chapter  10
Mathematical Epistemological Beliefs
Pages 18

Epistemological beliefs are defined as beliefs about the nature and acquisition of knowledge. It is typically assumed that epistemological beliefs have an influence on how people think and reason, as well as on their motivational processes (Hofer & Pintrich, 1997). Much of the research on people’s epistemological beliefs is situated within specific subject-matter domains, including mathematics. For that domain, there are two distinct views on the nature and the acquisition of knowledge, namely an absolutist (Platonist) and a fallibilist perspective (Ernest, 2014). Adherents of the absolutist perspective assume mathematical knowledge to be absolutely secure, fixed, and objective. They believe that mathematical objects are real and exist outside the human mind. To acquire mathematics knowledge, mathematical truths have to be discovered rather than invented. By contrast, adherents of the fallibilist perspective view mathematics as the outcome of social processes. Mathematical knowledge is seen as fallible and open to revision. Rather than emphasizing the acquisition of a fixed set of mathematical concepts and procedures, fallibilists focus on doing mathematics-within the social conventions in a particular context-and its human side. Going beyond the dichotomy of naïve and sophisticated epistemological beliefs, Ernest (2014) argues that neither the absolutist nor the fallibilist perspective is right or wrong, but that both perspectives have their own legitimacy. Most theoretical frameworks on teachers’ and students’ mathematics-related epistemological beliefs somehow relate to Ernest’s (2014) basic distinction between the absolutist and fallibilist perspective, although there is a large diversity in the way in which differences in epistemological beliefs are expressed in the mathematics educational literature. For instance, the labels “static” (Felbrich, Kaiser, & Schmotz, 2012) and “realist” (Bolden & Newton, 2008) are also used in the literature to label epistemological beliefs similar to Ernest’s absolutist perspective, whereas labels such as “dynamic” (Felbrich et al., 2012) and “relativist” (Bolden & Newton, 2008) reflect a more fallibilist perspective. Besides this difference in terminology to describe

mathematics epistemological beliefs, there are still three other issues on which the available frameworks take different perspectives.