situation that emphasizes algebraic teaching, it is suggested to approach Arithmetic in the aulic context of production of significant knowledge (linked to constructivism) in collaborative work between student peers. In it, two proposals will be addressed: one effectively implemented with a group of 5 students in the second year of secondary education, and the other, as a suggestion to develop.