History of Matrices

Commognitive Conflicts and Reflections on Metadiscursive Rules
  • Aline Bernardes
  • Tatiana Roque
Part of the ICME-13 Monographs book series (ICME13Mo)


This chapter contains a teaching proposal based on the history of matrices inspired by the conceptual and methodological framework introduced by Kjeldsen (2011) to integrate history into the teaching of mathematics. Kjeldsen’s conceptual framework is based on Sfard’s (2008) theory of thinking as communicating. Our goal is to create conflicting situations in which students are encouraged to reflect upon the metadiscursive rules related to matrices and determinants, comparing them with those found in some historical writings. Two teaching modules were created, dealing with two episodes in the history of matrices, based on the works of the mathematicians Sylvester and Cayley, and on the historical interpretation of Brechenmacher (2006). Two field studies were conducted with undergraduate mathematics students, from two universities in Rio de Janeiro. In this chapter we also explain how some historical metadiscursive rules were identified.


History of matrices Teaching of matrices Metadiscursive rules Commognitive conflicts 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Federal University of the State of Rio de Janeiro (UNIRIO)Rio de JaneiroBrazil
  2. 2.Federal University of Rio de Janeiro (UFRJ)Rio de JaneiroBrazil

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