Towards cultural analysis of content: Problems with variations in primary school

Mathematical knowledge needed for teaching is now in the foreground in international Conferences (e. g. Bartolini Bussi et al. 2011). The theoretical construct of Cultural Analysis of Content (CAC) has been introduced in mathematics teacher education by Boero & Guala (2008) as follows: “presenting mathematics as an evolving discipline, with different levels of rigor both at a specific moment in history (according to the cultural environment and specific needs), and across history, and as a domain of culture as a set of interrelated cultural tools and social practices, which can be inherited over generations (p. 223)”. According to these authors, “CAC can lead teachers to radically question their beliefs concerning mathematics in general and specific subject matter in particular (p. 223)”. Boero & Guala (2008) highlight the difficulty of finding suitable tasks for teacher education in well established school mathematics area. Bartolini Bussi (2011) has analyzed, according to CAC, the topic of place value representation of whole numbers in workshops for pre-primary and primary school teachers. In this paper, a further example is discussed concerning the area of word problems in primary school. Teachers’ questioning on their own beliefs is prompted by the intercultural analysis of a meaningful example hinting at the Chinese teaching method of problems with variation. Some intercultural workshops for primary school teachers (each running for around 12-16 hours and involving 20-30 participants) have been held since 2007 (in-service and preservice education). In the workshops, the method of problems with variation is contextualized, with also homeworks and additional readings, within Chinese culture, with some “rudiments” about written language and numerals, system of values, curricula (Spagnolo and Di Paola, 2010), classroom organization, traditional artefacts and textbooks, because outlandish and isolated teaching strategies could not substantially influence teachers’ beliefs and general school practice. Problems with variation have been introduced by means of the careful analysis of a paradigmatic case of a system of nine problems (see the table 1), taken from the Chinese textbook “Mathematics” for the second semester of the second grade (Shu Xue, 1996).