The aim of this study is to present the insights of the mathematics teachers beliefs’ on mathematical knowledge, and its teaching and learning. The case study method is used in this study. tThe study pursued along with the participation of one secondary mathematics teacher in the fall semester of 2007-2008 instruction year in Trabzon providence. The interviews realized during approximately 45 minutes with the interwiewee for the four times. In the interviews, three data collection forms were used as the data collection tool. These are: a) Semi-structured interview form, b) Hypothetical situations called “episodes” as a means to initiate responses from the informant, c) Documents that are including pictures reflecting different classroom settings and about the nature of mathematical knowledge. By using Magolda’s Epistemological Reflection Model, the data obtained were analyzed descriptively in a qualitative manner. Besides holding some strict beliefs on nature of mathematical knowledge, evaluation, and mathematical teaching, participant have some flexible beliefs about mathematics and its teaching,in addition, it was concluded that participant open to some new perceptions. However, we believe that by conducting similar studies with larger samples it might be possible to contribute to teacher training researches in our country. 

This study aims to understand the relationship between teachers’ and students’ beliefs about effective ways of learning English and elucidate whether teachers’ and students’ beliefs are congruent with their self-reported practices in Turkey. Semi-structured interviews were conducted to 5 teachers of English and 6 of their students and qualitative analysis of the interview protocols revealed consistency between their beliefs about effective ways of learning English. On the other hand, teachers and students were in agreement about the disconnection between their beliefs and practices. Although they believe that English should be learned communicatively, they claimed that their current practices solely focus on structural and lexical units of English. Different factors were discussed leading to this mismatch such as the content of university examination, course books, the status of English, overloaded syllabus, etc. and the disconnection between beliefs and practices is reported to be a factor hindering the satisfaction gained from current teaching and learning procedures.