@article {MATHEDUC.06412126,
author = {Bravo, Ana Soledad and Cantoral Ariza, Ricardo},
title = {The calculus textbooks and the phenomenon of transposition didactics. (Los libros de texto de c\'alculo y el fen\'omeno de la transposici\'on did\'actica.)},
year = {2012},
journal = {Educaci\'on Matem\'atica},
volume = {24},
number = {2},
issn = {1665-5826},
pages = {91-122},
publisher = {Mexican Society for the Divulgation of Mathematics Education - Sociedad Mexicana de Investigaci\'on y Divulgaci\'on de la Educaci\'on Matem\'atica, Mexico City},
abstract = {Summary: The textbook is a tangible object for the analysis of transformations affecting the mathematical knowledge in the process of becoming objects of teaching. In this work we present results from the analysis of some calculus books considered either formal books or either books of current use, which are characterized by their extension and graphic resources. Specifically, we made a tracing of the concept of line integral in order to explain why the textbooks of physics and chemistry use the concept of inexact differential to mathematically represent ``small changes in heat" or ``small amounts of work", for enunciating of the first law of thermodynamics. However, in the analyzed calculus textbooks this concept is not refered as such. We report anormalies identified in the follow up of the explanations on function line integral, linear differential equations and vector field, which are given in eight calculus textbooks. On the basis of the theory of didactics transposition, these anomalies were typified as empty explanatory, ruptures in the logical sequence of explanations, and inconsistencies between the given formal definitions and the solved examples.},
msc2010 = {U25xx (I55xx M55xx I15xx)},
identifier = {2015b.00932},
}