From Chinese counting rods to Fangcheng method: an experience of cultural transposition in lower secondary school

Abstract

We proposed, to a class of sixth-graders, a path of discovery of Chinese mathematical tradition and its typical problems, akin to system of equations, to be solved with counting rods and the ancient method Fangcheng. The proposed methodology is laboratory didactics, using artifacts such as rods and scales as well as audio-video supports. According to the theory of the semiotic analysis of artifacts (Rabardel, 1999; Bartolini Bussi, Mariotti & Ferri, 2005) and the theory of cultural transposition (Bartolini Bussi, Sun & Ramploud, 2013; Mellone & Ramploud, 2015), we intend to demonstrate the potential of a formative use of ancient instruments and counting techniques, ailing from a different cultural, historical and geographical context. The aim is to rethink first, and then boost, students’ awareness about addition and subtraction algorithms while also directing them toward the use of pre-algebraic methods based upon the concept and principles of equivalence.