Intervention and intended change

A search for mathematical views that can be agreed upon as didactically desirable

Abstract

There is a broad consensus in mathematics beliefs research that teachers' beliefs influence their classroom practice significantly. Therefore, several studies have attempted to change beliefs by using specific mathematical-didactical interventions. Aside from being interpreted as stable, or difficult to change, beliefs are generally classified as descriptive. An intervention to change beliefs, however, implies some predefined goals that are considered didactically desirable and, therefore, normative. Consequently, the question arises which beliefs can be considered as desirable, and which should be changed through targeted interventions. As a starting point for this discussion, this paper elaborates a potential theoretical framework for the domain-specific mathematical normative approach to beliefs. This framework is based on the ideas of the "Nature of Science" research and is referred to as "Nature of Mathematics". Additionally, to support the theoretical framework, representative beliefs are cited that have either been found to be beneficial or detrimental to learning in other studies. Through the combination of the theoretically based framework and empirically evaluated desirable and non-desirable beliefs, this paper facilitates the localization and differentiation of mathematical beliefs research, especially those which focus on beliefs-change through intervention, while opening a discourse on beliefs' normativity.