Case Study about Area Measurement
This paper reports on case study that investigated the development of mainly tacit and mainly explicit components of knowledge of area measurement of a student-pair. The research covered two terms or periods of the students’ learning of the subject: when they were aged 11 to 12 and when they were aged 12 to 13. The data analysis was based on Ernest’s model of mathematical knowledge, with reference to its mainly tacit and mainly explicit components, and Kitcher’s ideas about the development of mathematics practice. The results of the research reinforced our hypothesis that students’ mathematical knowledge displays a very similar structure to that of the mathematical knowledge of the mathematicians.
Introduction: The concept of tacit knowledge does not have a single meaning. As discussed in Frade’s (2004) work some researchers address what can be called Polanyi’s psychological version of tacit knowledge: knowledge that functions as subsidiary to the acquisition of other knowledge. Other researchers use the words tacit and explicit as opposites to refer to different, but complementary ontological dimensions of the same component of a certain practice. Whatever meaning we choose – psychological or ontological – the researchers quoted by Frade (ibid) share in some way Polanyi’s (1969) epistemological thesis that all knowledge is tacit or constructed from tacit knowledge: put it in another way, language alone is not enough to render knowledge explicit. Keep reading..
