How do Colombian textbooks promote dimensional change in relation to the area of polygonal regions? ¿Cómo promueven el cambio dimensional los libros de texto colombianos en relación con el área de regiones poligonales?

Abstract

The  dimensional  change  in  the  way  of  seeing  on  the two-dimensional  figures  is  a  basic  operation  for  the  development and  understanding  of  mathematical  tasks,  but,  for  the  students  the incorporation of this operation is complex, even impossible to do. The study of the dimensional change must be an object of reflection. The area of polygonal regions and the textbooks allow us to understand how the  dimensional  change  is  promoted  in  the  classroom.  This  research work  analyzes  how  textbooks  of  the  three  main  publishersin  south-western  Colombian  arouse,  in  the  first  cycles  of  compulsory  basic education, the incorporation of dimensional changesto find the area of polygonal regions. An amount of 1281 tasks were analyzed. Two classes of  dimensional  changes  were  identified:  Fixed  and  Operative,  where the first dimensional change was the most considered. Research shows that textbooks propose limited opportunities for dimensional change to be  apprehended.  Educators  must  design  tasks  to  complement  the  tasks exhibited by the books, consequently, so they must appropriate a visual theory that allows them to make the relevant decisions