The incongruity between beliefs and practice can also be explained through the agitation and unpredictability of classroom life and the external pressures put on teachers. Thompson (1985) affirmed that these incongruities might be due to the frequency of unexpected occurrences which teachers face in the classroom. The high frequency of these incidents does not permit the teacher to reflect on alternative responses; rather, teachers have time only to react. Jackson (1968) suggested that elementary teachers engage in more than one thousand interactions with students in a single day.
Another source of incongruity lies in the personal resolution of conflicting beliefs. Orton (1991) suggested that teachers’ commitment to progressive beliefs is not always a guarantee that these beliefs are going to be translated into practice because sometimes teachers have to compromise their progressive beliefs for the crude reality of traditional oriented educational environments. For example, a teacher might be motivated to provide rote-learning activities in class when that teacher knows that his or her students will be tested on basic skills in a district proficiency exam. In this case, the teacher might perceive that drill and repetitive practice is the best strategy to attain a temporary goal. Consequent to this strategy, the teacher suspends his or her own progressive beliefs for others that are more central at that particular time. Teacher’s resistance to adopting new approaches in the teaching of mathematics may be part of a defense mechanism that teachers adopt to avoid changes in their own mental structures (Clarke, 1997) because “changing beliefs causes feelings of discomfort, disbelief, distrust, and frustration” (Anderson & Piazza, 1996, p. 53). Orton (1991) stated that it is not easy to change a long-cherished mathematical belief since this belief proved before to be rewarding and useful to the teacher in the performance of his or her professional duties.
Furthermore, changing a particular belief implies a re-structuring of the whole network of one’s belief system, a feeling that might cause anxiety and emotional pain (Rokeach, 1968). Concerning teachers’ resistance to change, it has been observed that teachers holding more relativistic orientations to teaching mathematics are more likely to consider and adopt new ideas (Arvold & Albright, 1995). School cultures also influence teachers’ mathematical beliefs (Anderson, 1997). This is particularly true when teachers are found holding beliefs different from the school culture in which they work. For example, a certain school environment might
effectively foster values associated with progressive practices and this influence might be stronger than in other schools. In many instances, teachers are caught in a conflict of interest between their “technicalpositivist” and their “constructivist” beliefs and therefore they compromise (Taylor, 1990).
Moreover, teachers know that although administrators and supervisors promote reform efforts, professional
assessment is in terms of the traditional paradigm and therefore they tend to conform to the status quo to minimize disturbance and professional risk in an ethical-practical way (Anderson & Piazza, 1996; Doyle & Ponder, 1977). Research also shows that teachers may not hold consistent belief systems. Sosniak et al. (1991) analysed mathematical beliefs and self-perceptions of practice of US teachers representing 178 typical eighth grade classes. Based on those responses, the researchers attempted to profile teachers in either a traditional or progressive orientation to the curriculum. However, it was found by statistical analysis that teachers lack a consistent theoretical orientation towards the curriculum. According to the authors, within each teacher’s belief system there are beliefs that appear to be ideologically incompatible with the others. Andrews and Hatch (1999), working mainly with secondary mathematics teachers in the United Kingdom, and Howard et al. (1997) in Australia, reached similar conclusions.
Finally, Richardson (1996) adds that in some cases teachers cannot articulate a particular belief because they are unfamiliar with a specific educational innovation. According to Richardson (1996):
… it cannot be assumed that all changes in beliefs translate into changes in practices, certainly not practices that may be considered worthwhile. In fact, a given teacher’s belief or conception could support many different practices or no practices at all if the teacher does not know how to develop or enact a practice that meshes with a new belief. (p. 114)
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