Digraphs in the Analysis of Systems’ Representation of Mathematical Knowledge

  • Patricia Esperanza Balderas-CañasEmail author


One of the main goals in education is to narrow the teaching according to students’ knowledge and skills; therefore, many topics may emerge and become important, and many research questions may be posed and studied. In this context and using a systemic approach, I present and discuss a methodology to analyze the visual reasoning processes given with the use of mathematical representations when learning differential calculus at a high school level. The interest is knowing how learners acquire and use some of the systems of mathematical representation and how they organize these systems to produce acceptable responses in the school environment. The representation systems used by the participants were modeled by digraphs, which turned out to be complete, entirely disconnected, and transitive; strong, weak, and idiosyncratic systems of representation were identified. Also, based on the conclusions, some teaching recommendations were created for making decisions in the classroom for students to acquire solid systems of representation by which acceptable answers may be given to solve differential calculus problems.


Systemic approach Visual thinking Math representations Advanced calculators Differential calculus 

Supplementary material

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Authors and Affiliations

  1. 1.Department of Systems, Faculty of EngineeringNational Autonomous University of MexicoMexico CityMexico

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