Many current problems in research in mathematics education emerge from pairs of contradictory dialectical categories. In effect, these pairs characterize the problems. When an epistemological study is made to determine the object of research in which a problem is immersed, it is possible to find essential pairs of dialectical categories that become more profound and thus provide enough elements for the determination of appropriate didactic actions to solve the problem under research.
Pupo, Mauro García and Nápoles Valdes, Juan E.
"A dialectical invariant for research in mathematics education,"
The Mathematics Enthusiast: Vol. 12
, Article 33.
Available at: http://scholarworks.umt.edu/tme/vol12/iss1/33