On the Relationships Between Beliefs and Knowledge

The relationship between beliefs and knowledge is usually left undefined in educational papers. Furinghetti & Pehkonen (2002) point out that when discussing on beliefs it is better distinguish between objective (formal, public) knowledge and subjective (informal, personal) knowledge. Here we understand beliefs as an individual’s subjective knowledge and emotions concerning objects and their relationships, and they are based usually on his personal experience. Therefore, beliefs are not necessarily reasoned in a generally accepted way, and they represent some kind of tacit knowledge. The affective domain has been a neglected area in research of mathematics education, until McLeod and Adams highlighted it with their famous book (McLeod & Adams 1989). The main components of affect are often considered to be beliefs, attitudes, and emotions (cf. McLeod 1992). Two decades ago an individual’s attitude toward mathematics formed one of the central research topics in the affective domain of mathematics education; the well-known Fennema-Sherman attitude scale (Fennema & Sherman 1976) represents this phase. In recent research the focus has changed to beliefs. Another direction of change in research has been in the concept of mathematics itself. Today we are no more considering attitudes toward mathematics as an entity, but researchers distinguish e.g. attitudes or beliefs on geometry or problem solving. There are several difficulties in defining concepts related to beliefs. Some researchers consider beliefs to be part of knowledge (e.g. Pajares, 1992; Furinghetti, 1996), some think beliefs are part of attitudes (e.g. Grigutsch, 1998), and some consider they are part of conceptions (e.g. Thompson, 1992). There can be differences also depending on the discipline. For example emotions can have different meaning in psychology than in mathematics education (e.g. McLeod, 1992). In addition it is possible that researchers use same terminology although they study different phenomena. This all makes it hard to understand studies and compare them to each other (e.g. Ruffell, Mason & Allen