System of Mathematics Teachers’ Beliefs about Effective Teaching/Learning and Practice as a Complex Adaptive System

Abstract

The outcomes of the research on teachers’ beliefs and their relatedness to their work routine are often contradictory, hard to systematize and predict. This may be evidence that research on teachers’ beliefs need a change in research paradigm: it should regard various approaches, in other words, research should be carried out in the Holistic paradigm framework. As a field inquiry concerned with the holistic exploration of phenomena and events, systems theory pertains to both epistemological and ontological situations. The present article suggests to emphasize in inquiries on mathematics teachers’ beliefs the bond of teachers’ beliefs with their practice and analyze the system of mathematics teachers’ beliefs and practice (SMTBP) from the position of Complex Adaptive System (CAS). The aim of the article is to show that the basic features of CAS are present in SMTBP as well and that there exist some features of CAS that have not been sufficiently regarded in previous research on teachers’ beliefs but that could be used to characterize the change of teachers’ beliefs and the processes of practical implementation of teachers’ beliefs in their work. The article is focused on the external factors that may affect these processes, and the principle of Bronfenbrenner ecological system theory has been used for systematizing them. Application of CAS Theory for the studies of SMTBP will provide a unified approach to interpreting the outcomes concerning teachers’ beliefs that, in turn, will make it possible to account for a large number of revelations that were impossible to account for within the framework of non-holistic paradigms.